Simple Neural Network.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maths Derivation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    a = np.exp(z)\n",
    "    b = np.exp(-z)\n",
    "    return (a - b)/(a + b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Derivative of sigmoid**\n",
    "$$ (e^{x} - e^{-x})' = e^{x} + e^{-x} $$\n",
    "$$ (e^{x} + e^{-x})' = e^{x} - e^{-x} $$\n",
    "$$ \\phi'(x) = \\frac{(e^{x} - e^{-x})'(e^{x} + e^{-x}) - (e^{x} + e^{-x})'(e^{x} - e^{-x})}{(e^x+e^{-x})^2} = \\frac{(e^{x} + e^{-x})^2 - (e^{x} - e^{-x})^2}{(e^x+e^{-x})^2} = \\frac{4}{(e^x + e^{-x})^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid_d(z):\n",
    "    return 4 / ((np.exp(z) + np.exp(-z))**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\nabla_w f_w(x) = \\left[ \\begin{smallmatrix} \n",
    "\\frac{\\partial f_w(x)}{\\partial w_1} \\\\ \n",
    "\\frac{\\partial f_w(x)}{\\partial w_2} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_3} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_4} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_5} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_6} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_7} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_8} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_9} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_{10}} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_{11}} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_{12}} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_{13}} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_{14}} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_{15}} \\\\\n",
    "\\frac{\\partial f_w(x)}{\\partial w_{16}}\n",
    "\\end{smallmatrix} \\right] = \\left[ \\begin{smallmatrix} \n",
    "\\phi (w_2x_1+w_3x_2+w_4x_3+w_5) \\\\\n",
    "w_1\\phi' (w_2x_1+w_3x_2+w_4x_3+w_5)x_1 \\\\\n",
    "w_1\\phi' (w_2x_1+w_3x_2+w_4x_3+w_5)x_2 \\\\\n",
    "w_1\\phi' (w_2x_1+w_3x_2+w_4x_3+w_5)x_3 \\\\\n",
    "w_1\\phi' (w_2x_1+w_3x_2+w_4x_3+w_5) \\\\\n",
    "\\phi (w_7x_1+w_8x_2+w_9x_3+w_{10}) \\\\\n",
    "w_6\\phi' (w_7x_1+w_8x_2+w_9x_3+w_{10})x_1 \\\\\n",
    "w_6\\phi' (w_7x_1+w_8x_2+w_9x_3+w_{10})x_2 \\\\\n",
    "w_6\\phi' (w_7x_1+w_8x_2+w_9x_3+w_{10})x_3 \\\\\n",
    "w_6\\phi' (w_7x_1+w_8x_2+w_9x_3+w_{10}) \\\\\n",
    "\\phi (w_{12}x_1+w_{13}x_2+w_{14}x_3+w_{15}) \\\\\n",
    "w_{11}\\phi' (w_{12}x_1+w_{13}x_2+w_{14}x_3+w_{15})x_1 \\\\\n",
    "w_{11}\\phi' (w_{12}x_1+w_{13}x_2+w_{14}x_3+w_{15})x_2 \\\\\n",
    "w_{11}\\phi' (w_{12}x_1+w_{13}x_2+w_{14}x_3+w_{15})x_3 \\\\\n",
    "w_{11}\\phi' (w_{12}x_1+w_{13}x_2+w_{14}x_3+w_{15}) \\\\\n",
    "1\n",
    "\\end{smallmatrix} \\right] $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the Jacobian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ Dr(w) = \\left[ \\begin{smallmatrix} \n",
    "\\frac{\\partial r_1(w)}{\\partial w_1} & \\frac{\\partial r_1(w)}{\\partial w_2} & \\dots & \\frac{\\partial r_1(w)}{\\partial w_{16}} \\\\ \n",
    "\\frac{\\partial r_2(w)}{\\partial w_1} & \\frac{\\partial r_2(w)}{\\partial w_2} & \\dots & \\frac{\\partial r_2(w)}{\\partial w_{16}} \\\\ \n",
    "\\\\\n",
    "\\dots & \\dots & \\dots & \\dots \\\\\n",
    "\\\\\n",
    "\\frac{\\partial r_N(w)}{\\partial w_1} & \\frac{\\partial r_N(w)}{\\partial w_2} & \\dots & \\frac{\\partial r_N(w)}{\\partial w_{16}} \\\\ \n",
