notebooks/ImageCorruptionMNIST_masknoise05_SVI.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/bccp/DeepUQ/blob/master/ImageCorruptionMNIST_masknoise05_SVI.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5221b8hT_4PL"
   },
   "source": [
    "### Commented example of noisy masked 4 with comparison of EL2O with Stochastic Variational inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 88
    },
    "colab_type": "code",
    "id": "D-Fe5G8m1FTC",
    "outputId": "e48ffc61-2e4e-4327-a63b-324e5fee0cc6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/IPython/core/magics/pylab.py:161: UserWarning: pylab import has clobbered these variables: ['rec', 'indices', 'seed', 'var']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n",
      "  \"\\n`%matplotlib` prevents importing * from pylab and numpy\"\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "%pylab inline\n",
    "import pickle\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 53
    },
    "colab_type": "code",
    "id": "GbM9eAbNvLiP",
    "outputId": "31065546-2b00-4412-fbd4-d897cbef5d0a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[K     / 10.6MB 3.0MB/s\n",
      "\u001b[?25h  Building wheel for corner (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
     ]
    }
   ],
   "source": [
    "# for making nice plots of sampled posteriors\n",
    "! pip install -q https://github.com/dfm/corner.py/archive/master.zip\n",
    "import corner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 53
    },
    "colab_type": "code",
    "id": "zvFZpFJb_14d",
    "outputId": "0b7fd4e7-d42b-40b9-8e4a-051fbdc11558"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mounted at /content/gdrive\n",
      "/content/gdrive/My Drive/BDL2019_2\n"
     ]
    }
   ],
   "source": [
    "PROJECT_PATH = os.path.abspath('../')\n",
    "print(PROJECT_PATH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-AEYmOsH1FTI"
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "import tensorflow_hub as hub\n",
    "tfd = tfp.distributions\n",
    "tfb = tfp.bijectors\n",
    "from tensorflow.contrib.distributions import softplus_inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "8puPFE90P0aD"
   },
   "outputs": [],
   "source": [
    "# pathes to trained generative models\n",
    "generator_path   = os.path.join(PROJECT_PATH,'modules/decoder1/decoder')\n",
    "encoder_path     = os.path.join(PROJECT_PATH,'modules/encoder1/encoder')\n",
    "nvp_func_path    = os.path.join(PROJECT_PATH,'modules/nvp1/')\n",
    "minima_path      = os.path.join(PROJECT_PATH,'minima/')\n",
    "plot_path        = os.path.join(PROJECT_PATH,'plots/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "nFzYYSxY1FTL"
   },
   "outputs": [],
   "source": [
    "# functions to load mnist dataset\n",
    "import gzip, zipfile, tarfile\n",
    "import os, shutil, re, string, urllib, fnmatch\n",
    "import pickle as pkl\n",
    "\n",
    "def _download_mnist_realval(dataset):\n",
    "    \"\"\"\n",
    "    Download the MNIST dataset if it is not present.\n",
    "    :return: The train, test and validation set.\n",
    "    \"\"\"\n",
    "    origin = (\n",
    "        'http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz'\n",
    "    )\n",
    "    print('Downloading data from %s' % origin)\n",
    "    urllib.request.urlretrieve(origin, dataset)\n",
    "\n",
    "def _get_datafolder_path():\n",
    "    full_path = os.path.abspath('.')\n",
    "    path = full_path +'/data'\n",
    "    return path\n",
    "\n",
    "def load_mnist_realval(\n",
    "        dataset=_get_datafolder_path()+'/mnist_real/mnist.pkl.gz'):\n",
    "    '''\n",
    "    Loads the real valued MNIST dataset\n",
    "    :param dataset: path to dataset file\n",
    "    :return: None\n",
    "    '''\n",
    "    if not os.path.isfile(dataset):\n",
    "        datasetfolder = os.path.dirname(dataset)\n",
    "        if not os.path.exists(datasetfolder):\n",
    "            os.makedirs(datasetfolder)\n",
    "        _download_mnist_realval(dataset)\n",
    "\n",
    "    f = gzip.open(dataset, 'rb')\n",
    "    train_set, valid_set, test_set = pkl.load(f, encoding='latin1')\n",
    "    f.close()\n",
    "    x_train, targets_train = train_set[0], train_set[1]\n",
    "    x_valid, targets_valid = valid_set[0], valid_set[1]\n",
    "    x_test, targets_test = test_set[0], test_set[1]\n",
    "    return x_train, targets_train, x_valid, targets_valid, x_test, targets_test\n",
    "  \n",
    "x_train, targets_train, x_valid, targets_valid, x_test, targets_test = load_mnist_realval()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2VEVi4K0AYY5"
   },
   "source": [
    "Choose you settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ft_jIh-W1FTN"
   },
   "outputs": [],
   "source": [
    "data_dim    = 28*28 # data dimensionality\n",
    "data_size   = 1     # number of corrupted input data, always 1\n",
    "sigma_n     = 0.1   # noise level used in the likelihood, determined during VAE training or measured\n",
    "hidden_size = 10    # latent space dimensionality of the VAE\n",
    "sample_size = 512   # number of samples drawn in each step of the ELBO minimization (for stochastic VI only)\n",
    "n_channels  = 1     # mnist is b/w -> 1 channel\n",
    "seed        = 777   # random seed\n",
    "\n",
    "### choose one of the following to run different examples\n",
    "\n",
    "# settings for reconstruction with uncorrupted data\n",
    "# corr_type   = 'none'\n",
    "# num_mnist   = 6\n",
    "# label       = 'uncorrupted'\n",
    "# noise_level = 0.0\n",
    "# num_comp    = 2\n",
    "\n",
    "# settings for reconstrcution with rectangular mask\n",
    "# corr_type   = 'mask'\n",
    "# num_mnist   = 6\n",
    "# label       = 'solidmask'\n",
    "# noise_level = 0.0\n",
    "# num_comp    = 5\n",
    "\n",
    "#settings for reconstruction with sparse mask \n",
    "# corr_type   = 'sparse mask'\n",
    "# num_mnist   = 1\n",
    "# label       = 'sparse95'\n",
    "# noise_level = 0.\n",
    "# num_comp    = 2\n",
    "\n",
    "# settings for reconstruction with noise\n",
    "# corr_type   = 'noise'\n",
    "# num_mnist   = 6\n",
    "# label       = 'noise05'\n",
    "# noise_level = 0.5\n",
    "# num_comp    = 2\n",
    "\n",
    "# settings for reconstruction with noise and mask\n",
    "corr_type   = 'noise+mask'\n",
    "num_mnist   = 6\n",
    "label       = 'masknoise05'\n",
    "noise_level = 0.5\n",
    "num_comp    = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GivmkSHyR-jC"
   },
   "outputs": [],
   "source": [
    "plot_path = os.path.join(plot_path,'%s/'%label)\n",
    "\n",
    "if not os.path.isdir(plot_path):\n",
    "  os.makedirs(plot_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "nxcZOE0MLGJ1"
   },
   "outputs": [],
   "source": [
    "def plot_image(image, save=True, directory='./plots/',filename='plotted_image', title='image',vmin=None,vmax=None, mask=None):\n",
    "  \"\"\"\n",
    "  plots and saves a single image of mnist format\n",
    "  \"\"\"\n",
    "  \n",
    "  if np.any(mask==None):\n",
    "    mask=np.ones_like(image)\n",
    "  mask = np.reshape(mask,(28,28))\n",
    "  plt.figure()\n",
    "  #plt.title(title)\n",
    "  plt.imshow((image).reshape((28,28))*mask,cmap='gray',vmin=vmin, vmax=vmax)\n",
    "  plt.axis('off')\n",
    "  #plt.colorbar()\n",
    "  if save: \n",
    "    plt.savefig(directory+filename+'.pdf',bbox_inches='tight')\n",
    "  plt.show()\n",
    "  \n",
    "  return True\n",
    "\n",
    "def get_custom_noise(shape, signal_dependent=False, signal =None, sigma_low=0.07, sigma_high=0.22, threshold=0.02 ):\n",
    "  \"\"\"\n",
    "  adds the model error and the noise level in the data to obtain the total sigma that is used in the likelihood (option to make the reconstruction error signal dependent is not used) \n",
    "  \"\"\"\n",
    "  sigma = np.ones(shape)*sigma_n\n",
    "  \n",
    "  if signal_dependent: \n",
    "    for ii in range(data_size):\n",
    "      sigma[ii][np.where(signal[ii]<=threshold)]= sigma_low\n",
    "      sigma[ii][np.where(signal[ii]>threshold)]= sigma_high\n",
    "      \n",
    "  data_noise = np.ones_like(sigma)*noise_level\n",
    "  \n",
    "  sigma = np.sqrt(sigma**2+data_noise**2)\n",
    "  \n",
    "  return sigma\n",
    "  \n",
    "\n",
    "def make_corrupted_data(x_true, corr_type='mask'):\n",
    "  \"\"\"\n",
    "  creates the corrupted image according to chosen corruption type\n",
    "  \"\"\"\n",
    "  \n",
    "  mask = np.ones((28,28))\n",
    "  \n",
    "  if corr_type=='mask':\n",
    "    \n",
    "    minx = 10\n",
    "    maxx = 24\n",
    "    \n",
    "    mask[0:28,minx:maxx]=0.\n",
    "    mask = mask.reshape((28*28))\n",
    "    \n",
    "    corr_data = x_true*[mask]\n",
    "    \n",
    "  elif corr_type=='sparse mask':\n",
    "    \n",
    "    mask    = np.ones(data_dim, dtype=int)\n",
    "    percent = 95\n",
    "    np.random.seed(seed+2)\n",
    "    indices = np.random.choice(np.arange(data_dim), replace=False,size=int(percent/100.*data_dim))\n",
    "    print('precentage masked:', len(indices)/data_dim)\n",
    "    mask[indices] =0 \n",
    "  \n",
    "    corr_data = x_true*[mask]\n",
    "    \n",
    "  elif corr_type=='noise':\n",
    "    \n",
    "    np.random.seed(seed+2)\n",
    "    noise = np.random.randn(data_dim*data_size)*noise_level\n",
    "    \n",
    "    corr_data = x_true+noise\n",
    "    \n",
    "  elif corr_type=='noise+mask':\n",
    "    \n",
    "    np.random.seed(seed+2)\n",
    "    noise = np.random.randn(data_dim*data_size)*noise_level\n",
    "    \n",
    "    minx = 14\n",
    "    maxx = 28\n",
    "    \n",
    "    mask[0:28,minx:maxx]=0.\n",
    "    mask = mask.reshape((28*28))\n",
    "    \n",
    "    corr_data = x_true+noise\n",
    "    corr_data = corr_data*[mask]\n",
    "    \n",
    "  elif corr_type=='none':\n",
    "    \n",
    "    corr_data = x_true\n",
    "    \n",
    "  corr_data = np.expand_dims(corr_data,-1)\n",
    "  \n",
    "  mask = mask.flatten()\n",
    "  \n",
    "  return corr_data, mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9TIQArTJHE87"
   },
   "outputs": [],
   "source": [
    "def fwd_pass(generator,nvp,z,mask):\n",
    "  \"\"\"\n",
    "  a pass through the forward model (nvp+VAE generator)\n",
    "  \"\"\" \n",
    "  \n",
    "  fwd_z           = nvp({'z_sample':np.zeros((1,hidden_size)),'sample_size':1, 'u_sample':z},as_dict=True)['fwd_pass']\n",
    "\n",
    "  gen_z           = tf.boolean_mask(tf.reshape(generator(fwd_z),[data_size,data_dim,n_channels]),mask, axis=1)\n",
    "\n",
    "  return gen_z\n",
    "\n",
    "\n",
    "def get_likelihood(generator,nvp,z,sigma,mask):\n",
    "  \"\"\"\n",
    "  compute the likelihood for a given latent space vector\n",
