exp_3/nn_classification_bigger_nn.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contrastive learning: learning a Gaussian mixture pdf using a neural net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm, multivariate_normal, rv_continuous\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data - setting up distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is our Gaussian mixture class.\n",
    "\n",
    "It's not implemented very robustly but is enough to generate samples and compare the neural net to its pdf p."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Mixture(rv_continuous):\n",
    "    def __init__(self, *args):\n",
    "        self.distns = args\n",
    "        super().__init__()\n",
    "        \n",
    "    def pdf(self, x):\n",
    "        return np.mean([d.pdf(x) for d in self.distns])\n",
    "    \n",
    "    def rvs(self, size=1):\n",
    "        samples = [d.rvs(size=size) for d in self.distns]\n",
    "        indices = np.random.randint(low=0, high=len(self.distns), size=size)\n",
    "        return np.array([samples[indices[i]][i] for i in range(size)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use one component with mean (1,1)^T, the other with (-1,-1)^T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "mixture_component_1 = multivariate_normal([1, 1], [[0.25, 0], [0, 0.25]])\n",
    "mixture_component_2 = multivariate_normal([-1, -1], [[0.25, 0], [0, 0.25]])\n",
    "true_mixture = Mixture(mixture_component_1, mixture_component_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualise the pdf..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1, x2 = np.mgrid[-2:2:0.01, -2:2:0.01]\n",
    "pos = np.dstack((x1, x2))\n",
    "_ = plt.contourf(x1, x2, np.array([[true_mixture.pdf(x) for x in p] for p in pos]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...and check it lines up with samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1, x2 = true_mixture.rvs(size=10000).T\n",
    "_ = sns.kdeplot(x=x1, y=x2, shade=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use a standard multivariate normal for the noise, and again visualise the pdf and some samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = multivariate_normal([0,0], [[1, 0], [0, 1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualising the noise pdf\n",
    "x1, x2 = np.mgrid[-2:2:0.01, -2:2:0.01]\n",
    "pos = np.dstack((x1, x2))\n",
    "_ = plt.contourf(x1, x2, np.array([[noise.pdf(x) for x in p] for p in pos]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualising our noise samples\n",
    "x1, x2 = noise.rvs(size=10000).T\n",
    "_ = sns.kdeplot(x=x1, y=x2, shade=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data - generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.concatenate([\n",
    "    true_mixture.rvs(size=N),\n",
    "    noise.rvs(size=N)\n",
    "])\n",
    "y = np.concatenate([\n",
    "    np.ones(N),\n",
    "    np.zeros(N)\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use this if you don't care about having a train/test split - we'll use one for validation\n",
    "# permutation = np.random.permutation(20000)\n",
    "# X = X[permutation]\n",
    "# y = y[permutation]\n",
    "# y[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 0., 0., ..., 0., 1., 1.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model - construction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we use a bigger network with two hidden layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(20, input_dim=2, activation='relu'))\n",
    "model.add(Dense(20, activation='relu'))\n",
    "model.add(Dense(10, activation='relu'))\n",
    "model.add(Dense(1, activation='sigmoid'))\n",
    "model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.4139811 ],\n",
       "       [0.38664767],\n",
       "       [0.44877553],\n",
       "       [0.42573914],\n",
       "       [0.46204093]], dtype=float32)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(X_train[0:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/10\n",
      "2500/2500 [==============================] - 3s 1ms/step - loss: 0.4838 - accuracy: 0.7725 - val_loss: 0.4668 - val_accuracy: 0.7849\n",
      "Epoch 2/10\n",
      "2500/2500 [==============================] - 2s 975us/step - loss: 0.4654 - accuracy: 0.7849 - val_loss: 0.4669 - val_accuracy: 0.7829\n",
      "Epoch 3/10\n",
      "2500/2500 [==============================] - 2s 970us/step - loss: 0.4618 - accuracy: 0.7858 - val_loss: 0.4596 - val_accuracy: 0.7886\n",
      "Epoch 4/10\n",
      "2500/2500 [==============================] - 2s 960us/step - loss: 0.4605 - accuracy: 0.7865 - val_loss: 0.4590 - val_accuracy: 0.7883\n",
      "Epoch 5/10\n",
      "2500/2500 [==============================] - 2s 964us/step - loss: 0.4601 - accuracy: 0.7865 - val_loss: 0.4593 - val_accuracy: 0.7880\n",
      "Epoch 6/10\n",
      "2500/2500 [==============================] - 2s 960us/step - loss: 0.4600 - accuracy: 0.7864 - val_loss: 0.4580 - val_accuracy: 0.7891\n",
      "Epoch 7/10\n",
      "2500/2500 [==============================] - 2s 964us/step - loss: 0.4597 - accuracy: 0.7867 - val_loss: 0.4575 - val_accuracy: 0.7890\n",
      "Epoch 8/10\n",
      "2500/2500 [==============================] - 2s 967us/step - loss: 0.4596 - accuracy: 0.7870 - val_loss: 0.4588 - val_accuracy: 0.7889\n",
      "Epoch 9/10\n",
      "2500/2500 [==============================] - 2s 967us/step - loss: 0.4597 - accuracy: 0.7866 - val_loss: 0.4597 - val_accuracy: 0.7876\n",
      "Epoch 10/10\n",
      "2500/2500 [==============================] - 2s 965us/step - loss: 0.4595 - accuracy: 0.7869 - val_loss: 0.4584 - val_accuracy: 0.7887\n"
     ]
    }
   ],
   "source": [
    "history = model.fit(\n",
    "    X_train,\n",
    "    y_train,\n",
    "    batch_size=64,\n",
    "    epochs=10,\n",
    "    validation_data=(X_test, y_test)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe7604c9490>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(history.history['val_accuracy'], label='Accuracy')\n",
    "plt.plot(history.history['val_loss'], label='Loss')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot contour maps to check out the densities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1, x2 = np.mgrid[-2:2:0.01, -2:2:0.01]\n",
    "pos = np.dstack((x1, x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First let's recall our true pdf p:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.contourf(x1, x2, np.array([[true_mixture.pdf(x) for x in p] for p in pos]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's solve for our approximation to p:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$d = \\frac{p}{p + q} \\implies p = \\frac{qd}{1 - d}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Model was constructed with shape (None, 2) for input Tensor(\"dense_input:0\", shape=(None, 2), dtype=float32), but it was called on an input with incompatible shape (None, 400, 2).\n"
     ]
    }
   ],
   "source": [
    "d = model.predict(pos).reshape(400,400)\n",
    "q = noise.pdf(pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = q * d / (1 - d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.contourf(x1, x2, p)\n",
    "plt.savefig('figures/nn_classification_bignn.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The components are nicer and more round than the single-layer model previously."
   ]
  }
 ],
 "metadata": {
  "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}