    "\\end{smallmatrix} \\right] = \\left[ \\begin{smallmatrix} \n",
    "\\frac{\\partial f_w(x^{(1)})}{\\partial w_1} & \\frac{\\partial f_w(x^{(1)})}{\\partial w_2} & \\dots & \\frac{\\partial f_w(x^{(1)})}{\\partial w_{16}} \\\\ \n",
    "\\frac{\\partial f_w(x^{(2)})}{\\partial w_1} & \\frac{\\partial f_w(x^{(2)})}{\\partial w_2} & \\dots & \\frac{\\partial f_w(x^{(2)})}{\\partial w_{16}} \\\\ \n",
    "\\\\\n",
    "\\dots & \\dots & \\dots & \\dots \\\\\n",
    "\\\\\n",
    "\\frac{\\partial f_w(x^{(N)})}{\\partial w_1} & \\frac{\\partial f_w(x^{(N)})}{\\partial w_2} & \\dots & \\frac{\\partial f_w(x^{(N)})}{\\partial w_{16}}\n",
    "\\end{smallmatrix} \\right] $$\n",
    "$$ = \\left[ \\begin{smallmatrix} \n",
    "\\nabla_w f_w(x^{1})^T \\\\ \n",
    "\\nabla_w f_w(x^{2})^T \\\\\n",
    "\\nabla_w f_w(x^{3})^T \\\\\n",
    "\\\\\n",
    "\\dots \\\\\n",
    "\\\\\n",
    "\\nabla_w f_w(x^{N})^T\n",
    "\\end{smallmatrix} \\right] = \\left[ \\begin{smallmatrix} \n",
    "\\nabla_w f_w(x^{1}) & \\nabla_w f_w(x^{2}) & \\dots & \\nabla_w f_w(x^{N}) \\end{smallmatrix} \\right]^T\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derive the closed form for the minimizer\n",
    "Need to find $$ \\min_{w} \\left\\lVert r(w^k) + Dr(w^k)(w-w^k) \\right\\rVert^2 + \\lambda\\left\\lVert w \\right\\rVert^2 + \\lambda^k\\left\\lVert w-w^k \\right\\rVert^2$$\n",
    "Have $A_1, A_2, A_3, b_1, b_2, b_3$ such that $$\\left\\lVert r(w^k) + Dr(w^k)(w-w^k) \\right\\rVert^2 + \\lambda\\left\\lVert w \\right\\rVert^2 + \\lambda^k\\left\\lVert w-w^k \\right\\rVert^2 = \\left\\lVert A_1w-b_1 \\right\\rVert^2 + \\left\\lVert A_2w-b_2 \\right\\rVert^2 + \\left\\lVert A_3w-b_3 \\right\\rVert^2$$\n",
    "$$A_1 = D_r(w^k), b_1=Dr(w^k)w^k-r(w^k) $$\n",
    "$$A_2 = I, b_2 = w^k $$\n",
    "$$A_3 = I, b_3 = 0$$\n",
    "$$\\left\\lVert r(w^k) + Dr(w^k)(w-w^k) \\right\\rVert^2 + \\lambda\\left\\lVert w \\right\\rVert^2 + \\lambda^k\\left\\lVert w-w^k \\right\\rVert^2 = \\left\\lVert \\left[ \\begin{smallmatrix} A_1 \\\\ \\sqrt{\\lambda^k}A_2 \\\\ \\sqrt{\\lambda}A_3 \\end{smallmatrix} \\right]w - \\left[ \\begin{smallmatrix} b_1 \\\\ \\sqrt{\\lambda^k}b_2 \\\\ \\sqrt{\\lambda}b_3 \\end{smallmatrix} \\right] \\right\\rVert^2 $$\n",
    "Therefore,\n",
    "$$ A = \\left[ \\begin{smallmatrix} Dr(w^k) \\\\ \\sqrt{\\lambda^k}I \\\\ \\sqrt{\\lambda}I \\end{smallmatrix} \\right], b = \\left[ \\begin{smallmatrix} Dr(w^k)w^k - r(w^k) \\\\ \\sqrt{\\lambda^k}w^k \\\\ 0 \\end{smallmatrix} \\right] $$\n",
    "To find the minimizer, \n",
    "$$ A^TAw = A^Tb $$\n",
    "$$ \\left[ \\begin{smallmatrix} Dr(w^k)^T & \\sqrt{\\lambda^k}I & \\sqrt{\\lambda}I \\end{smallmatrix} \\right]\\left[ \\begin{smallmatrix} Dr(w^k) \\\\ \\sqrt{\\lambda^k}I \\\\ \\sqrt{\\lambda}I \\end{smallmatrix} \\right]w = \\left[ \\begin{smallmatrix} Dr(w^k)^T & \\sqrt{\\lambda^k}I & \\sqrt{\\lambda}I \\end{smallmatrix} \\right]\\left[ \\begin{smallmatrix} Dr(w^k)w^k - r(w^k) \\\\ \\sqrt{\\lambda^k}w^k \\\\ 0 \\end{smallmatrix} \\right] $$\n",
    "$$ \\left(Dr(w^k)^TDr(w^k) + (\\lambda^k+\\lambda)I \\right)w = Dr(w^k)^TDr(w^k)w^k - Dr(w^k)^Tr(w^k) + \\lambda^kw^k $$\n",
    "$$ w^* = \\left(Dr(w^k)^TDr(w^k) + (\\lambda^k+\\lambda)I \\right)^{-1} \\left( Dr(w^k)^TDr(w^k)w^k - Dr(w^k)^Tr(w^k) + \\lambda^kw^k \\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simple Neural Network (Feed-forward)\n",