    "  \"\"\"\n",
    "  gen_z           = fwd_pass(generator,nvp,z,mask)\n",
    "  \n",
    "  sigma           = tf.boolean_mask(sigma,mask, axis=1)\n",
    "\n",
    "  likelihood      = tfd.Independent(tfd.MultivariateNormalDiag(loc=gen_z,scale_diag=sigma))\n",
    "\n",
    "  return likelihood\n",
    "\n",
    "def get_prior():\n",
    "  \"\"\"\n",
    "  return the Gaussian prior\n",
    "  \"\"\"\n",
    "  \n",
    "  return tfd.MultivariateNormalDiag(tf.zeros([data_size,hidden_size]), scale_identity_multiplier=1.0, name ='prior')\n",
    "\n",
    "def get_log_posterior(z,x,generator,nvp,sigma,mask, beta):\n",
    "  \"\"\"\n",
    "  returns the negative log posterior (or rather joint dsitribution) - log(p(x,z)), where x is the corrupted input image \n",
    "  \"\"\"\n",
    "  \n",
    "  likelihood      = get_likelihood(generator,nvp,z,sigma,mask)\n",
    "  \n",
    "  prior           = get_prior()\n",
    "  \n",
    "  masked_x        = tf.boolean_mask(x,mask, axis=1)\n",
    "  \n",
    "  log_posterior   = prior.log_prob(z)+likelihood.log_prob(masked_x)*beta\n",
    "  \n",
    "  return log_posterior\n",
    "\n",
    "\n",
    "def get_recon(generator,nvp, z,sigma,mask):\n",
    "  \"\"\"\n",
    "  forward models a given point in latent space to data space\n",
    "  \"\"\"\n",
    "  \n",
    "  prob = get_likelihood(generator,nvp, z,sigma,mask)\n",
    "  \n",
    "  recon= prob.mean()\n",
    "  \n",
    "  return recon\n",
    "\n",
    "def get_hessian(func, z):\n",
    "  \"\"\"\n",
    "  computes the hessian of function func at point z\n",
    "  \"\"\"\n",
    "  \n",
    "  hess             = tf.hessians(func,z)\n",
    "  hess             = tf.gather(hess, 0)\n",
    "  \n",
    "  return(tf.reduce_sum(hess, axis = 2 ))\n",
    "\n",
    "\n",
    "def get_GN_hessian(generator,nvp,z,mask,sigma):\n",
    "  '''\n",
    "  computes the Gauss Newton approximation to the Hessian\n",
    "  '''\n",
    "\n",
    "  gen_z            = fwd_pass(generator,nvp,z,mask)\n",
    "  \n",
    "  sigma            = tf.boolean_mask(sigma,mask, axis=1)\n",
    "\n",
    "  grad_g           = tf.gather(tf.gradients(gen_z/(sigma),z),0)\n",
    "\n",
    "  grad_g2          = tf.einsum('ij,ik->ijk',grad_g,grad_g)\n",
    "\n",
    "  one              = tf.linalg.eye(hidden_size, batch_shape=[data_size],dtype=tf.float32)\n",
    "\n",
    "  hess_GN          = one+grad_g2\n",
    "  \n",
    "  return hess_GN\n",
    "  \n",
    "def compute_covariance(hessian):\n",
    "  \"\"\"\n",
    "  computes the covariance by inverting the hessian (symmetrization for numerical stability)\n",
    "  \"\"\"\n",
    "  \n",
    "  cov = tf.linalg.inv(hessian)\n",
    "  \n",
    "  cov = (cov+tf.linalg.transpose(cov))*0.5\n",
    "  \n",
    "  return cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "I6_BmwzlnSLc"
   },
   "outputs": [],
   "source": [
    "def get_neg_elbo(x,approx_posterior, generator, nvp, sigma, mask):\n",
    "  \"\"\"\n",
    "  computes the negative evidence lower bound (ELBO)\n",
    "  \"\"\"\n",
    "  \n",
    "  prior          = get_prior()\n",
    "  kl_divergence  = tfd.kl_divergence(approx_posterior, prior) \n",
    "  \n",
    "  z_sample       = tf.reshape(approx_posterior.sample(sample_size),[-1,hidden_size])\n",
    "  \n",
    "  fwd_z          = nvp({'z_sample':np.zeros((1,hidden_size)),'sample_size':1, 'u_sample':z_sample},as_dict=True)['fwd_pass']\n",
    "  gen_z          = tf.boolean_mask(tf.reshape(generator(fwd_z),[sample_size,data_size,data_dim,n_channels]),mask, axis=2)\n",
    "  sig            = tf.boolean_mask(sigma,mask, axis=1)\n",
    "\n",
    "  likelihood     = tfd.Independent(tfd.MultivariateNormalDiag(loc=gen_z,scale_diag=sig))\n",
    "\n",
    "  masked_x       = tf.boolean_mask(x, mask, axis=1)\n",
    "  like_prob      = likelihood.log_prob(tf.expand_dims(masked_x,0))\n",
    "\n",
    "  elbo           = tf.reduce_mean(like_prob)- kl_divergence\n",
    "  \n",
    "  return -elbo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LpfC0EH2zeQI"
   },
   "outputs": [],
   "source": [
    "def minimize_neg_elbo(x,custom_mask,noise,my_sess,full_rank=False):\n",
    "  \"\"\"\n",
    "  function to run a ELBO minimzation for stochastic VI.\n",
    "  \"\"\"\n",
    "  \n",
    "  \n",
    "  if full_rank:\n",
    "    sets = zip([1e-3,1e-4,1e-6],[5000,3000,2000])\n",
    "  else:\n",
    "    sets = zip([1e-3,1e-4,1e-5],[4000,2000,1000])\n",
    "  \n",
    "  elbo_loss = []\n",
    "  start = time.time()\n",
    "  for lrate, numiter in sets:\n",
    "    print('lrate', lrate)\n",
    "    for jj in range(numiter):\n",
    "      if full_rank:\n",
    "        _, ll = my_sess.run([opt_op_elbo_fr,neg_elbo_fr],feed_dict={input_data: x, mask:custom_mask, sigma_corr:noise, lr: lrate})\n",
    "      else:\n",
    "        _, ll = my_sess.run([opt_op_elbo,neg_elbo],feed_dict={input_data: x, mask:custom_mask, sigma_corr:noise, lr: lrate})\n",
    "      elbo_loss.append(ll)\n",
    "      if jj%1000==0:\n",
    "        print('iter', jj, 'loss', ll)\n",
    "        #if full_rank:\n",
    "        #  print(my_sess.run([mu_vi,post_vi.covariance()],feed_dict={input_data: x, mask:custom_mask, sigma_corr:noise, lr: lrate}))\n",
    "  end= time.time()\n",
    "  print('time taken',end-start)\n",
    "  loss    = ll\n",
    "  plt.figure()\n",
    "  plt.plot(elbo_loss)\n",
    "  plt.ylabel('loss')\n",
    "  plt.xlabel('iteration')\n",
    "  plt.show()\n",
    "  \n",
    "  return True\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "QGyi6PVWx1qd"
   },
   "outputs": [],
   "source": [
    "def minimize_posterior(initial_value, x, custom_mask, noise, my_sess, annealing =True):\n",
    "  \"\"\"\n",
    "  function to run several minimizations of the posterior\n",
    "  \"\"\"\n",
    "  \n",
    "  ini = np.reshape(initial_value,[data_size,hidden_size])\n",
    "  \n",
    "  my_sess.run(MAP_reset,feed_dict={input_data: x, MAP_ini:ini, mask:custom_mask,sigma_corr:noise})\n",
    "  \n",
    "  pos_def = False\n",
    "\n",
    "  start = time.time()\n",
    "  posterior_loss = []\n",
    "  for lrate, numiter in zip([1e-1,1e-2,1e-3],[1100,400,100]):\n",
    "    print('lrate', lrate)\n",
    "    for jj in range(numiter):\n",
    "      if annealing and lrate==1e-1:\n",
    "        inv_T= np.round(0.5*np.exp(-(1.-jj/numiter)),decimals=1)\n",
    "      else:\n",
    "        inv_T= 1.\n",
    "      _, ll = my_sess.run([opt_op_MAP,loss_MAP],feed_dict={input_data: x, mask:custom_mask, sigma_corr:noise, lr: lrate, inverse_T:inv_T})\n",
    "      posterior_loss.append(ll)\n",
    "      if jj%1000==0:\n",
    "        print('iter', jj, 'loss', ll,r'inverse T', inv_T)\n",
    "  end = time.time()\n",
    "  print('time taken',end-start)\n",
    "  z_value = my_sess.run(MAP,feed_dict={input_data: x, mask:custom_mask, sigma_corr:noise})\n",
    "  \n",
    "  eig     = my_sess.run(tf.linalg.eigvalsh(hessian),feed_dict={input_data: x, mask:custom_mask,sigma_corr:noise})\n",
    "  if np.all(eig>0.):\n",
    "    pos_def = True\n",
    "  \n",
    "  loss    = ll\n",
    "  plt.figure()\n",
    "  plt.plot(posterior_loss)\n",
    "  plt.ylabel('loss')\n",
    "  plt.xlabel('iteration')\n",
    "  plt.show()\n",
    "  \n",
    "  return z_value, loss, pos_def\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "oiAie-wjUcHN"
   },
   "outputs": [],
   "source": [
    "def get_laplace_sample(num,map_value,x,mymask,noise,my_sess):\n",
    "  \"\"\"\n",
    "  samples from the Laplace approximation around the deepest minimum\n",
    "  \"\"\"\n",
    "  \n",
    "  my_sess.run(MAP_reset,feed_dict={MAP_ini:map_value})\n",
    "  my_sess.run(update_mu)\n",
    "  my_sess.run(update_TriL,feed_dict={input_data: x, mask: mymask, sigma_corr:noise})\n",
    "  \n",
    "  samples=[]\n",
    "  for ii in range(num):\n",
    "    my_sess.run(posterior_sample,feed_dict={input_data: x, sigma_corr:noise})\n",
    "    samples.append(my_sess.run(recon,feed_dict={input_data: x, sigma_corr:noise}))\n",
    "    \n",
    "  samples=np.asarray(samples)\n",
    "  return samples\n",
    "\n",
    "def get_gmm_sample(num,x,mymask,noise,my_sess):\n",
    "  \"\"\"\n",
    "  samples from the Gaussian mixture posterior fit\n",
    "  \"\"\"\n",
    "  \n",
    "  samples=[]\n",
    "  for ii in range(num):\n",
    "    samples.append(my_sess.run(gmm_recon,feed_dict={input_data: x, sigma_corr:noise}))\n",
    "    \n",
    "  samples=np.asarray(samples)\n",
    "  return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "SXhLJToHcp7b"
   },
   "outputs": [],
   "source": [
    "def plot_samples(samples, mask, title='samples', filename='samples'):\n",
    "  \"\"\"\n",
    "  plots a compilation of samples\n",
    "  \"\"\"\n",
    "  plt.figure()\n",
    "  plt.title(title)\n",
    "  for i in range(min(len(samples),16)):\n",
    "      subplot(4,4,i+1)\n",
    "      imshow(np.reshape(samples[i,:],(28,28)),vmin=-0.2,vmax=1.2, cmap='gray')\n",
    "      axis('off')\n",
    "  plt.savefig(plot_path+filename+'.png',bbox_inches='tight')\n",
    "  plt.show()\n",
    "  \n",
    "  if corr_type in ['mask', 'sparse mask', 'noise+mask']:\n",
    "    plt.figure()\n",
    "    plt.title('masked'+title)\n",
    "    for i in range(min(len(samples),16)):\n",
    "        subplot(4,4,i+1)\n",
    "        imshow(np.reshape(samples[i,0,:,0]*mask,(28,28)),vmin=-0.2,vmax=1.2, cmap='gray')\n",
    "        axis('off')     \n",
    "    plt.savefig(plot_path+filename+'masked.png',bbox_inches='tight')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LYAt6f7MQSpa"
   },
   "outputs": [],
   "source": [
    "def get_random_start_values(num, my_sess):\n",
    "  \"\"\"\n",
    "  returns random starting values drawn from the prior\n",
    "  \"\"\"\n",
    "  result=[]\n",
    "  for ii in range(num):\n",
    "    result.append(my_sess.run(get_prior().sample()))\n",
    "  return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "BaFIFXBnQ3o-"
   },
   "outputs": [],
   "source": [
    "def get_chi2(sigma,data,mean,masking=True, mask=None,threshold=0.02):\n",
    "  \"\"\"\n",
    "  computes chi2 between data and mean\n",
    "  \"\"\"\n",
    "  \n",
    "  if masking:\n",
    "    mask = np.reshape(mask,data.shape)\n",
    "    data = data[np.where(mask==1)]\n",
    "    mean = mean[np.where(mask==1)]\n",
    "    sigma= sigma[np.where(mask==1)]\n",
    "    \n",
    "  \n",
    "  low = min(sigma.flatten())\n",
    "  high= max(sigma.flatten())\n",
    "  \n",
    "  chi2_tot = np.sum((data-mean)**2/sigma**2)\n",
    "  dof_tot  = len(np.squeeze(data))\n",
    "  \n",
    "  if corr_type not in ['noise','noise+mask']:\n",
    "    chi2_low = np.sum((data[np.where(data<=threshold)]-mean[np.where(data<=threshold)])**2/sigma[np.where(data<=threshold)]**2)\n",
    "    dof_low  = len(np.squeeze(data[np.where(data<=threshold)]))\n",
    "    chi2_high= np.sum((data[np.where(data>threshold)]-mean[np.where(data>threshold)])**2/sigma[np.where(data>threshold)]**2)\n",
    "    dof_high = len(np.squeeze(data[np.where(data>threshold)]))\n",
    "  else:\n",
    "    chi2_low = None\n",
    "    dof_low  = None\n",
    "    chi2_high= None\n",
    "    dof_high = None\n",
    "  \n",
    "  return chi2_tot, dof_tot, chi2_low, dof_low, chi2_high, dof_high, masking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "yGtEbpIZ2vhx"
   },
   "outputs": [],
   "source": [
    "def plot_minima(minima, losses, var):\n",
    "  \"\"\"\n",
    "  plot the minima for comparison with their width estimated from the variance at these points -> helps decide whether minima are separate\n",
    "  \"\"\"\n",
    "  plt.figure()\n",
    "  plt.title('Minimization result')\n",
    "  plt.plot(np.arange(len(losses)),losses,ls='',marker='o')\n",
    "  plt.xlabel('# iteration')\n",
    "  plt.ylabel('loss')\n",
    "  plt.savefig(plot_path+'minimzation_results_%s.png'%(label),bbox_inches='tight')\n",
    "  plt.show()\n",
    "  \n",
    "  colors = matplotlib.colors.Normalize(vmin=min(losses), vmax=max(losses))\n",
    "  cmap   = matplotlib.cm.get_cmap('Spectral')\n",
    "  \n",
    "  var = np.squeeze(var)\n",
    "  plt.figure()\n",
    "  plt.title('value of hidden variables at minima')\n",
    "  for ii in range(len(minima)):\n",
    "  \n",
    "    yerr_= np.sqrt(var[ii])\n",
    "\n",
    "    plt.errorbar(np.arange(hidden_size),np.squeeze(minima)[ii], marker='o',ls='', c=cmap(colors(losses[ii])), mew=0, yerr=yerr_, label ='%d'%losses[ii])\n",
    "  plt.legend(ncol=4, loc=(1.01,0))\n",
    "  plt.xlabel('# hidden variable')\n",
    "  plt.ylabel('value')\n",
    "  plt.savefig(plot_path+'hidden_values_at_minima_%s.png'%(label),bbox_inches='tight')\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "80BR72DX58VQ"
   },
   "outputs": [],
   "source": [
    "def probe_posterior(minimum, x, noise, mymask, my_sess, filename=label):\n",
    "  \"\"\"\n",
    "  probes the real posterior along each latent space direction around the minimum and compares to posterior fits\n",
    "  \"\"\"\n",
    "\n",
    "  _ = my_sess.run(MAP_reset,feed_dict={input_data: x, MAP_ini:minimum, sigma_corr:noise})\n",
    "  _ = my_sess.run(update_mu,feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "  _ = my_sess.run(update_TriL,feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "  \n",
    "  exact_hessian = sess.run(hessian,feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "  approx_hessian= sess.run(GN_hessian,feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "  ll0 = sess.run(loss_MAP,feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "  \n",
    "  mean_vi, sig_vi, ll0_vi = sess.run([mu_elbo,sigma_elbo, nlPost_elbo],feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "  \n",
    "  \n",
    "  mean_fr, h_fr, ll0_fr   = sess.run([mu_vi,hess_fr, nlPost_vi],feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "  \n",
    "  \n",
    "  print(mean_vi)\n",
    "  print(minimum)\n",
    "  \n",
    "  print(ll0,ll0_vi,ll0_fr)\n",
    "  \n",
    "  plt.figure(figsize=(4*3,3))\n",
    "  \n",
    "  \n",
    "  jj =0\n",
    "  for nn in [5,6,7]:#np.arange(hidden_size):\n",
    "    H    = exact_hessian[0,nn,nn]\n",
    "    Hfr  = h_fr[0,nn,nn]\n",
    "    H_vi = 1./sig_vi[0,nn]**2\n",
    "    \n",
    "    losses=[]\n",
    "    \n",
    "    print(H_vi,H)\n",
    "    \n",
    "    subplot(1,3,jj+1)\n",
    "    \n",
    "    title('latent space direction %d'%nn)\n",
    "    \n",
    "    Delta   = 0.5\n",
    "    steps   = 2000\n",
    "    steps_fine = 10000\n",
    "    delta_z = np.zeros((steps,hidden_size))\n",
    "\n",
    "    delta_z[:,nn] = (np.arange(steps)-steps//2)*Delta/steps\n",
    "    new_ini       = delta_z+minimum\n",
    "    new_ini_vi    = delta_z+mean_vi\n",
    "    new_ini_fr    = delta_z+mean_fr\n",
    "    \n",
    "    full_span     = np.ones((steps_fine,hidden_size))*minimum\n",
    "    full_span_min = min(min(new_ini_vi[:,nn]),min(new_ini[:,nn]),min(new_ini_fr[:,nn]))\n",
    "    full_span_max = max(max(new_ini_vi[:,nn]),max(new_ini[:,nn]),max(new_ini_fr[:,nn]))\n",
    "    full_span_    = np.linspace(full_span_min,full_span_max,steps_fine)\n",
    "    full_span[:,nn]= full_span_\n",
    "\n",
    "    for ii in range(steps_fine):\n",
    "      _ = sess.run(MAP_reset,feed_dict={input_data: x, mask:mymask, MAP_ini:np.expand_dims(full_span[ii],axis=0), sigma_corr:noise})\n",
    "      ll = sess.run(loss_MAP,feed_dict={input_data: x, mask:mymask, sigma_corr:noise})\n",
    "      losses.append(ll)\n",
    "    \n",
    "  \n",
    "    plt.plot(full_span[:,nn],losses,label='probed posterior', color='crimson',lw=2)\n",
    "    plt.plot(new_ini[:,nn],ll0+H*delta_z[:,nn]**2,label='EL2O estimate (full rank)',lw=2)\n",
    "    plt.plot(new_ini_vi[:,nn],ll0_vi+H_vi*delta_z[:,nn]**2,label='mean field SVI estimate',lw=2)\n",
    "    plt.plot(new_ini_fr[:,nn],ll0_fr+Hfr*delta_z[:,nn]**2,label='full rank SVI estimate',lw=2)\n",
    "    \n",
    "    plt.xlabel('z',fontsize=16)\n",
    "    plt.ylim(min(min(losses),ll0_fr),max(max(losses),ll0_fr+0.5))\n",
    "    if jj==0:\n",
    "      plt.ylabel('negative log posterior',fontsize=14)\n",
    "      plt.legend(loc='upper right',fontsize=12,framealpha=0.9)\n",
    "    jj+=1\n",
    "  plt.tight_layout()\n",
    " \n",
    "  \n",
    "  \n",
    "  \n",
    "  plt.savefig(plot_path+'probing_posterior_%s.pdf'%(filename),bbox_inches='tight')\n",
    "  plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qrZDSLzEIKrn"
   },
   "outputs": [],
   "source": [
    "\n",
    "def get_gmm_parameters(minima, x, noise, mymask, offset):\n",
    "  \"\"\"\n",
    "  Gaussian mixture model (could be coded more elegantly with softmax function)\n",
    "  \"\"\"\n",
    "  \n",
    "  mu   =[]\n",
    "  w    =[]\n",
    "  sigma=[]\n",
    "  for ii in range(num_comp):\n",
    "\n",
    "    # do Laplace approximation around this minimum\n",
    "    mu+=[minima[ii]]\n",
    "    sess.run(MAP_reset,feed_dict={MAP_ini:minima[ii]})\n",
    "    sigma+=[sess.run(update_TriL,feed_dict={input_data: x, sigma_corr:noise, mask: mymask})]\n",
    "\n",
    "    # correct weighting of different minima according to El20 procedure, with samples at the maxima and well seperated maxima\n",
    "    logdet  = sess.run(tf.linalg.logdet(approx_posterior_laplace.covariance()),feed_dict={input_data: x, sigma_corr:noise, mask: mymask})\n",
    "    logprob = sess.run(nlPost_MAP,feed_dict={input_data: x, sigma_corr:noise, mask: mymask})\n",
    "    w+=[np.exp(0.5*logdet+logprob+offset)]\n",
    "    \n",
    "  print('weights of Gaussian mixtures:', w/np.sum(w))\n",
    "  mu     = np.reshape(np.asarray(mu),[1,num_comp,hidden_size])\n",
    "  sigma  = np.reshape(np.asarray(sigma),[1,num_comp,hidden_size,hidden_size])\n",
    "  w      = np.squeeze(np.asarray(w))\n",
    "                         \n",
    "  return mu, sigma, w\n",
    "                                 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "gQXNNSN7TecV"
   },
   "outputs": [],
   "source": [
    "def plot_prob_2D_GMM(samples, indices):\n",
    "    '''\n",
    "    makes corner plots of the posterior samples\n",
    "    '''\n",
    "\n",
    "    samples = samples[:,0,:]\n",
    "\n",
    "    samples = np.hstack((np.expand_dims(samples[:,indices[0]],-1),np.expand_dims(samples[:,indices[1]],-1)))\n",
    "\n",
    "    figure=corner.corner(samples)\n",
    "    axes = np.array(figure.axes).reshape((2, 2))\n",
    "\n",
    "    axes[1,0].set_xlabel('latent space variable %d'%indices[0])\n",
    "    axes[1,0].set_ylabel('latent space variable %d'%indices[1])\n",
    "    plt.savefig(plot_path+'posterior_contour_GMM_%s_latent_space_dir_%d_%d.png'%(label,indices[0],indices[1]),bbox_inches='tight')\n",
    "    plt.show()\n",
    "    \n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bj_BnTfZ0Un5"
   },
   "outputs": [],
   "source": [
    "def add_small_offset(x):\n",
    "  \"\"\"offset added to the diagonal of the covariance, needed to make SVI stable\"\"\"\n",
    "  return tf.add(x,1e-8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8aubiinPFSQL"
   },
   "source": [
    "after defining all necessary functions, it's time to build the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 410
    },
    "colab_type": "code",
    "id": "yvTEYw44O_5q",
    "outputId": "09784a73-14fb-404a-c386-0c2ef0bffe9a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n",
      "INFO:tensorflow:Saver not created because there are no variables in the graph to restore\n"
     ]
    }
   ],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "#### Variables ####\n",
    "#noise level \n",
    "sigma_corr  = tf.placeholder_with_default(np.ones([data_size,data_dim,n_channels], dtype='float32')*sigma_n,shape=[data_size,data_dim,n_channels])\n",
    "\n",
    "#mask\n",
    "mask        = tf.placeholder_with_default(np.ones([data_dim], dtype='float32'),shape=[data_dim])\n",
    "\n",
    "#corrupted input data\n",
    "input_data  = tf.placeholder(shape=[data_size,data_dim,n_channels], dtype=tf.float32)\n",
    "\n",
    "#temperature used for annealed minimzation\n",
    "inverse_T   = tf.placeholder_with_default(1., shape=[])\n",
    "\n",
    "#learning rate\n",
    "lr          = tf.placeholder_with_default(0.001,shape=[])\n",
    "####################\n",
    "\n",
    "\n",
    "#### Modules ####\n",
    "generator   = hub.Module(generator_path, trainable=False)\n",
    "nvp_funcs   = hub.Module(nvp_func_path, trainable=False)\n",
    "#################\n",
    "\n",
    "#EL2O:\n",
    "\n",
    "#### Maximum a Posteriori estimate ####\n",
    "MAP_ini     = tf.placeholder_with_default(tf.zeros([data_size,hidden_size]),shape=[data_size,hidden_size])\n",
    "MAP         = tf.Variable(MAP_ini)\n",
    "MAP_reset   = tf.stop_gradient(MAP.assign(MAP_ini))\n",
    "\n",
    "nlPost_MAP  = get_log_posterior(MAP, input_data, generator,nvp_funcs, sigma_corr,mask, inverse_T)\n",
    "loss_MAP    = -tf.reduce_mean(nlPost_MAP)\n",
    "\n",
    "optimizer   = tf.train.AdamOptimizer(learning_rate=lr)\n",
    "opt_op_MAP  = optimizer.minimize(loss_MAP, var_list=[MAP])\n",
    "\n",
    "recon_MAP   = get_recon(generator,nvp_funcs, MAP,sigma_corr,mask)\n",
    "\n",
    "#######################################\n",
    "\n",
    "\n",
    "##### Laplace approximation around a point ####\n",
    "hessian     = get_hessian(-nlPost_MAP,MAP)\n",
    "GN_hessian  = get_GN_hessian(generator,nvp_funcs,MAP,mask,sigma_corr)\n",
    "ini_val  = np.ones((data_size,(hidden_size *(hidden_size +1)) // 2),dtype=np.float32)\n",