    "def f(w, x):\n",
    "    return w[0]*sigmoid(w[1]*x[0]+w[2]*x[1]+w[3]*x[2]+w[4]) + \\\n",
    "        w[5]*sigmoid(w[6]*x[0]+w[7]*x[1]+w[8]*x[2]+w[9]) + \\\n",
    "        w[10]*sigmoid(w[11]*x[0]+w[12]*x[1]+w[13]*x[2]+w[14]) + w[15]\n",
    "\n",
    "# Error on each data point\n",
    "def r(w, x, y):\n",
    "    return f(w, x) - y\n",
    "\n",
    "# Error on the entire dataset\n",
    "def rn(w, X, Y):\n",
    "    return np.array([r(w, x, y) for x,y in zip(X, Y)])\n",
    "\n",
    "# Jacobian\n",
    "def Dr(w, X):\n",
    "    ret = np.zeros((N, 16))\n",
    "    for i,x in enumerate(X):\n",
    "        phi1 = sigmoid(w[1]*x[0]+w[2]*x[1]+w[3]*x[2]+w[4])\n",
    "        phi1d = sigmoid_d(w[1]*x[0]+w[2]*x[1]+w[3]*x[2]+w[4])\n",
    "        phi2 = sigmoid(w[6]*x[0]+w[7]*x[1]+w[8]*x[2]+w[9])\n",
    "        phi2d = sigmoid_d(w[6]*x[0]+w[7]*x[1]+w[8]*x[2]+w[9])\n",
    "        phi3 = sigmoid(w[11]*x[0]+w[12]*x[1]+w[13]*x[2]+w[14])\n",
    "        phi3d = sigmoid_d(w[11]*x[0]+w[12]*x[1]+w[13]*x[2]+w[14])\n",
    "        ret[i][0] = phi1\n",
    "        ret[i][1] = w[0]*phi1d*x[0]\n",
    "        ret[i][2] = w[0]*phi1d*x[1]\n",
    "        ret[i][3] = w[0]*phi1d*x[2]\n",
    "        ret[i][4] = w[0]*phi1d\n",
    "        ret[i][5] = phi2\n",
    "        ret[i][6] = w[5]*phi2d*x[0]\n",
    "        ret[i][7] = w[5]*phi2d*x[1]\n",
    "        ret[i][8] = w[5]*phi2d*x[2]\n",
    "        ret[i][9] = w[5]*phi2d\n",
    "        ret[i][10] = phi3\n",
    "        ret[i][11] = w[10]*phi3d*x[0]\n",
    "        ret[i][12] = w[10]*phi3d*x[1]\n",
    "        ret[i][13] = w[10]*phi3d*x[2]\n",
    "        ret[i][14] = w[10]*phi3d\n",
    "        ret[i][15] = 1\n",
    "    return ret\n",
    "\n",
    "# Loss: sum of squared errors + regularization error\n",
    "def l(w, X, Y, lamb):\n",
    "    loss = 0\n",
    "    for x,y in zip(X,Y):\n",
    "        loss += r(w, x, y)**2\n",
    "    return loss + lamb*np.linalg.norm(w)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Non-linear function to approximate\n",
    "def g(x):\n",
    "    return x[0]*x[1] + x[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Levenberg-Marquardt algorithm (Reference: Algorithm 18.3 on textbook Pg.392)\n",
    "# Choose small residual as the stopping criteria\n",
    "# Max iteration is 1000 by default\n",
    "# Threshold for small residual is 0.5 by default \n",
    "# 0.5 is effective on original g(x), might need adjustments on g2(x)\n",
    "def LM(X, Y, wk, lamb, lambk, max_iter=1000, thresh=0.5):\n",
    "    losses = []\n",
    "    for i in range(max_iter):\n",
    "        D = Dr(wk, X)  # Jacobian\n",
    "        err = rn(wk, X, Y)\n",
    "        loss = l(wk, X, Y, lamb)\n",
    "        losses.append(loss)  # loss append\n",
    "#         if i % 100 == 0:\n",
    "#             print(\"Iteration: {:3d} with loss: {:.5f}\".format(i, loss))\n",
    "        \n",
    "        # Stopping criterium: small residual, have almost solved fw(x) = y\n",
    "        if np.linalg.norm(err)**2 < thresh:\n",
    "            break\n",
    "            \n",
    "        # Closed form to find minimizer\n",
    "        wk_new = np.matmul(np.linalg.inv(np.matmul(D.T, D) + (lambk + lamb)*np.identity(16)),\n",
    "                           (np.matmul(np.matmul(D.T, D), wk) - np.matmul(D.T, err) + lambk*wk))  \n",