    "with tf.variable_scope(\"Laplace_Posterior\",reuse=tf.AUTO_REUSE):\n",
    "  mu_new      = tf.Variable(np.ones((data_size,hidden_size),dtype=np.float32), dtype=np.float32)\n",
    "  sigma_new_t = ini_val\n",
    "  sigma_new_t2= tf.Variable(tfd.matrix_diag_transform(tfd.fill_triangular(sigma_new_t), transform=tf.nn.softplus),dtype=tf.float32)\n",
    "  \n",
    "approx_posterior_laplace = tfd.MultivariateNormalTriL(loc=mu_new,scale_tril=sigma_new_t2)\n",
    "\n",
    "update_mu          = mu_new.assign(MAP)\n",
    "covariance         = compute_covariance(hessian)\n",
    "variance           = tf.linalg.diag_part(covariance)[0]\n",
    "update_TriL        = sigma_new_t2.assign(tf.linalg.cholesky(covariance))\n",
    "\n",
    "posterior_sample   = approx_posterior_laplace.sample()\n",
    "\n",
    "recon              = get_recon(generator,nvp_funcs, posterior_sample ,sigma_corr,mask)\n",
    "################################################\n",
    "\n",
    "\n",
    "##### Gaussian mixture model fit around minima #####\n",
    "ini_val2    = np.ones((data_size,num_comp,(hidden_size *(hidden_size +1)) // 2),dtype=np.float32)\n",
    "with tf.variable_scope(\"corrupted/gmm\",reuse=tf.AUTO_REUSE):\n",
    "  mu_gmm      = tf.Variable(np.ones((data_size,num_comp,hidden_size)), dtype=np.float32)\n",
    "  sigma_gmm   = tf.Variable(tfd.fill_triangular(ini_val2))\n",
    "  w_gmm       = tf.Variable(np.ones((num_comp))/num_comp, dtype=np.float32)\n",
    "  \n",
    "sigma_gmmt    = tfd.matrix_diag_transform(sigma_gmm, transform=tf.nn.softplus)\n",
    "w_positive    = tf.math.softplus(w_gmm)\n",
    "w_rescaled    = tf.squeeze(w_positive/tf.reduce_sum(w_positive))\n",
    "\n",
    "gmm           = tfd.MixtureSameFamily(mixture_distribution=tfd.Categorical(probs=w_rescaled),components_distribution=tfd.MultivariateNormalTriL(loc=mu_gmm,scale_tril=sigma_gmmt))\n",
    "\n",
    "mu_ini        = tf.placeholder_with_default(tf.zeros([data_size,num_comp,hidden_size]),shape=[data_size,num_comp,hidden_size])\n",
    "sigma_ini     = tf.placeholder_with_default(tf.ones([data_size,num_comp,hidden_size, hidden_size]),shape=[data_size,num_comp,hidden_size, hidden_size])\n",
    "w_ini         = tf.placeholder_with_default(tf.ones([num_comp])/num_comp,shape=[num_comp])\n",
    "\n",
    "update_w      = tf.stop_gradient(w_gmm.assign(softplus_inverse(w_ini)))\n",
    "update_mugmm  = tf.stop_gradient(mu_gmm.assign(mu_ini))\n",
    "update_TriLgmm= tf.stop_gradient(sigma_gmm.assign(tfd.matrix_diag_transform(sigma_ini, transform=softplus_inverse)))\n",
    "\n",
    "gmm_sample    = gmm.sample()\n",
    "gmm_recon     = get_recon(generator,nvp_funcs, gmm_sample ,sigma_corr,mask)\n",
    "####################################################\n",
    "\n",
    "\n",
    "#ELBO\n",
    "\n",
    "########## Syochastic VI estimates by minimizing the elbo #############\n",
    "\n",
    "#### mean field VI ####\n",
    "with tf.variable_scope(\"posterior_elbo_mean\",reuse=tf.AUTO_REUSE):\n",
    "  mu_elbo      = tf.Variable(np.zeros((data_size,hidden_size)), dtype=np.float32)\n",
    "  sigma_elbo   = tf.Variable(np.ones((data_size,hidden_size)), dtype=np.float32)\n",
    "  \n",
    "update_mu_elbo = tf.stop_gradient(mu_elbo.assign(MAP))\n",
    "\n",
    "approx_posterior_elbo = tfd.MultivariateNormalDiag(loc=mu_elbo,scale_diag=sigma_elbo, name='approxposterior_elbo')\n",
    "\n",
    "neg_elbo       = get_neg_elbo(input_data, approx_posterior_elbo, generator, nvp_funcs, sigma_corr, mask)\n",
    "opt_op_elbo    = optimizer.minimize(neg_elbo,var_list=[mu_elbo,sigma_elbo])\n",
    "\n",
    "nlPost_elbo    = -tf.reduce_mean(get_log_posterior(mu_elbo, input_data, generator,nvp_funcs, sigma_corr,mask, 1))\n",
    "#######################\n",
    "\n",
    "\n",
    "### full rank VI ###\n",
    "ini_val1     = np.zeros((data_size,(hidden_size *(hidden_size +1)) // 2),dtype=np.float32)\n",
    "with tf.variable_scope(\"posterior_elbo_fullrank\",reuse=tf.AUTO_REUSE):\n",
    "  mu_vi      = tf.Variable(np.ones((data_size,hidden_size)), dtype=np.float32)\n",
    "  sigma_vi   = tf.Variable(ini_val1)\n",
    "sigma_vit    = tfd.matrix_diag_transform(tfd.fill_triangular(sigma_vi), transform=tf.nn.softplus)\n",
    "sigma_vit    = tfd.matrix_diag_transform(sigma_vit, transform=add_small_offset)\n",
    "post_vi      = tfd.MultivariateNormalTriL(loc=mu_vi,scale_tril=sigma_vit)\n",
    "\n",
    "neg_elbo_fr    = get_neg_elbo(input_data, post_vi, generator, nvp_funcs, sigma_corr, mask)\n",
    "opt_op_elbo_fr = optimizer.minimize(neg_elbo_fr,var_list=[mu_vi,sigma_vi])\n",
    "\n",
    "hess_fr        = tf.linalg.inv(post_vi.covariance())\n",
    "nlPost_vi      = -tf.reduce_mean(get_log_posterior(mu_vi, input_data, generator,nvp_funcs, sigma_corr,mask, 1))\n",
    "\n",
    "recon_fr       = get_recon(generator,nvp_funcs, mu_vi ,sigma_corr,mask)\n",
    "recon_elbo     = get_recon(generator,nvp_funcs, mu_elbo ,sigma_corr,mask)\n",
    "####################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "Soh1tnGH1FTW",
    "outputId": "b002cf96-f907-4c9a-93c5-9bfd0999b11c"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAABltJREFUeJzt3U+IjXscx/F5bnejSCOM7NiK1Gws\nMFb+ZCkrQixIWVhISRasbU0pRWz8KRZEsrKYHY00uyFRxCRqdiPO3d26tznfwznjDD6v19Kn5zwn\nvHvKz5nTtFqtAeDP99d8vwGgP8QOIcQOIcQOIcQOIf7u582apvFP//CTtVqtZrZf92SHEGKHEGKH\nEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKH\nEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEH/P9xtgYGD5\n8uXlfuPGjXIfGxtru128eLG89tWrV+X+p1q8eHG5b968udwfPHhQ7l++fPnh9/SzebJDCLFDCLFD\nCLFDCLFDCLFDCLFDCOfsfTA4OFjuExMT5d7pTPj9+/dtt9Rz9IGB+vftyZMn5bXLli0r9+Hh4XKf\nnJws9/ngyQ4hxA4hxA4hxA4hxA4hxA4hHL3NgaVLl5b79evXy33JkiXlfuHChXI/duxYuac6ffp0\n223VqlXltYcPHy73X/ForRNPdgghdgghdgghdgghdgghdgghdgjRtFqt/t2safp3sz7aunVrud+/\nf7+n11+xYkW5T01N9fT6v6s1a9aU+/Pnz9tut2/fLq89cOBAuU9PT5f7fGq1Ws1sv+7JDiHEDiHE\nDiHEDiHEDiHEDiHEDiF8nv07VV+rvGvXrp5e+9ChQ+XuHH12jx496vq1O52z/8rn6N3yZIcQYocQ\nYocQYocQYocQYocQYocQztm/0/nz59tue/fuLa/t9PXAN2/e7Oo9/ek2bdpU7kNDQ+V++fLlttu1\na9e6eUu/NU92CCF2CCF2CCF2CCF2CCF2CCF2COGc/TtVP1//27dv5bVv374t95mZma7e0+9gwYIF\nbbdTp06V1x49erTcO33nwcGDB8s9jSc7hBA7hBA7hBA7hBA7hBA7hHD01gc7d+4s94cPH5b758+f\ny310dPSH39NcGRkZKfctW7a03TZs2NDTvW/dutXT9Wk82SGE2CGE2CGE2CGE2CGE2CGE2CFE0+lj\ngnN6s6bp383m2PDwcNvtzp075bUrV67s6d5N05R7P/8M/+9nvreXL1+W+/bt28v9xYsXXd/7d9Zq\ntWb9Q/FkhxBihxBihxBihxBihxBihxBihxA+z/6dqq9dXrduXXnt+vXry73TefGJEyfKfWpqqu12\n5cqV8tpeXb16tdyfPXvW9WuPjY2Ve+o5erc82SGE2CGE2CGE2CGE2CGE2CGE2CGEz7PTk9WrV5f7\n5ORk2218fLy8dtu2beVe/f+CZD7PDuHEDiHEDiHEDiHEDiHEDiHEDiF8np2enDlzptyr/8dx8uTJ\n8lrn6HPLkx1CiB1CiB1CiB1CiB1CiB1COHqjtHv37nLft29fuU9PT7fdPn782NV7ojue7BBC7BBC\n7BBC7BBC7BBC7BBC7BDCOTulHTt29HT93bt3225Pnz7t6bX5MZ7sEELsEELsEELsEELsEELsEELs\nEMJXNlN69+5duS9cuLDcR0ZG2m7O2X8OX9kM4cQOIcQOIcQOIcQOIcQOIcQOIXyePdyRI0fKfWho\nqNw/fPhQ7s7Sfx2e7BBC7BBC7BBC7BBC7BBC7BDC0Vu4TkdvnT4Cfe/eva7vvWjRonIfHBws99ev\nX3d970Se7BBC7BBC7BBC7BBC7BBC7BBC7BDCOTs9+fr1a7nv2bOn7Xb8+PHy2omJiXLfv39/ufNf\nnuwQQuwQQuwQQuwQQuwQQuwQQuwQwlc2hxsfHy/3tWvXlnvTzPrtwP+q/n5dunSpvPbcuXPl/ubN\nm3JP5SubIZzYIYTYIYTYIYTYIYTYIYTYIYRz9nAbN24s97Nnz5b748ePy310dLTt9unTp/LamZmZ\ncmd2ztkhnNghhNghhNghhNghhNghhNghhHN2+MM4Z4dwYocQYocQYocQYocQYocQYocQYocQYocQ\nYocQYocQYocQYocQYocQYocQYocQYocQYocQYocQYocQYocQYocQff1R0sD88WSHEGKHEGKHEGKH\nEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKHEGKH\nEP8Ae6Qji3rRingAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTDB2wARjB0wwdsAEYwdMMHbABGMHTPwP3SWUsZlgvscAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n5gvrUfe1IgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neLZQmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting search for minima\n",
      "progress in % 0.0\n",
      "lrate 0.1\n",
      "iter 0 loss 86.56891 inverse T 0.2\n",
      "iter 1000 loss 161.66711 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 313.01395 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 311.87534 inverse T 1.0\n",
      "time taken 12.313082695007324\n"
     ]
    },
    {
     "data": {
      "image/png": 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Xc/VBSFkSG2rDzG4DTgYmmdk64BvAyWZ2DNGZd6uBTwO4+xIzuwNYCnQDl7p7NqnaRGqJ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\n5N8ZFQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.15497555 -0.31399307  1.0669369   0.42347446 -1.2496713  -0.4100478\n",
      "   1.1228383  -0.60017407  0.25277945  0.8127882 ]]\n",
      "hessian postive definite\n",
      "progress in % 10.0\n",
      "lrate 0.1\n",
      "iter 0 loss 87.62459 inverse T 0.2\n",
      "iter 1000 loss 158.67552 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 304.40723 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 304.2309 inverse T 1.0\n",
      "time taken 11.263373374938965\n"
     ]
    },
    {
     "data": {
      "image/png": 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Bs2EOCLM62bxF7a7CbHxwQJjVCU9LYbabA8Ksjie2MxvmgDCr4zEIs2EOCLM62dXX2l2F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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.26020896  0.38073534 -0.41022104  1.0105224  -1.9619846  -0.39485592\n",
      "   0.6341232  -1.3844284   0.3402839   0.1768981 ]]\n",
      "hessian postive definite\n",
      "progress in % 20.0\n",
      "lrate 0.1\n",
      "iter 0 loss 90.62492 inverse T 0.2\n",
      "iter 1000 loss 175.00984 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 339.8741 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 339.73895 inverse T 1.0\n",
      "time taken 11.011464357376099\n"
     ]
    },
    {
     "data": {
      "image/png": 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+/9aY5by4dx+HzRlgzb/7zbG/4qXsr/LRRox12RRpRPDzl0cZ6Ovj1XP6ESLbDxkfC8hr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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.19354981  0.4288391   0.76593804  0.28073877 -0.2660083  -0.35428235\n",
      "   0.01303882  0.48811963 -0.33551088 -0.88986516]]\n",
      "hessian postive definite\n",
      "progress in % 30.0\n",
      "lrate 0.1\n",
      "iter 0 loss 87.75638 inverse T 0.2\n",
      "iter 1000 loss 161.55832 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 312.17087 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 311.8712 inverse T 1.0\n",
      "time taken 10.47121787071228\n"
     ]
    },
    {
     "data": {
      "image/png": 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MLo6Z0kkx7UF4DMJq4YAwK/H1nz/Kph37ALjxno1ll9k7WOAf73ikqtd9aud+nkp7IKuf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\nPcrz1Tz4BgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.53444654 -0.51293427  0.9879566   0.05945762 -0.10398544 -0.07377732\n",
      "   0.52641124 -1.3543847   0.8319721   0.11445535]]\n",
      "hessian postive definite\n",
      "progress in % 40.0\n",
      "lrate 0.1\n",
      "iter 0 loss 82.018845 inverse T 0.2\n",
      "iter 1000 loss 161.88821 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 312.16537 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 311.8732 inverse T 1.0\n",
      "time taken 11.091197729110718\n"
     ]
    },
    {
     "data": {
      "image/png": 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N296wTP/m7fzfnD2eebO7pq5AaxsOCLMqO4ezS4Ct+9IZdJZKdJREOXXkd5TE4NAIg0Nl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\nrkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.5350348  -0.5135459   0.9883485   0.05934711 -0.10403962 -0.07404163\n",
      "   0.5264579  -1.3544562   0.8317612   0.11482619]]\n",
      "hessian postive definite\n",
      "progress in % 50.0\n",
      "lrate 0.1\n",
      "iter 0 loss 89.38075 inverse T 0.2\n",
      "iter 1000 loss 158.67697 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 304.67334 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 304.3126 inverse T 1.0\n",
      "time taken 11.2956862449646\n"
     ]
    },
    {
     "data": {
      "image/png": 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SDAWESI4PWqMxIhsvPZEt7RkA2tozbPigjfZMhpQZrR0Zhg2sprYqzcjBNZ3rHrX/aAC2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\n3wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.02943627  0.43602023 -0.5243673   0.74939805 -1.9458894  -0.3543505\n",
      "   0.9370585  -1.3704278   0.281512    0.08567784]]\n",
      "hessian postive definite\n",
      "progress in % 60.0\n",
      "lrate 0.1\n",
      "iter 0 loss 84.66598 inverse T 0.2\n",
      "iter 1000 loss 175.01733 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 339.81638 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 339.73962 inverse T 1.0\n",
      "time taken 11.096110582351685\n"
     ]
    },
    {
     "data": {
      "image/png": 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zHN9cx2yUA8IsxzfXMRvlgDDL8RiE2SgHhFlOJYIOfyvMAAeE2TY8BmE2ygFhlpONQTgg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\nOSDMzKyQA8LMzAo5IMzMrJADwszMCv1/I649vQJEaw4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.8644920e-01  4.2152613e-01  7.5660515e-01  2.7801698e-01\n",
      "  -2.6561064e-01 -3.6272392e-01 -7.2355405e-04  4.9694893e-01\n",
      "  -3.3726168e-01 -8.9003587e-01]]\n",
      "hessian postive definite\n",
      "progress in % 70.0\n",
      "lrate 0.1\n",
      "iter 0 loss 91.73829 inverse T 0.2\n",
      "iter 1000 loss 158.61974 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 304.4286 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 304.23114 inverse T 1.0\n",
      "time taken 10.736321926116943\n"
     ]
    },
    {
     "data": {
      "image/png": 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AgnQ7B7ikwLpsHHhh6xCVSuxxfkTw9Ivb+OR1y/jSLY8wcOH/5dolq1k1+CJD5Uphdfk4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\nHBBmZpbr/wOz/om/WimC9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.26026565  0.38083062 -0.41014087  1.0106142  -1.9620478  -0.39476606\n",
      "   0.634245   -1.3845389   0.3403529   0.17685123]]\n",
      "hessian postive definite\n",
      "progress in % 80.0\n",
      "lrate 0.1\n",
      "iter 0 loss 91.76339 inverse T 0.2\n",
      "iter 1000 loss 162.13145 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 305.44342 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 304.3571 inverse T 1.0\n",
      "time taken 10.533259630203247\n"
     ]
    },
    {
     "data": {
      "image/png": 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ndTFJLhQQIhk27WjjjF88xspNO0mlvde8Jxo3sasjOH/zlqdXUX/ZvSx8LdsLFudHOkwI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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.0133394   0.48257348 -0.5991152   0.723976   -1.9428226  -0.32445502\n",
      "   0.9013575  -1.366099    0.25010458  0.11908284]]\n",
      "hessian postive definite\n",
      "progress in % 90.0\n",
      "lrate 0.1\n",
      "iter 0 loss 85.3296 inverse T 0.2\n",
      "iter 1000 loss 174.99069 inverse T 0.5\n",
      "lrate 0.01\n",
      "iter 0 loss 339.86697 inverse T 1.0\n",
      "lrate 0.001\n",
      "iter 0 loss 339.74503 inverse T 1.0\n",
      "time taken 10.652498722076416\n"
     ]
    },
    {
     "data": {
      "image/png": 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pfT0s+Y+zJ17YrMt5sD6znPA1A2YHOSDMcrLbc3a6CrOpwQFhlhMelsLsIAeEWY4HtjMb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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nC0ZV9yCncQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.1902987   0.42951155  0.7641596   0.27617052 -0.25902402 -0.3561756\n",
      "   0.01074018  0.4913659  -0.33487946 -0.8877177 ]]\n",
      "hessian postive definite\n",
      "analysing the posterior minima:\n"
     ]
    },
    {
     "data": {
      "image/png": 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og9TzgEXA8em1KCI+O8hmO4GZEXECxW06Zks6kWKw+xjgOKAJOD/1fw/w+vS6gOLHeWZm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\ncpMo3oN6DwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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92wC8raq7ReQ3ADJVdRmAtwAsFJFcACfgSSyDQgwDpbHxKI2NR3e2MJLXhZI1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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "reconstruction from lowest minimum\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhB0IQdiBEIQdCPEvjDvoNabb5WgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "masked reconstruction\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQ4h/AR8C/iaK1YbsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting stochastic VI on the posterior\n",
      "lrate 0.001\n",
      "iter 0 loss [364.44553]\n",
      "iter 1000 loss [314.91864]\n",
      "iter 2000 loss [315.22012]\n",
      "iter 3000 loss [315.40253]\n",
      "lrate 0.0001\n",
      "iter 0 loss [314.9166]\n",
      "iter 1000 loss [315.14142]\n",
      "lrate 1e-05\n",
      "iter 0 loss [315.1457]\n",
      "time taken 129.07305002212524\n"
     ]
    },
    {
     "data": {
      "image/png": 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ucBLBRUUZLd8HwIvABD+d4eezlu+NxPkOcY0DgVeBs4Bn/LZTsla/7hXsHRAp\n914AugPL8edaU7nWkNrPAd6Jut50PMRUBCTedbzCt6WCvs65pjvSrwP6+unWau7w38Uf0hhL8K08\nZev1h2zmARuAlwm+UVc75+pDtt1cl3+9BujVgfX+X+CHQKN/3iuFawVwwEtmNsfMrvNtqfheGAJU\nAg/5w3d/MrOuKVprS1cAj/vpyOpNx4DoFFwQ/SnVxczM8oC/Azc557YkvpZq9TrnGpxzYwi+nZ8I\njIi4pFBmdgGwwTk3J+pa9sOpzrlxwGTgW2Z2euKLKfReyCA4jHufc24ssJ3gEE2zFKq1mT/fdCHw\nt5avdXS96RgQq4FBCc8H+rZUsN7M+gP4nxt8e2s1d9jvYmaZBOHwmHPuH6lebxPnXDUwneAwTYGZ\nZYRsu7ku/3p3YFMH1XsKcKGZrQD+SnCY6bcpWisAzrnV/ucG4GmCAE7F90IFUOGcm+WfP0UQGKlY\na6LJwFzn3Hr/PLJ60zEg3gOG+V4iWQS7ctMirqnJNKCpx8HVBMf6m9qn+F4L44Eav8v5InCOmfXw\nPRvO8W2HlJkZ8ACwyDn3605Qb6GZFfjpXILzJYsIguKyVupt+j0uA17z39SmAVf4nkNDgGHA7ENZ\nq3PuVufcQOdcMcF78TXn3JdTsVYAM+tqZvlN0wT/hgtIwfeCc24dsMrMhvumicCHqVhrC1/i08NL\nTXVFU28yT7Sk6oPg7P9SguPSP4mohseBtcBugm861xIcS34VWAa8AvT08xrwe1/vB0BJwnq+BpT7\nxzVJqvVUgt3aMmCef5yXwvUeD7zv610A/NS3H0nwoVlOsPue7dtz/PNy//qRCev6if89lgCTk/ye\nOINPezGlZK2+rvn+sbDp/08KvxfGAKX+vfBPgl49KVmr305Xgj3C7gltkdWrK6lFRCRUOh5iEhGR\ndlBAiIhIKAWEiIiEUkCIiEgoBYSIiIRSQIgAZvau/1lsZlce4nX/OGxbIqlO3VxFEpjZGcAPnHMX\n7McyGe7TcZPCXt/mnMs7FPWJdCTtQYgQfIj7yTuB0/x4/N/1g/7dZWbv+TH3v+HnP8PM3jKzaQRX\n52Jm//QD2C1sGsTOzO4Ecv36Hkvclr8C9i4zW2DB/RUuT1j36/bpfQwe81ezi3SojH3PIpJWbiFh\nD8J/0Nc4504ws2zgHTN7yc87DhjlnFvun3/NObfZD+/xnpn93Tl3i5nd4IKBA1u6hOBK39FAb7/M\nm/61scCxwBrgHYIxm94+9L+uSOu0ByHStnMIxruZRzDEeS+CcY4AZieEA8CNZjYfmEkwWNow2nYq\n8LgLRp5dD7wBnJCw7grnXCNzlII7AAAA50lEQVTB0CbFh+S3EdkP2oMQaZsB33bO7THYmT9Xsb3F\n838huEnPDjN7nWDcpANVlzDdgP6vSgS0ByGyp60Et1Vt8iLwTT/cOWZ2tB/FtKXuQJUPhxEEt4Bs\nsrtp+RbeAi735zkKCW5De8hHYBU5UPpWIrKnMqDBHyr6M8G9GYqBuf5EcSVwcchyLwD/ZmaLCEZT\nnZnw2lSgzMzmumAo7yZPE9ynYj7BaLk/dM6t8wEjEjl1cxURkVA6xCQiIqEUECIiEkoBISIioRQQ\nIiISSgEhIiKhFBAiIhJKASEiIqEUECIiEur/A4ghatlnQnTBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lrate 0.001\n",
      "iter 0 loss [392.1004]\n",
      "iter 1000 loss [320.15265]\n",
      "iter 2000 loss [316.37735]\n",
      "iter 3000 loss [315.56442]\n",
      "iter 4000 loss [311.12775]\n",
      "lrate 0.0001\n",
      "iter 0 loss [310.75754]\n",
      "iter 1000 loss [310.67578]\n",
      "iter 2000 loss [310.5462]\n",
      "lrate 1e-06\n",
      "iter 0 loss [310.6961]\n",
      "iter 1000 loss [310.6805]\n",
      "time taken 185.34911704063416\n"
     ]
    },
    {
     "data": {
      "image/png": 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zK/H/c7vS96Ud59zdzrmJzrlKYtvueefc3wBLgRv8bL3Xueu7uMHP73z/B/3V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\nIpKQAkJERBJSQIiISEIKCBERSeh/ANbaCzDI7ywrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "full rank reconstruction\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIOxACMIOhCDsQAjCDoQg7ECI/wBQ09STAtoKsQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean field reconstruction\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhB0IQdiBEP8BXPriRg77O4AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "samples from Laplace approximation around deepest minimum (EL2O)\n"
     ]
    },
    {
     "data": {
      "image/png": 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LnJ2dtZiCHnLGBZIP8+LiotVJXrMnfo/sqVKpyHHN/p76HKngqVQqMHepV8Hz\nbbVa8gCSAVEG9Xo9dMPgQ02Zaaag+3kCwT6amjXwOPw8lVfLVn8O8BQ3CjOoAG+zJTjvjHrBa63X\n6/Ie5ZBKpUI7SvH/5kMcJi/dxYzv837X63WrUQmfLT0Cu5ehNx3KTy9+gLfYUnd1Jz5zQ6FOVqvV\nwHBRwJMtNzU+59RFrbuUcaVSsRrE8Nkol8uhDYLC4HyyDg4ODl3EijJZMivA3120vwQAHnroITER\niEKhYHU01+Y/j8sdXI9m5k7E7+upDLodn+5nCwQniy53x1pN8HorlYqcu+laWbNmjTAgzSDJBsw2\nj81m02K3sVgs0JsXCLoXKCs9qcEcY61dRWRyvQ49D46gi4vukvHxcdy9exeAb2lls1mROeWr9S7M\nfWO6uvj5YrEY8PXy85Qvz4f3U8c+ehn0MwP+c02dolzWrVtn+a/j8bjVC1k/92bb1EQiIczVbIWq\n3QGmG0ifF9Fut12rQwcHB4dewKpMq9UOf9OHFYvFrKkJU1NT8r4ZWNCz14mwGVL87Xg8LpkE3Pn1\njsXPk31oVtzL0BM8KVv6uSnHcrkcmN8FeDs6mRB3d+3TI5uiJaCntTI4QfYfj8flPvH4fX19gUAX\n4Mu90+lYAYVeR7vdlnM2G2IvLCxY1kC5XBZmyr/aSjKDgZVKxdJn3rOhoSGRuQ66kGXxuDxWp9NZ\n9kTV1QT1dGZmRlg7dVA/92ZQrN1uW9lGepKy6Y/W89moizr+c/v2bQDBxt78Ta472mpbbkN0x2Qd\nHBwcuogVZbJ6Z9EpMfr/2WzWmqWeTqexbt06AH6WwObNm+VYJjOtVqvyW9zlufNrH6H+y12J36Pv\nKxaLWf6YXgR32MHBQWGuvBZee39/v5VOlclk7uunWlhYEH932Ogg3h/ew0QiYaXf6d2exyDjSiQS\nkfAZagwMDAgb4nXwGmKxmDApXvfGjRtFz6jDenzKtWvXAPi6G4vFrKwQfj6Xy4lctRVhRr6jNn6G\nujs0NCSy1dkZQNCi1J/husHUNv6/Xq+Lb5qZIbVaLeDfBhB4HsieCZ3CqGeBAcGc26/Dit4BLlwb\nN24U89NUjMXFRbnwXbt2AQC2bt0qF0fFZoBhaWlJLpbpYLqAgArLYFomk8HWrVsB+IGF4eFhUfLr\n168DCA6xM4Xfi6CSAXZASgea1q9fD8DfpDZu3Cifv3jxIgDg0qVLADw3DZWSx6jX61bKFx+EdDqN\njRs3AggWQvBe8x7z/8PDw5GZ86UXMp0SB/gLXqPRkAKXhx9+GADwyCOPYNu2bQB8XaSOTU9PyzPB\n71UqFbkfOi2Px+cizrzQ8fFsCN0WAAAgAElEQVRxkSHPg4vLyMhIJBZZPqt6pLw5r2xxcTEwvwvw\ndPeZZ54BAOzYsQOA/5yfPXs2MFQRCKZpceGlrPRzwEBcLpeT3zKLJJLJ5LLz5527wMHBwaGLWNFt\njrtAtVqVHYc7Ldliu92WssD9+/cD8FgB2dWpU6cAAKdPnwbgMVkGrriT6zHJNF/Jcvv7+4Uh8++t\nW7dw4cIFAMGke/5fT7vsVehgH5kiGRd39Hw+L+6WV155BQCwadMmHD16NPA9MtpWqyX3gqyq2WwK\nk6WMaV3s27cPu3fvBuCbdIcPHw6kzwF+sLPZbEZmTLgOkJjXQ7aTSqXESvq7v/s7AMDevXtlJPXJ\nkycBAMeOHQMA3Lx5U3SXxyCjBXz50orQrivKLZPJBCqmAASS9pdr0q4meI6FQkH+zevTjJbsk3q9\nf/9+/PSnPwXgP7f/+Z//CcDTYbPaM5fLiTuBaxEtu4MHD8rxP/nkEwDe2kJd188X4Ml2uUVKjsk6\nODg4dBErymR1cIm+O/qp6IgeHBwUNvT0008D8HaRL7/8EgDw0UcfAfB9L+vXrxdmwb+Dg4MYHR0F\nEEzFAjymcPDgQQC+H/PWrVvit9GJ+EAw7aOXwV21Xq8LezeT/5PJpPgKH330UQCeb+/cuXMAfCuB\nu/batWuFFVE+uniA/2YKzr59+/Dqq68CAK5cuQLA842RefAcqQeVSiUSJcuAf/21Wi3QNwBAoHfG\nnj17APhWUrvdxvvvvw8A+O1vfxv43po1awIBX36e+qYLFPiXx+d7c3Nz4i80a/VnZ2cDActeR7FY\nFOZIHdFWJN/bvn07AODFF18Uf+7vfvc7AL6My+WyyEE3hCJDprz5PLzwwgu4fPkyAOCrr74CEJQt\n7zHXkVartWzZroq7ICyHjULNZrNC4bds2QIAOHr0KA4dOgQAuHHjBgA/tzWdTlsL4+joqAiDiy2V\n84UXXhDB0ny7fv26mApUXpq0uiFKL4Py0xVtVFAucmNjY6KgjHj/+c9/xltvvQXArpwrl8vW5jM4\nOGi5eB555BEAwGuvvSYb19mzZ+UceB48BuWZy+Wsev5ehW5KonNa9XsTExOYnJwE4HfC+tOf/iQP\nPrNgKPt6vS7EgHqXSqWkWQzBTWxsbEwWFX7+6NGjors8H/4dHR2NRGYMF7JsNmvprgblQFfXI488\nIm7DN998E4AXrAW8wK4ZVI/FYqK7vD+vvfaaHIuETAeMTfehPhbv49chGhru4ODgEFGsCpNNJpNC\ntXXXHCBYj6xz2siQzOqhVqsluzVdEKVSSczQffv2AQCeeuopAJ6znK4GOrgvXLhgsQBdScK0mV6G\nTtUxuwlxR1+zZo0EvijHEydOBFgq4JtEi4uLVk7x/Py83B+mJtEyGB4elgAlZXvnzh2rrlz/3wwo\n9DoKhYLIzgyKjIyMWD1gL126FAi8AP79qNfrFivWaUM0d6nXe/bskdQ7WnTXr18XmVPnea+ioLdA\n0DXAczerPgE/KKitMV47n2nKZ9OmTcJMiaWlJZHp888/D8ALTAKe1XbmzJnA53W7RJ6j7guyXDei\nY7IODg4OXcSKMln6OXXdr5kOMz09LSkvTLjO5/N47LHHAPisgX6omZkZq8lxPB4XP+EvfvELAMAT\nTzwBwHNqk2V9+umnAII7KEEWkEqlItG7QCdNm52tdFcnWgdMuK7VavJdsind+Nj0d7daLQnWMHjG\nhPBOpyPMgoEvwK/C0QUePFZUAjOUSafTkWCgyVCbzabIlTKv1WrCwMg+dec5s2G6TlViTIKpjDt2\n7BBZ8lj6t8yqxUajEYl+srz2fD5vdefTvlCuH4yz1Ot10R/KhUVFU1NTluWUyWQk6P39738fgB/b\n+f3vfy+pi8TIyIgV+NJd6VwKl4ODg0MPYEWZLFkrYEfrNNu6evUqAOBvf/sbAGDnzp2yA9HnwgR6\nANI9h7vM3r178eyzzwKARHu5m/31r38VBqvHe3DnNHulttttK9rbi6APq91uiwVAedDXGtaHYd++\nfbh58yYASB09ZaVnLrGYY2JiQhgsZUyGcejQIbkvZBTpdNryDVPGqVQqMuNnNMMyfXGaLbJklte6\nd+9ei93q/qnmRISBgQHJrnnhhRcAAC+//DIAT5YnTpwAECx9NiPxtPa07HsZ9KfqHiIEZa2ziJhB\nsGXLFin+YMyFFtTQ0FBgzhzg+XKps7RcmfHx+eefy33RkyjMHgpk3eVyednZBavStDuXywVa8wG+\nqVqr1eSh1zX4Zo0y8zEXFxdx/vx5AL7CTkxMiKLyvT/+8Y8APGHSHNMmNpWR50MBTk9PR6L+m9c+\nNjYmymK23btz5448nMzjfPTRR2WBZn4gTdFEIiH3jPLcuXOn3AsG0bh53rhxQxYZQrdLNBu065ze\nXgflMD4+Lv82B0TevHlTgiebNm0C4KUK/fjHPwbgEwOmt01PTwuhYPOYwcFBvPTSSwB8dwzvz9zc\nnKQyHjlyBADEtQbAcmvpiqVehg6I36+6stPpiF4zbWt0dFTWA270xMDAgNXEvN1ui+uGROSdd94B\n4BEMHl/PDTNbKep0RBf4cnBwcOgBrErgK5lMBoYeAj6TzWazQuHJis6dOydVSUy5mJiYkGMysZhU\nfmJiQnYcBrnoemg2mxYz1cEX7k563E0UeheQtZZKpUDiPODvvhcvXpQAAZnswYMHxR3C1Bh+LxaL\nSZCHTFYHw7jj897dvHlTGLVO6NaBNP1eoVCITOBLJ7brwg+N2dlZfP755wB8y+Jf/uVfhD0999xz\nAPyAVqPRCBQOAB4D1u4dwGfRR44csfpMFItFq1iGOtzf3x+Jpt0ssIjFYoEAIxBM+6PL6u233wbg\n6RsD4lxbGMjSLFQP8NTPCeBbBHfv3rWe83a7bQ1p1e1XHZN1cHBw6AGsKJMN21XJhrT/kL4unVpE\nhz/r68ksJiYmJBhGJrZp0ybxddF/o3cp3WEL8HYs02+om05HoXcBZdVoNCw/nB6FcvjwYQB+onun\n0xHZU478v752MrOpqSkpDGHA4vjx4wCAjz/+WKwQPfZH+9uB4GjsqPST5TmHNcTWKVO8VvbYKJfL\nkk5IRkvLa3R0VKwIPb6a95IMjH7X//7v/5b7x2cpl8sF+s0CCAwXjIJ8dZqUWcbK84/FYnJ91LHb\nt2/jz3/+MwA/hkKLIJvNihXG2MEvf/lLkQ3XEQbRFhcXRT/5m9lsVu6FqbvfpBx8RRfZsBtuVgPp\nCZ46/5CvmZT++PHj0qZw586d8nmaAzQx9ENi5s/p3zcnipqf61Xoqae6YQngX5ueqfWXv/wFgBeE\noYlFZeQGtri4KPJmn4KnnnpKFgs+/Ox9cP78efkuEba58W+j0YjEIgCETxgwJyJns1lLt65cuSLZ\nL9RnLgQDAwNW+8eXXnpJZE2XwK9//WsAnmmrJ3wA3gJlBpH1e1HI8day1fPiAF9/tF7pWV9m/iqz\nZxYXFwNNpwAvuEiZchNkkF3rqSZ85rOkp44sV3edu8DBwcGhi1hRJqundOq8TiC4m/E9UvRCoRCo\nOAL8HNf5+XnpT/Dtb38bgLcL0gwgi+AxtcOau1Oj0bDmVoXNS4oCdMNy0z2Ty+UsB/758+eFGZgm\nWr1elzSYxx9/HADwk5/8RBgZ3QRM/VpYWLDyngH/HpumYL1ej4x8w1xLesQOP6P1DPBMd7IsWld0\nZaVSKXkmmOe5Zs0aOcYXX3wBwE/9mpqaErnqHE3TdA0zv3sZ2lViph3q3GrT6u3r6xM5m83fZ2Zm\nRM/+8R//EYDnpvn9738PAOJ+ZFCxXC5bAUcN3mM9d225AfHevwMODg4OEcaKMlldj2z6OML8nkw3\nqlQqsjubu1kul8M//MM/APC7FR05cgQff/xx4FgM9CQSCfHV6GCX6dDWk16j4DfUCd2UrTkeRacf\n6WGIDNaY6XSALw+mzG3evFl8sSzq4DHHxsaswXOtVuu+PTnj8XgkCj0A2/8KwEo3isViop86eV2/\nDwQZMNOXWJnY398vTJfpRfQzDg8PB+IUJvibOkgTBSZLJBIJy6IM69KmqzH5Pq0EWl71el0CjgcO\nHADgpWmRwerqU8CzDExWXCqVrN/XPYSdT9bBwcGhB7CiNII7he6+RMaodwx+Tiet899mLfG2bduk\nhJG72EcffSRRQ9MfWK/XhRlof8/92FYymYzEMDqdlqazCfgaP2MmeWsfNY+hWQR9f8zcSKfTMo6d\njFZnC+jULcBjYTodTp9Xq9WKTM9TIplMinyou/q6dDctwizZ1mmL/DyLQ+bm5mQMCsubzTHZ+lg6\nTcuMJwCIhO5qpm92DdOxG64RWh6mrhO5XE6sA5Ysv//++6Kz/DzTEZeWlgI9rYGgT5v3iefwTQas\nroqt1ul07itMvg8EFzwzUEaFGhsbk+bRVMqFhYVAA28eA/CU2AxqJZNJ63x0c4momLSE+dCZgRqN\nZrMpCsQFT+cnM12LytjpdORzWuF4fJqzevSNlrM+j3w+H4lqOiAYCDU3L71JmW6vdDptkQZtEtOk\nZRVYvV6XRZZBSrq6qtWqlSKmA0JEmOuol6HdLmYwMUy2Wq9N94JeR9hjg59ZXFyU3G66BLRrzcyJ\nBXBf3U2lUsteF5y7wMHBwaGLWFGKFuYaeFBwRu8iZBJkBdzVdu7cKbsSO+vMzMzI+3QN6BZ/PA8d\n7DKPq829KNTX6z4FZlK6nnYatvuawRqi0+mI3GlyLS4uSsUN0+jopunr67PGdfA4YedaLpcjk8JF\n/UkkEpb5T7TbbSvIVS6XrSIMXTjC9ENaCqdOnbKqFMlodTUkA2ZhVmFYL45ehk41NBmsdhHoFpl8\nL6yYCfDWCVYwsrvWtWvXRGd1YJbQzb0B736ZTet1sHy5uuuYrIODg0MXsaJMVvu1zKRjvSuYNdjN\nZlNeIxvgzr99+3b5Lp3aQ0NDUoRgNqluNptyXLKNeDweqAUHfBZRq9Ui4ZM1x38DwZExQNCvpVku\nXzMLFZrNplgH3MFv375t1XGzDDTM56vZAKHZlT7fXoZmo2bqjmY5YSWuDD5R58nW1q9fL2mK1Ltr\n165Z7Iz3Sje11myV7/O8tJ87Cj5ZbbmaqZRap0xLOBaLWT5Tfmbr1q0Sj2Ej74WFBasvil4LdM8H\nfSzADsYnk8llp8et6OqhHf9m8ERXgxFhbgUuBKz1jsVi0p+AD7tuwEuB8fd07puZq6vPkeh0OpFY\nZAm9aBIPatOnr92cINxoNKSBiW6cYz4IXCDu3btn9S4Im0ir3RdRgV74zE1DZ82Y1w9AGpWwukgH\nFnkfqK+lUslq0RdGRPT5mC0teV90tkMvI8zsNnuJ6M9ocmTqot7wSLBYyQX4umq6BxcXFwNTGIBg\nQDwsk2S5DdGdu8DBwcGhi1iV3gU6bcjMY9XshrtHJpMRJsWdijv/zMyMtDjU7eVY0WGmhGhWqhmV\nmd+onexRYFxmUAWwg3jazA1rO2gyokqlIu8zPW7Lli0iWzOwls/nLUahO22ZpnRY+lGvgvqhJy2H\ndXMzWXoymRRGZeZ0xmIxSZHjszEzMyO6bbKnsOem0+ncl1lXq9VINO3WvQvCOonxM6aOa3PerAit\n1WqS+qarHMk++Zu0gvXoG93Zy3QJ6P8vN8fbMVkHBweHLmJVnI1hzviwvqPawW36ZJmK8dlnn8mI\nGe4y165dk/4EZqVGp9OxxrN0Op37+sHi8XgkZtdrSyCsyg0IsnjNzO7XsHx8fFwCX5999hkAT7bs\nCmUytFqtZgVhdHCCCAt09DpMmQJ2nEAHFk22q7/Lv+vWrcO7774bOP7x48fleGaqoX4tLEXOjB1E\nKZYAeGzeTOHSMjB1C7DjKlxHBgcHZV1g343jx49LcNz0VeseE2GWn9kV7JtYYNHQcAcHB4eIYkW3\nOr1Lmd2a5ISSSYsF6PG7Jns4efKkxYYeNCxRD0bU7O9+5xPml+lFhO2spn9Zy4TpLYlEwioW4C5f\nKpWEyZ48eRIAcOzYMev4vBfZbFbSlfibup+B2a9CH6PXoX2DvA5TbtpC04zTvA/E+fPnpceGTp97\nEBvWvlj+NX3eYZ/vZejRSYQZ6QdsCzgej1vMl0zzxIkTuHjxIgBfjjMzM+KTpRWmn42wDAJzEgWh\nS/2/DqtW8WU2iNYKpdsM8q9J08OURy8c/LxpemUyGSuNqVwu3zeVTN/IqMCUDa+pUqlY7hNt4prB\nR6YeAX5ruHw+H9rOEAif0aTr0ZkapvN3w1KeehE619is+NItBs3m0QBCm8bw+9RLbk75fN4ygXW9\nPAmCGegBwhvNR2GR1cRGp8NpdDody5zXz6b5jGazWZEtXYeZTMZaLPUibaZ26oVU5+zzt5dLvnqf\nojk4ODhEGLGosTQHBweHKMExWQcHB4cuwi2yDg4ODl2EW2QdHBwcugi3yDo4ODh0EW6RdXBwcOgi\n3CLr4ODg0EW4RdbBwcGhi3CLrIODg0MX4RZZBwcHhy5iRXsXTE5OdoBgnTFrg9lgd35+XmqOOWJG\nT/zkZNTh4WEAXs0xa4jZ9CGfz8uoDx6fjSHi8bgcgxM/w9r9sQZdN5Y+f/788jpCrAK2bdvWAbzz\nZt0350exHvzmzZuYmZkB4Ld/m5mZkbps9nnQk1BZx826+Hq9Lk1jeA90L4KrV68CADZu3AjAq8k3\nZ09t2rQJgFdTzvE2n3zySc/KFgB27drVAYI17mb/gFgsJvqjG0zzc3yPeh2Px0V21N1cLmeNTaG+\nZrNZTE1NAQjqv1nnzzFM1WpV7u3p06d7Vr5cFwD/uWMrU64LlAHg63M+n5e1whxnlc1mrbE9fX19\nsi5QRux3ks1m5Tf1+Bkel88G9bVYLMpzcuLEiQfKdlW6cCUSCbkQjpfmxdTrdavJhu5kFCZUs9dj\nuVy2mnLozk9hXbv4XSolm5m0Wq1IDKPjyO6ZmRlRzHPnzgHwFSqZTMp1UR59fX3y4FIGunM/5cz3\nisWiyJaLge6eNDo6CsBfIKrVqrzG43KRHh0dFcXudehBfbxec0Gt1+uBxjtAcEinOW8ul8vJe5TR\nzMyM6D/ly02qWCyKXHn8SqUSkLX+m8lk5H73MnRDHDZz0dMSzM8R+jmnrKj7iURCjsVNbW5uTuTB\nhjw8ZrVaFVKiCZfZBIiyLRQKy+7Xu6KLLNlku92WE6RQuBDcuHFDLjas4xY7Q/FYMzMz8hoXjkaj\nIbs7j6+VzZxgWyqVrG47fBBqtVokhtFxZEmr1RJFINvhNS0sLMhiTOXN5XLyGhc/soZ0Oi0PvB45\nQzZgbkiFQgFzc3MAEHhYeC94jrzX09PTgU5fvQw9UI8LIuVF3SmXywGGCQQHSVJOeioq9ZibTSwW\nkwWAG5v+az4T9XpdZG12l6vVapFo06m7uFF+1COi2WwKc+T1lUoleU75nFOf9PgZTSgoW94DzXzJ\navX4Hr7Pz+uOdstdZHv/Djg4ODhEGCvKZMmGNDM0afvk5KQwHqKvr092NnNQnza59K6kfaqAv1uW\nSiXZ7cj4RkdHrV6VURs/w+vVg/7MpsJ79uyRJtFkBfrf5jj0wcFBYQr0sWrznvLmPSwWi8JSw2bX\n68bXgHdfoyBbIMhkTTcJ2ejWrVvF9ULWms/n5fPUe15/o9Gwrl+7rviXcgsb4pjJZISx6cbfgMfm\nTH9tL4JMvN1uyzVrsxwA1q9fL2sA5agtJ20lm6CM0+m05RakHEulksiKllwul7PcjqZ/fTlwTNbB\nwcGhi1hRJstdodFoBAaeAf7OtbCwYDmZW62W7CRkCDrAYDKwVCoVOk4Z8NgBdyoyik6nY3XoJ2NL\nJBKRCB5oP3NYYA/w/N18j9dULBbFx0qGz2PdvHkT4+PjACBZCYlEQpivGaQoFArW6BQGHQCfbXAM\n89DQUCRGVgPBkTxmoFUPoKRszBH2wIOnFNAfSN0H7AGJyWRS9FJn6JgsS+t3FIK21LvFxUUrnqAD\n3dRZ6men0xGmS93isRYWFkS3tHz4Gr+nn3v62LW8KWc+N2ZwcTlwTNbBwcGhi1iVmcHZbFbYj8k4\nE4mE7Db8G4/H8dBDDwHwU5W4YyWTSRnzS0ZWrVZl9yLb0syXfkN+plqtWtkF3OHy+bywjF6GznEl\nizLzOJPJpDCyy5cvA/AYArM5eC+4y+/Zs0f+TRlfv35dGEXYeGTztXv37gkLMPN2S6VSJDI3AJ9p\nDg8PW35+bS2R4Wh/La+bfzWon/Tl1mo1i9Vq/58ZO0in04F/67+5XC4SM754vdpi5GuMNeg0Tn6u\nr68P27ZtA+DnrzI+cPfuXZGpXkfMGWk8pl4X+Nvtdlt+y8zDHRkZWba/e0UXWT6AmUxGhEEh8iLm\n5+flNabK7Nu3D88//zwA34ygyXnjxg25cAq10+mIQp8/fx6AL7jNmzeLSceFY2lpSYRvBo2q1aoI\nv5ehc1xpOpmLbSKREFOLm9QjjzyCAwcOAAA2bNgAAOIiyOfzuHbtGgDg008/ld/hd2mW0szK5/Mi\nR254w8PDslDzfBjY1Btqr4MPsXZPmdNh9WZNHdu5cycefvhhAL5O3b59G4Cnu1w0+TzEYjGRlzl4\nMcytNTg4KLLmJqmHgC53oupqYmRkRP5tXjN1ZmFhQTY3rgHPP/88Hn30UQD+enD06FEAnquLz7wO\njPO+mLnOsVhM9Joy0wTLvE96s/06OHeBg4ODQxexKu6CarVqMVldtsmdePPmzQCA73//+7Jjffnl\nlwCAd999F4BX1cTdiUGBsbExYaRkdTz+M888I0yBu97hw4fl3DSjIHRJX69CB0zIbExWkEqlsGXL\nFgCeHADgZz/7GXbu3AnAd+6T4V+6dElYPHfygYEBa8cnK0ilUpKmx3syMDAgJhfTx8iUAT+g1uvQ\nJjutAXP8uU7+pxn7gx/8QFxdZ86cAQCcPn0agHefaNpTztoE5f0jYx4aGpL7Rytvenpa3jdLUSuV\nSiTcBbpyju4TPre8lunpadHB3bt3AwBefPFFcR/S/cX1oVwuy3u6XFbfKyCYameOBOdzBMCqQi2X\ny8t2Fzgm6+Dg4NBFrAqTrdVqgYYtQDD5mCxo3759AICHH35Y2Oa///u/AwD++te/AvB8izqxnsek\nf4rMdGxsDIAXOCMbYDOTVqsln+P5kAHkcjnZXXsZugZbNwgBfEa0YcMG/PjHPwbgM9nNmzcLC6CM\nP/roIwCej5vHMP19gM9kKatsNivs4ZFHHgHgJejTr0sGSD/XjRs3LLbdqyCTWVxcFDZk1s2nUilh\n6fRzP/bYY6Jnf/rTnwD4TFY3OCHCCg54D7Zv345XXnkFgG8pfPDBB2IhmInynU4nMsUegBcE1L0H\nAP/aU6lUII4AALt27cJXX30FAHjnnXcA+FbYunXr5Lu6/wZfo+4ydrNt2zaxBmlxLC0tWYFZfi+R\nSCy7IGFFF1ntIqBCmBFawO/SdPDgQXnt888/BwAcOnQIgL8Ybtq0KaBUfI/KxcWcgbMnnnhCBEU3\nQKVSkc+ZJkCj0ZD3ehlcuGq1msiBix/l+corr+AXv/gFAP8B/s1vfoMPPvgAgO8+uXTpEgAvx5VB\nCZqnGpQVq8Hq9bq4Hl5++WUAnhnM8+HxtfkWdtxeBIN1OheY5iRdUclkEtu3bwfgLwQzMzP41a9+\nBcAnBrqfhq6TB7yAitkbgSbtG2+8IZvj9evXAXgLE++l7okAeAuBGSjrRei8Y/NZ5rOaTCYl+PjY\nY48B8K6X68Hx48cBBLOIzFztQqEQyCYAgBdeeAEA8PjjjwvZuHv3LgCvf4LZu0DnJy83IO7cBQ4O\nDg5dxIoyWb3T8t/cUbj7xuPxQD9HwGOa3JF37doFIFiPbKZZzM/Pixnw5JNPAvDN45GRETHXmPah\ne3JyJ6VpUiwWLad3L0LnDROUAZnmwYMHhZmSAbz77rv45JNPAPhBKF3BRbncuHEDgGca0yRjwGvr\n1q0AvHQlMjgyunK5LCyQZjVNXbKxKEB30KKOUL6Ug3aX7NixAwBw7NgxYUjUazKyTCYjcqXuZjIZ\nK1ebVthzzz0n95kuiKmpKbEMaN3pXOUouAt0jrwZfOK6oNMyqT+zs7MiP1qbZJd9fX1Wi8mbN2+K\nbJ5++mkAvkuyv79fPk+LO5lMWusCv99sNpftLnBM1sHBwaGLWFEmq30Yukk34O/CpVJJdnXdTJop\nXEwROnnyJABvdyLzIlOo1+uS/vW9730PgOeLBbxUD36XSeF9fX0WW+U56F4HUUAmk7F6lPL/ZFAA\nJBgFeJ3PAJ+ZkdEODg4K26c86vW63DPKTCeHP/vss4HPHz9+XFgXz0f7MKPAtAC7Fyzg+1H19dBS\noD43Gg1hn2S5urm82Tu5UqmITBg8+9GPfgQA2LJli/i1v/jiCwDB+n0z0Nlut79Rt6jVAp/bsEkR\nlHu1WrXWjEqlIq9peQPes21WiDWbTbEwGEAkkz1z5owci/dCB9TN4Hez2Vx2oYdjsg4ODg5dxIoy\nWY6a0R33zWh+MpmUz3HXXrNmjSR079+/H4C/Wz/22GPSU1J3SadvkN+j3+fUqVP4+OOPAfgRY53a\nwfMy5171Onj+lUrFKhHWc4rIKnl9P/zhDyWaSrkQmUxGvks2n0ql5LiULdnrgQMHhMkxG+Stt97C\nhQsXAMDKehgeHo4E0wL8SL9msiYLD/Nhj4+P46WXXgLg6xuzEnSmgp7jRcvju9/9LgDf0rhx4wZ+\n97vfAfD0GPD85zyGZoSAd//JcnsZZl8ADd1djr7SixcvAvBSEplpwGPQ8komk2Ix0ILes2ePWMRk\nsGSjd+/elWdDZ2fwvphTEJY7FQFY4UWWC5auCTZ7BbRaLTEraRIlk0m8/vrrAPyAyp49ewB4pjAD\nCxTI1NSUvM+HggvIF198IXlwOl2ECsobzXMtFouBB6tXwQd4cnJSNh0utsyj/OCDDyRwyBaTIyMj\nIivmeHKhvHHjhpi6VHkjqagAACAASURBVLy5uTlxDzA1bO/evQC8RZlBtP/6r/8C4G2U2pwG/A1y\ncXExEosA4J9zf3+/yFfPpgI8/eOGwgd7dHQUjz/+OAB7JlgymZRj0UUzOzsrvQ64iXET/Oyzz6SH\nBBfq/v7+wLMDBOexRaFNJ12AIyMjVgN+PReN5IuyKpVKsoFRZlyIBwcHA/nb/MscecqKa8ytW7fE\nPWk2l9KfJ2q1mjwHXwfnLnBwcHDoIlaUyeoGzmagiTuYnlhJ6j81NSWuA5pOTBsaGBiwqkT6+voC\no3sB4MMPPwQA/O1vfxPTzzSvAH/n5PlkMplI1H9zV11cXLTGvHDn/8Mf/iBmJoMwk5OTgVEmgB8o\ne/LJJyVQQMujXC4LO2LSPOX31VdfiSlH9lytVi23Be/T0NBQJGQL+LKpVqvW8EfKu1KpSO08Ge22\nbdtEP82hofl8PjBahr9jBsg4dfitt94SVsugTKvVEkuLx9K9FaIQWNQj0ql7ZiVgOp2Wa3nvvffk\ntaeeegqAN56Gr/FY5rOsx9nT+qAVfPr0aVlvqJ/NZlN02xx7lU6nl10J6pisg4ODQxexokw2zMFt\njvBot9uyW5CJzc7Oit+GTIzMbePGjdKXgAzr+eefF/ZEnxcT6Kempiz/qx61bP62bhbcy+Aun0gk\n5Pp4TWShFy9eFDkQsVhMdmkyIqYVbd26VQILPP7GjRuFNdCHS3Zw9epV/OEPfwDgy3toaCjQzYjn\nCHhsIipMltCDDs3m3e12W9gNrYczZ86Ib1w3mwY8RstjUSZ79+4V3eZ9O3bsGABP96nXmmGZo1DI\n0qIQSwCCAzZNv7JeF6gr1K333nsPJ06cAOAze11GrIuTAC9IznJvWgdHjhwB4D0bjOlQttraNgPg\niURi2Slcq9IgJhaLiQDMKQipVMqq+IrH41YNNj9z+/ZtacxNV8JPf/pTeZ8RQ1Z55XK50Gmuejqt\nRrVajcRCQFNU50aarQi1K4YPoDYpeZ3c0G7cuCEP+MTEBAAvG4GLK2XFQOLFixflvtJk1QEDXS3D\nv1GYpqqRyWSs+nddfWg+oKVSKXRhBDzdYq42Zf+jH/1IgpJ0kdHVVa1WLXNam8W83/q+R0G+Yc2v\neX26mk5POAC8bCVu4Obi3Gg0JJDFDezZZ58VWTFXnu6tRqMRWoWqexVo6EX/a69vWZ9ycHBwcPhf\nYUWZLHd3XS3B3SBsSid3p/7+fnmfuxJTNRYWFoS5sT/BxMREwFwDfJOh1WrJeZjObH0+mn1EIXhg\nsiQNPX6G4PVlMhlhwbwndLFcvXpV5MFa74mJCfkugzBkBR988IEEEhi86XQ6980p/Ca5hqsNnSZl\n9tugXLWFZgYR9ef5t1qtim7pHhtkZ0zXunLlCgDPwqArh/dZu1z4mk5/isK0Wr0W8Dk3O4tpt5ae\nx6erPAFf16vVqlhTTKF7+eWXRbYMTPIz2mLlMcKslv+Nq8sxWQcHB4cuYkWphA4qcWcw+0bqzkF6\nOCDBYACZbKPRkARjOrXj8bh0eKK/VvtheR5kGdq/wr+avS53YNpqQld5mUyLAZdOpyNyJtPS4374\nGtnB4OCgpMKxQmbXrl0SICDjZepLvV6X39LMmr40sxghkUhEis2aMLtedTody7cfVjHIe1WtViV9\niZbC2rVrpVqODJaW2tjYmNw/c2ot4D9Duujhfj7FXoL2JZv6qa0wk93q6cCUN3Wz1WqJHjPNa2xs\nTHonmyOadMzHTDnUx9evLVd3e3/1cHBwcIgwVpRGaLaqI8xAcFfgDqRn15tD5fR7LExg39Tp6Wnx\nDbIUTycYE3p4o+6orhEVnyxRr9cDvm/A34Xr9brIllkGOiKuS4kBL9XIHNx36dIlSTGitcCUGjJa\njWazKWyKf3VXJDP9qFehM1Eop7AUHuqU7vWgmTuAwAgUMll23CoWizh79iwAWH1otUWl08Z0ma7+\nHcC3+HoZuhjGfM71NZujqsI+p32m9F8zVlMqlSRWQyuM8YhGo2Glb7bbbWsclR5H05PjZ3TKix4V\ncz+YCyq/C/g3plAoSO09K2kWFhYkd9OsL+7v77dm/8Tjcaspr3ZjmHN+ehF6YaVLJawJj+kWSSaT\n1rRTpnBt2LBB6ueZ21mpVKwABD8/Pj4uyqtHDZnuCwYbkslkJEb7AMHgFvXHbDAdj8dDN2tdLcbP\n8VjcvEgQqtWqBBQJ3X+Ax6B+PqhdZDKZjETvAuqWfs7NxVMHFanPulmRGbSq1WrSz4C9NbQrkmuF\nJiK65wPgLaimu0cvti7w5eDg4NADWJUuXLqyI4zJhqVR6eos/V6z2RS2xV1qampKTFeabdq9YHZD\nAmDVf2tTMAoJ3WHXZCZvZ7PZwGgNILxTE5Phs9lsoFsXv0eTi4EZstFisSjH1Yndpgmo72sUqumA\noJvJTIvSqYBhaV38N+VE3Wo2m1JAw5S3jz76SORqutTS6bTVkpOvAz671a6xKAS+qLthuqC74plB\nMX1tekwNj0md3bZtGwCvgTx7avA50OuQWfGl152wApTl6q5jsg4ODg5dxKr4ZJvNplVfH7YraEe+\nydTIWrds2WKN32i327IrmSkapVLJ6qKkGQiPb/rdeh2Up5ajKat6vW6VYLbbbfGj6lJbwOuORFnx\n79LSkpSCkjXQr1ipVALNp3k+uok0EEw3iwqT1ZaNKUN9PdRT7Q+/n9WWzWZlTBKZ1blz5ySeYOpu\nu90OHfFt6ii/12q1IqO/gKfDpiWpn0Mz1bDT6Vif12yeFhcDtBcuXLD61erngP0P+BldNMXf1Pd3\nubq7oossBaKrJUxFCjvxWCxmBXF0xYv52tzcnDWnR0+uNAMQOvgTltMZhWm1OvhhTtjUsjNzAHO5\nnLgLzBzhO3fuiOnKhbjT6ciiaubJareDDiqawTadbRC2aPQ6tO4BCBAGsylLPB63ouK8P319fSIz\nyqtcLgd6IWho85/3US/ipkkbhYCtRrvdtipBwzbrMJiLYbvdluwCzrObnZ213GUMwupMAn0/KVuz\narLRaCx7XXDuAgcHB4cuYkWZrHYih9UCm9ATUgmTbVUqFSvYMDo6ajFT7dQ2d0S9S5qsOCqz67nj\n66bSulkx4O3QZopRWCcsXTVDhsW0lkKhIGYYOxjx+/Pz83J8nY+rOyMBvluiVqtFph2fdnWYpqZ2\nJZjpba1WK9CGEghaaxs2bADgp8+Vy2WLKeu/Zme1sLxoHfyMijsGCHbCMvuKaLeHTq/ULUkB31oo\nlUoBFwzgBcS1xaB/R/+W7gBm5kJrC2K5QUXHZB0cHBy6iFUpHNdVRrojEeDtWGb1BmDXvev6evbb\nZFL8oUOHpPuW6RCv1WpWvwSNMHYSJegxHWZCtw7wkV2Wy2WRJRkp/79mzRphtaz5bjQakizPajoy\nhrm5udD+BIR5/G8SPOgVZLNZq5IurJ5ds8v7TTo9cOAALl26BMC3FG7cuBEo5AB85q+rt8J6Q5jM\nKiqy5Xnryk6C/w/r5qYDe6a/f926daKf77//PgBvfWAQzPRX6/TDBxVA6PjGcnuaOCbr4ODg0EXE\nVjJZeXJy0vqxsNI0M71Lf8ZkoXrn02lMZvqSru/WKTc8vsmsNQPme+fPn+9ZehsmWzOCmkwmrVSv\neDweWoABBH2A9PMWi0XLB6i7I5lR2LCEce2b5WsXL17sWdkCwI4dOzpAUB9Mtq7lp1OJdI9TAIHB\nimZxDSd5AHbKV1gxQlgpqtZrvnb58uWele/27dvvuy6Y6X/6PQ2zEKNWq1lWhbY4zOGhel3QMQOT\nPfP42id74cKFB8p2VVod6vk4Dxo9EebI5/d0AIeKZgpJf1enjJkNNRqNRsBk4Wv6e1GBzj01U9V0\nOpVWMrPtpD4Wj8HATDabvW9jjLANWzcD0gptvtfr0BuJuZjptoNmE2kA1kbFz1erVVmAda6yThMC\nwnU3rD0gdVff9yi4vXTg2nTX8a9ubqS/Z64feggAZcVeHnpd4L91DrmZU5xIJKzGMHpTW24OsnMX\nODg4OHQRK+oucHBwcPj/GxyTdXBwcOgi3CLr4ODg0EW4RdbBwcGhi3CLrIODg0MX4RZZBwcHhy7C\nLbIODg4OXYRbZB0cHBy6CLfIOjg4OHQRbpF1cHBw6CJWtHeBbmJitsQzZ54DfiONZrMpdcKsQ9Zj\nS1hPzDrwQqEgTVFYz802cfF4HIuLiwD82VT1et2qb9atADnG4sSJEz1bCL5nz54OEJSV2Vpwfn5e\nXhseHpbvmo3NORIlm81ass1kMnKPWIuv+w9QzpR7Op2Wz7MOncdvNpvyuV6WLQDs2rWrAwR7BZhy\nLhaLUgvPsUe6QQzlwPd0nwnd34H6uX79egB+C89WqyXvrV27Vs6Nustnive2WCxiYGAAAHDkyJGe\nlS/XBd27gLrIa5mdnZXr47qge1+YM/lyuVxgOjYQ1F1z7FEsFhM5hx3f7D9RqVRkkvOxY8d6r0FM\nNpuVxgt6UQWC3W10L0l+zhyoqIfXrVmzRo7J7/Kh1w079EMOeMLk+GB+nueXyWQi0SSGStbX1yf/\n1oMl+decN5XP562eu/ovP8eFoVwuixKa849isZgs6Nys9CQBvmZ2TIoCdFMYLmrUKT5siUQi9FrN\nuXG64Qvfo3yLxaIcjwuqboJCPWWznUqlInrP+8jnIZ1OR2IkOBGLxayGQXp9oJ7p6SjmNes5czyW\nlq05K1CTCOq1Jlh6iKU+5jeZ6LGii6zePXjhZivCubk5eU+PgQgbrGYel0pZrVZF+HzoqZytVsti\nzzMzM7K46sWKICvuZegRL9z9KQ89moOKxAe3XC5b8qD8q9WqNYgyHo9bGx0XhXa7bTFf3S7OHFRX\nqVQi04WLaDQa2LJlCwBI83Ktp5SFvi7dGQoItu/TU4AJk92GDRPkPahWq4GRKECwYfj9Oqb1Eni+\n1WpVdNccJrm0tCS6qBc8c7AkZVWv1wMjmfg7piWsrQo+L3rh5vHNRVUPWfw6OJ+sg4ODQxexokxW\nm68mbeeuvXnzZtnVtQ+GZoP5PcBnWdz1EomE7OA8LvuhtlotMSn4GuDvVOawuzATphexsLAAwLs+\nyoE9SumX27BhA+7duwcgKFvKQZv4gCcDc9RKMpm0+vGSdehem/qeaGas/8ZiscB3ehna7WT2baVO\nrl+/HlNTUwB8SyibzQb6+QJB5kuQWWl3mTZ9+XneIz1yRg+tBHyWG4vFIuHq4mDORCIhMjWf6fXr\n11vDDwcGBkTvzfHcyWTSckvFYjG5L2ZMaGlpSRgsn5tMJmO5C/jbpVJp2euCY7IODg4OXcSKMlnu\nHsVi0WKmerqBOfa4VCrJ57mzcUdJpVKy22ifnzlgTfsFzbE2mUxGdj1z5Hg8HrdGUPQiyFZnZmaE\nmdI/yGvTQxN5fXpkN3d5sqX5+XkrUBaPx2UH135rfo9Mmd8bHh62RmJrRhsF2QK+7256eloYlTli\np1arCfvUPm/K3Iwn6OtnZLvdblvH4Gf6+vosv2EulxOWbTLaRCIRicAX4wTz8/NWTET7X7UvnzD9\n0Drjhe/RD6t1l88Lv6ezjh408ob3vlqtikXzdXBM1sHBwaGLWFEaoVNLyJa4y3BXaLfbVgqXjopv\n3rwZALB9+3YAwKZNmySFRTM2DqS7desWAN/v02g0ZIfjTlWpVCSqSbbB88rn85GI0PIcKSfAZ6t8\nLZlMyo7M10ZHR7Ft2zYAfgocxybfunUr4MsGPLZKnznlrf1hZipcp9ORe2tmJYyMjEQicwPwr6e/\nv99i35qhkonxtY0bN4pcyYZv374tx9R6RlC+zM/W1hhZFu+LZnj8S3nrQZi9DOqA9l+TjfNa9Lw5\nXlO73Rbd3bNnDwA/971Wq2F6ehqAN2adx9RxGCCYRkh2y3vCcwL8Z4lr0uDg4LJ9siu6yJLKFwoF\nUSRemF7IzImnw8PDePLJJwEATz31FAD/wS6Xy3IsHeyicPgaH/6ZmRl5jco7NDQkCwZvLs+r2Wxa\nZnEvgg9pMpkMuDoAXzGKxaK8tmnTJgDAK6+8gscffxyAr4ynTp0CAExNTYlCU/EGBgZEllRY/l42\nm5XFm/euv79fghN8SHTanpkU3qugvukcbxIF6kyj0ZBFgfJ97rnnsHXrVgCwNv5isWjla6ZSKVko\nKF/eM13YwIVpbGwsMBBUnw/vU6+D1wv4uqGfP8BLR9TuPQDYuXMnvvWtbwHwydfly5cBAFeuXJEU\nOwYj4/G4bFyULXVSu3p4DwuFgrgQzEnLyWQyQGgeBOcucHBwcOgiViXqUCwWhU2SIXHX5c4C+Obo\nk08+iTfeeAOAv4t98MEHAIAvvvhC2NadO3cAeFSeuwyPR5aWzWZl56fLoVaryY5FdqKrzfheL4PX\nmcvlZJcmA6fMdDrPhg0bAHhMa926dQCAr776CgBw7tw5AN69GR8fD/xOLBYTNkUWyp1/7dq1YhKT\nfdFNA8Ays2u1WiTS4wBfdrFYzHKXkAHFYjFhSgcOHAAAfO973xNXw/nz5wH4MimVSlawMZPJBFgt\nELTyyPRYEMHSW31cXYkXBVcXWXkymRTZmsHYer1uub+eeeYZvPjiiwB8Bvv2228DAM6ePSt6TRmk\nUikrqKXLbMmodSmvmX4X5hr6Ojgm6+Dg4NBFrCiT1akupi8uLPmffq0XXngBY2NjAIC//OUvAIA3\n33wTgLfbMLBABrCwsGAljOuyRTrJyWTPnj0ru6nJrNLpdCTYFtm8rn0nEyITr9frwkwnJycBAA89\n9BCuXLkCwLcO6MPasGFDIPka8HZys+yTDGDbtm0iWx7z9u3bgfsO+HqgffO9Dsrh3r17geYvgC/f\nRqMhOvvMM88A8HyFn332GQDIX8q3v79fGHJYWhvfo7xarRZ27doFANi7dy8A734wed5kgZVKJdCz\no1fB6y2XyyJb3YgF8K6JcnjooYcAePEZ3pf33nsPgC/jgYEBS366zNgsoNm+fbtYH3xPB8mo67QS\n+vr6JF3xa69vWZ/6PwIvKJFIWJVE+kGk05uKtG/fPjGFuBAwQrtu3TpRbAZY8vm85S6gCTAyMiKf\n50KcyWQCTU40lpaWlp0Pt5rQ7gIziEcZ5/N5cctQtolEAsePHwcAnDlzBkDQ3DQ7PGUyGatqhkHJ\nJ598UuTMBz4ej8tiH9a1KwqyBYKdrnQwhq8B3mbDzWvHjh0AvLxaEoLTp08DCFYN8YGmyyGdTovL\ngb+jg4hcZLkgzM/Py7mZWTmFQiES2QU8f92Mic8yZavXhcceewyAt9gySHvkyBEAwY2f5IubUCqV\nEjlTx5md8NJLL2FiYgKAH/jVempWlC0tLQU62T0Izl3g4ODg0EWsKJPlrprNZmX3Mhkn3wd8d0Ei\nkcCFCxcA+MEt3SKOqRo0+RcWFsQkM3tQ7tixQ3px0hyYm5uz+lhy10wkEpGor6fMdM22mXrWbDZl\ndydbqlarVqAsrAMZj9loNITB0TVABqDdC/xMp9MRk8/sw9putyNhzgK+66VQKFjtH3UHKKZrMejy\n2Wefie6a5ivg6zFltGbNGrkfzHvlPdu9ezeef/75wG/funVL8pp1pRcQ7D3RyyBL1P1kee2azdPq\nYdA2kUjIekD50VWWzWbFnKeMFxcX5TW6zfbt2wfAWxd4fxgk113idAojoSvPHgTHZB0cHBy6iBVl\nsmRPrVYr0PNS/221WuIv0VUwZs9M4ubNm5bvqtlsSjCGTnIGuXbs2CE7Pn1kujGwWasfBSYABFkV\n2bhZ1NFoNISZ6sbT3P3J8MkmKpWKlQA+OzsbCEjqv4BvadCn1ul05Ny48+v7FYUuUYCvu7r3BWWp\nLTSC8i2Xy6LHpi+70WgEKskALw2LzIu+x1deeQUAcPDgQfEh0m84NzcnVoNZZKM7+/cytBVmMnvq\nbq1WsxqiV6tVq+k/n9/r16/Lv3XPXloar776KgDg5ZdfBuDdC6bYXbt2DYB3X/ls8JnSjf6XC8dk\nHRwcHLqIFWWy9IdoBmNmF+iO49o3Qkb62muvAfBThGq1mhyLPpt169aJT4w7F/04t27dkp2KZY56\nhA0Zm06cj0KnKN2T0+yVqTuXcUc+duwYAC/FaPfu3YHP8b1SqRRgZIDH6OjHIoNlRP3s2bM4evQo\nAM/CAIKTKMhA+LdSqVg9U3sV9JO2221hrubkAt0PlX7SzZs34+mnnwbgW1WXLl0C4LEnHpf6t3Xr\nVjned7/7XQDAP/3TPwHw9PrLL78EAMkIOX36tDBZMj3d7Wy5pZ+rCd1hz7RsiWQyKesCCw8efvhh\nyeJ4/fXXAfiFNJppUh7r16/Hzp07Afi6S9/se++9JzJlz4NUKmV1/yMajcayy+1XdPXQTUbMdoZE\nsViUh5Dm/O7du0VRf/7znwMIzuxiioZulEHTl8rLBfvatWs4efIkgPBgG89Lp45Eob5ezzjiv812\nj/V6XTY6mkaHDh0S04mL5XPPPSffZ6qcbgrOz9GUoul66tQpqRrjPdEVR2YlU71et1JjehXUlcHB\nQbkO8+/MzIzIlS6V8fFx/PCHPwTgb1Tc6Obn52Ux1rpIlwDT7Cijq1ev4m9/+xsAyN9r164FGh0B\nvptNj/7pZeiGOLqyDgiOMeKGxGf55s2beOKJJwD4i6WeXWc2g2k0GrLRUQcpx0OHDoke62pUnocZ\ntK3X6653gYODg0MvYEW3OZ0IzB3WTJYeGRmR3YymZ6PREObKdBZ+ZmBgIJBWAQTZMI/PlK4PP/ww\n0JUHCLovzG47sVgsEr0LKAOdwmUmp8fjcdnpv/jiCwAe46T7hKYUmfvQ0JDs1mSt/f39IluyWzKA\nDz/8UJgc0Ww2rXE1PJ9cLheZwJe2dHgdDFaRbVUqFak4YhPu/fv3SwEBrSveq61bt0pRAe9Vf3+/\n1deDrrFjx47hk08+AeC7L3RgjfpM3e3r64tE4ItJ/fF43LK+9ABVXgtlkEgkZF1gRai2jHTfA4Jy\nZoD2448/BuCtNbS+NHs1q+8o22w2u+w2nY7JOjg4OHQRK8pkdfoDdyzuPNy94/G4FVg4ffq0BHbM\nBO1cLmf10xwZGZGdjcEwsoF79+5ZLFcnQZvpYLqMspcRlrZDFsodVzdEp7zPnTsnsqFs6d9au3at\nyJmBw4MHD0pQkfeEAYNTp04JgyM0s9D9KQDvXpN99Tp0b14z0Kp9s5QJ/165csVKPWLv06GhIemm\nRdY1ODgoxR38Hq2DN998ExcvXgQQHI/Ee2mm7AG2pdiL0FYjn2Wyc80WtcUAAIcPH5ZScFoVTLXL\nZrMib35P6y6DZ7TiZmZmrGKRTCYjsjTL7vWa8XVYlYqvdDotSqJn+PA93YQBCHbjNyswYrGYNEGm\n0v/whz8UAdMsoFD1Q61NAXOypc7bjYKiErFYTK6RD5/OnKC89XXquUUaN27cEFcJo7H79++XzzHI\ndfjwYQDeBmZmNACwmojr6rHlzq5fbZiNugE7Z1ITBGJ2dlbkH9Z2k68xC+aXv/yl3BtmaLD5iXbF\nhPUBMYNFnU4nEgRBu5P0NBTA1510Om1N9ajVavI53eaU7/E1BiF/8IMfiO4xqM5MAp2jS90NWxd4\nDjpr5usQDRrh4ODgEFGsyrTaTqdjTe7UrJI7cdhsI3O3LpfLsgPt378fgJeCRMbBunGyh1KpJDsh\ndyndiDrsXKNQX6/PV5uLgJ3jBwStCjPNR7eMJDjmY+fOnRLo+vTTTwH4LEK3LTRNZJ6bfi8qQS8g\nWHFoBkO07M2c4Gw2KxaW2S6vWq2KRfbwww8D8Kq8KCdaCCdOnADg6TCfG10lZaYXEVGxwvQzbTbN\n1znepmsplUqJO8qs0CyVSmKhsd/D/v37cfbsWQB+xznqbLlcDtxH/qZpJeh7v1xXl2OyDg4ODl3E\nqhQjaJg+UD0sjs7ver1uDZzjLrKwsCDMlMGZgYEB8bWw8IA7YqFQsFKKtC/SLJL4JjvWakKfN9mA\nyWw009K9I0zfkh5MySGLTDWKxWKSWseKOUJXwPCeLC0tyXmYwcVWq2WdY69Cp8WZMqRuxuNx+Rz1\nTesuP8/ATa1Wk8IDNvnu7++XtCIGFBlEGxkZsSzAer1uWXlmr+Zeh2nhAHa6n/Z364b8ZkyHVmel\nUpH1gFZCs9m0fLE8ZiqVkt/UvRFM8LUw//v9EI274ODg4BBRrMr4mU6nY+1UuneBrr0GvJ3F9I1w\nB+vr67PYwPDwsCQskwUwwqt9WPp8dGECgAA7iMIwOi2f+7F+INjVCPDY1f0YUCaTke5lGzduBOD5\nsujXYvK27gfKY/C3tZ/NTLXTfYV7HdpPZ3Zq04zGHNCXTqcDug0E/Y2UL/tHTE1Nia+b6Vr8vXQ6\nbZWht9vtgPz153Wvil6GLpox/d2E/r/uT2zGb3gv+vr6hMmy9LZer0uZOO+PLp83fzOskEaz7eX2\nk12VwFetVrNSuHRwJszMoYlg5gSm02lpCcc0mEajYbWj0+arruUHvEXcnD9FRCFwAASDSaYLRk/o\nNB90rUhmc46BgQHpY0Az9d69e7IwMidRBx/MdDCdpsRjaPMwCn0hAN+E1PpBHTQfRI1msym6zYdS\n6y57cjCv+9ChQxKk5X1jhZh27eiqufs1Vclms5GQL89RT6QlKFPdYlL3wDBzYfXGxwpG5iLPzc3J\ns2FWiWrwHLLZrKwLYQ1rltsXwrkLHBwcHLqIVRmkmEwmA0nGGjrQpJmYWaWlJ9oyKMMa6JmZGUkz\n4s6mZ68zNYm/rdNyTMTj8Uh0MtIVXzpRHfCvs1arWV2FOp2ONfKDGB8fx8GDBwH48j516pQEDcjq\ndLEB2Zp2EZCpmO0t6/V6JJLlgfBpypSXdmGZ19hoNKwiDMpm27ZtwmSpY8eOHROT1nwO9LRVWnZa\nN3VKIs8nCvLV7jhTfkSz2bRceolEwnqN96TT6YgbkT0jbt68KVaCaUkXCgXpUKfvK60087x05d/X\nwTFZBwcHhy5iPu9toAAABNxJREFUVXyy1WpVdgszEKNTuPSuYY6joI91cnJSar3JEG7cuCGlttzJ\ntc+V39UlcibL0COgo1CMoNmSLgAAfL90PB63/Ig6WKX7NQBeShzlwEbTs7Oz963nbjabUkOuS07N\ntCZaF2FFEr0Kfc1mcEYX1JgsV5drEmRHk5OTIjvW0F+/fl2Yv7b8AE8nmSbH+60tPzMgFwULDAha\nVabFqvsaEPq6+Gya6Ve6ATi77t25c8dqwq3vIf20ZsxGf/5/I9tVaRCj65BNpdSBGx0g4b/5YLNG\nedu2bda8sGPHjskEW1MoOnigFyPeRHNCQqPRiET3fnPBA+ygos5L1dkTZqWLbnVI1wAf7kajYcmU\nMms0GqHVRzw3s7qv2WxGIjADhOeemtcD2ME9HSAhUeBnMpmMNNTRLgE+3JQbN7pms2nlHOtJDeaC\nA/huhV6GzvIx3YFhvSLCvms2nEqlUiI/ZhjdvXtX7oG5/uicWB5DB9vMdarZbC57XXDuAgcHB4cu\nYkWZ7INMWt05KIwNmSam7srFnfvDDz8E4AVn/p/27h5HcSAIw3CtkCXE/WPOQIC4BiEBBwCECIyQ\nkMzfBqMyn6vN7mxQs7b0PgmrCXagp6n+qe5yTKzpCBmLWZuV0389FzmGO/Z6SyUeKdJkly4zzbqf\nz9vMP/v1em2X/779Utd1227+N9DZXawAprPVWI1rLGUkzbo3uPT9m1nRpmbd413ed+Nqo2mato/7\ndsFut2u3d/zVf/ftditWD9q+sVLY4/EotiqGSLdivG3ibTr9mSb4Yi0TjQv+2b0C3/F4bNstJr50\nW1BXZn03z/yVKlwAMAA/OpPVESvu0/Xtv+qIFQsk++M3lsulrVYrM3vPds/n8z9fIoi/Uwv4juFC\ngj45Veu1mnWLOcdZmJkVx2B8RK/r2ubzeef/2G637U2vuBq53+9F4ejJZFIkL7QfjOV+vSah4spG\nbxPGylx9t5j06NtisTCz9136w+HQ2c81e/99qqoqkmGauHTaX8fQd7XNYlzQFWnsW8/ns8gnaFF/\nf0iiz2T3+32bBItJV10BxttjZt2HwDpqFwDAAPyXKlx9+xkx660/0xEjXqM7nU7FiKIXCOKVTn2Y\noM4U4mO0dbYxhur98SF6ZuUeoO6/6mwsntzwdtlsNp1KaGZfM4x4vEZrp3omPB6k15/paiFeYx4q\nrScb2yte8DDrznz93/HRP+v1uv07aHY77l3razxOqBX6+07ljKHuhuZIYn/QnIq3Q1/VM72qbPa1\nN+tt6qtePZ0RY8BsNiv2wHVPu+/Y3ndzNT8aZPVN6RLI7M8B+PV6FRvhGoBj59WlcN/5trhEbZqm\nKACh5enGkDzQG0n+ZfeB5W+DxKeiz/ql1nPKsbSeJmFiArHv/WiBj7EEWe1bcWmqA1dfecmYfHWX\ny6VtLz1+9amIelVVxUCl3xVvX3+vegNtyHRwjwXdNanYVzTmU6nM6XTatreWJ4zJYD3PHfu19s1P\nCbDvYLsAABL9GstMAgDGiJksACQiyAJAIoIsACQiyAJAIoIsACQiyAJAIoIsACQiyAJAIoIsACQi\nyAJAIoIsACQiyAJAIoIsACQiyAJAIoIsACQiyAJAIoIsACQiyAJAIoIsACQiyAJAIoIsACQiyAJA\nIoIsACT6DSY1+Ys4L8y3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 16 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ulwtt/0mn0wkFuarVaqjWgT44wvTDNCtZnWroKljtIqDdOE5zuVzPw0yAN0/0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\nhNgkaxiGESH/B2YVqhG1lHG9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 16 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weights of Gaussian mixtures: [[9.9517381e-01]\n",
      " [4.8262030e-03]\n",
      " [1.2126811e-12]]\n",
      "samples from Gaussian mixture model (EL2O)\n"
     ]
    },
    {
     "data": {
      "image/png": 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j6XRa5Mv7PjQ0BMC5H/ysbpbv7t2724BzfdQtyoz9NGZmZqTElmuFLinm+/SE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\n",
      "text/plain": [
       "<Figure size 432x288 with 16 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PPZPfeOONdnyMu2JK1jAMI0baunzq1ZorPVd5rliNRkMUGJOJ+/r6JE2GKxb/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\nxCZZwzCMGLFJ1jAMI0ZskjUMw4iR/wdFRXtoHw9PbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 16 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KK69w9tlnb9XTQHw+H9/73vd4+umnee+997jiiitobW3lhz/8IdOnT+eOO+7I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\nwoiGORKJRCqM/w+rBzZWfnniBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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He3s7drud3Nxc82dg5IIB87SOvLy8Hmkdo5ew5IbFni6d4OvUWr9B9yy5Smv9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\nRCpANL6RSCRSAf4fPAqvxNK4DRwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8PubOnTtgPLlm5g0NDXR1dVFVVYXFYiEej+P3+4lEIni9XjOvrJQinU6bW7CN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\nb7yxzYE5lUrxxhtvsHz5cnw+H/fccw8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oIQ9YTRvIizZv7DxIGgK9l95LE0jXLUlIaPNo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\ngg==\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probing the postrior...\n",
      "[[ 0.35592958  0.48388115  0.17217307  1.3107345  -1.5813934  -0.87867516\n",
      "   1.8030049  -1.3423384   0.36180833  0.4919712 ]]\n",
      "[[-0.26026565  0.38083062 -0.41014087  1.0106142  -1.9620478  -0.39476606\n",
      "   0.634245   -1.3845389   0.3403529   0.17685123]]\n",
      "304.2308 305.81714 306.13754\n",
      "57.32655477481124 265.36533\n",
      "9.894808101901589 26.428526\n",
      "118.1375164729816 97.2289\n"
     ]
    },
    {
     "data": {
      "image/png": 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CZr6OuLtCegb22IQya2QNGTKEzp07U6NGDWrWrMmLL76Yb9mOHTvyn//8h379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\n5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H31QIGUss5Mv7GexLFVmij/9S9KvvqVqpWbjl2uj4si+JoRBF09HJ8u57m0V9lmkzz3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\nFEVRFEVRnOT/ATfRLp870z4TAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x216 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "  sess = tf.Session()\n",
    "  sess.run(tf.global_variables_initializer())\n",
    "  \n",
    "  # underlying truth\n",
    "  truth = x_test[num_mnist:num_mnist+data_size]\n",
    "  plot_image(truth, directory=plot_path, filename='truth_%s'%label, title='truth')\n",
    "  \n",
    "  # corrupted data\n",
    "  data, custom_mask = make_corrupted_data(truth, corr_type=corr_type)\n",
    "  plot_image(data, directory=plot_path, filename='input_data_%s'%label, title='data')\n",
    "  plot_image(custom_mask, directory=plot_path, filename='mask_data_%s'%label, title='mask')\n",
    "  \n",
    "  # noise\n",
    "  noise = get_custom_noise(data.shape, signal_dependent=False, signal=truth)\n",
    "  plot_image(noise, directory=plot_path, filename='noise_%s'%label, title='noise')\n",
    "  \n",
    " \n",
    "  tf.random.set_random_seed(seed)\n",
    "  inits = get_random_start_values(10, sess)\n",
    "  \n",
    "  # find minima\n",
    "  print('starting search for minima')\n",
    "  try:\n",
    "    assert(False)\n",
    "    minima, min_loss, min_var, recons = pickle.load(open(minima_path+'minima_%s.pkl'%label,'rb'))\n",
    "    print('loaded saved minima')\n",
    "  except:\n",
    "  \n",
    "    minima  =[]\n",
    "    min_loss=[]\n",
    "    min_var =[]\n",
    "    recons  =[]\n",
    "    for jj,init in enumerate(inits):\n",
    "      print('progress in %', jj/len(inits)*100)\n",
    "      min_z, min_l, pos_def    = minimize_posterior(init, data,custom_mask,noise,sess)\n",
    "      rec                      = sess.run(recon_MAP, feed_dict={sigma_corr:noise})\n",
    "      var                      = sess.run(variance, feed_dict={input_data: data,mask:custom_mask,sigma_corr:noise})\n",
    "  \n",
    "      plot_image(rec, directory=plot_path, filename='recon_%s_minimum%d'%(label,jj), title='reconstruction with loss %.1f'%min_l)\n",
    "      print(min_z)\n",
    "      if pos_def:\n",
    "        print('hessian postive definite')\n",
    "        minima.append(min_z)\n",
    "        min_loss.append(min_l)\n",
    "        min_var.append(var)\n",
    "        recons.append(rec)\n",
    "    \n",
    "    order    = np.argsort(min_loss)\n",
    "    min_loss = np.asarray(min_loss)[order]\n",
    "    minima   = np.asarray(minima)[order]\n",
    "    min_var  = np.asarray(min_var)[order]\n",
    "    \n",
    "    pickle.dump([minima, min_loss, min_var,recons],open(minima_path+'minima_%s.pkl'%label,'wb'))\n",
    "\n",
    "  print('analysing the posterior minima:')\n",
    "  plot_minima(minima, min_loss, min_var)\n",
    "  \n",
    "  # set MAP value to lowest minimum\n",
    "  lowest_minimum = sess.run(MAP_reset, feed_dict={MAP_ini:minima[0]})\n",
    "  # and plot\n",
    "  print('reconstruction from lowest minimum')\n",
    "  rec     = sess.run(recon_MAP, feed_dict={sigma_corr:noise})\n",
    "  plot_image(rec, directory=plot_path, filename='lowest_minimum_%s'%(label), title='reconstruction', vmin=0, vmax=1)\n",
    "  if corr_type in ['mask', 'sparse mask', 'noise+mask']:\n",
    "    print('masked reconstruction')\n",
    "    plot_image(rec, directory=plot_path, filename='lowest_minimum_%s_masked'%(label), title='masked reconstruction', vmin=0, vmax=1, mask = custom_mask)\n",
    "    \n",
    "    \n",
    "  print('starting stochastic VI on the posterior')\n",
    "  sess.run(update_mu_elbo, feed_dict={input_data: data,mask:custom_mask,sigma_corr:noise})\n",
    "  minimize_neg_elbo(data,custom_mask,noise,sess)\n",
    "  minimize_neg_elbo(data,custom_mask,noise,sess, full_rank=True)  \n",
    "  \n",
    "  print('full rank reconstruction')\n",
    "  rec     = sess.run(recon_fr, feed_dict={sigma_corr:noise})\n",
    "  plot_image(rec, directory=plot_path, filename='full_rank_VI_%s'%(label), title='reconstruction', vmin=0, vmax=1)\n",
    "  print('mean field reconstruction')\n",
    "  rec     = sess.run(recon_elbo, feed_dict={sigma_corr:noise})\n",
    "  plot_image(rec, directory=plot_path, filename='mean_field_VI_%s'%(label), title='reconstruction', vmin=0, vmax=1)\n",
    "    \n",
    "\n",
    "\n",
    "  print('samples from Laplace approximation around deepest minimum (EL2O)')\n",
    "  samples = get_laplace_sample(16,minima[0],data,custom_mask,noise,sess)\n",
    "  plot_samples(samples, custom_mask, title='Samples from Laplace approximation', filename='samples_laplace_deepest_minimum_%s'%label)  \n",
    "  \n",
    "  # here, the separate minima have to be set by hand\n",
    "  mu_, sigma_, w_ = get_gmm_parameters([minima[0],minima[4],minima[7]], data, noise, custom_mask, min_loss[0])\n",
    "  _ = sess.run([update_w, update_mugmm,update_TriLgmm], feed_dict={mu_ini:mu_, w_ini:w_, sigma_ini:sigma_ })\n",
    "  \n",
    "  \n",
    "  \n",
    "  samples = get_gmm_sample(16,data,custom_mask,noise,sess)\n",
    "  print('samples from Gaussian mixture model (EL2O)')\n",
    "  plot_samples(samples, custom_mask, title='GMM samples', filename='gmm_samples_%s'%label)\n",
    "  \n",
    "  more_samples = []\n",
    "  for ii in range(10000):\n",
    "    more_samples+=[sess.run(gmm_sample,feed_dict={input_data: data, sigma_corr:noise})]\n",
    "  more_samples=np.asarray(more_samples)\n",
    "  \n",
    "  for indices in [[0,1],[1,2],[3,8]]:\n",
    "    plot_prob_2D_GMM(more_samples, indices)\n",
    "    \n",
    "  print('probing the postrior...')\n",
    "  probe_posterior(minima[0], data, noise, custom_mask, sess)\n",
    "  \n",
    "  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "CUUVYB2Lex8k"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0ye6CFt1Ku0n"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "ImageCorruptionMNIST-masknoise05_SVI.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
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 },
 "nbformat": 4,
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}