    "        \n",
    "        # Check tentaive iterate\n",
    "        norm = np.linalg.norm(err)**2\n",
    "        newnorm = np.linalg.norm(rn(wk_new, X, Y))**2\n",
    "        if newnorm < norm:\n",
    "            lambk = 0.8*lambk  # reduce lambda\n",
    "            wk = wk_new  # accept iterate\n",
    "        else:\n",
    "            lambk = 2*lambk  # increase lambda and do not update w\n",
    "    \n",
    "    return wk, losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 500\n",
    "X = random.randn(N, 3)\n",
    "Y = np.array([g(x) for x in X])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:   0 with loss: 1595.41204\n"
     ]
    }
   ],
   "source": [
    "w_initial = random.randn(16)\n",
    "w, losses = LM(X, Y, w_initial, 1e-5, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Training loss curve')\n",
    "plt.xlabel('iteration')\n",
    "plt.ylabel('loss')\n",
    "plt.plot(losses)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The training loss decreased with iterations and luckily with this initalization of w, it converges within 100 iterations**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try different initializations & effect on final model training loss error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:   0 with loss: 1595.41320\n",
      "Iteration: 100 with loss: 2.17376\n",
      "Iteration: 200 with loss: 2.17375\n",
      "Iteration: 300 with loss: 2.17375\n",
      "Iteration: 400 with loss: 2.17375\n",
      "Iteration: 500 with loss: 2.17375\n",
      "Iteration: 600 with loss: 2.17375\n",
      "Iteration: 700 with loss: 2.17375\n",
      "Iteration: 800 with loss: 2.17375\n",
      "Iteration: 900 with loss: 2.17375\n",
      "Iteration:   0 with loss: 1595.41192\n",
      "Iteration:   0 with loss: 1595.41191\n"
     ]
    }
   ],
   "source": [
    "w2, losses2 = LM(X, Y, w_initial, 1e-4, 1)\n",
    "w3, losses3 = LM(X, Y, w_initial, 1e-6, 1)\n",
    "w4, losses4 = LM(X, Y, w_initial, 1e-7, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,8))\n",
    "plt.title('Training loss curve for different lambda but same lambda_k=1')\n",
    "plt.xlabel('iteration')\n",
    "plt.ylabel('loss')\n",
    "plt.xlim(0, 200)\n",
    "plt.plot(losses2)\n",
    "plt.plot(losses)\n",
    "plt.plot(losses3)\n",
    "plt.plot(losses4)\n",
    "plt.legend(['lambda=1e-4', 'lambda=1e-5', 'lambda=1e-6', 'lambda=1e-7'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Test & Tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build test set\n",
    "NT = 100\n",
    "X_test = random.randn(NT, 3)\n",
    "Y_test = np.array([g(x) for x in X_test])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use mean squared error (MSE) to evaluate the neural network\n",
    "def calc_error(w, X, Y):\n",
    "    Y_pred = np.array([f(w, x) for x in X])\n",
    "    return ((Y_pred - Y)**2).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0007839129078666426"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Using the weights returned from lambda = 1e-5, lambda_k = 1\n",
    "calc_error(w, X_test, Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try different values of $N_T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "NT_list = [50 + 50 * n for n in range(6)]\n",
    "errors = []\n",
    "for NT in NT_list:\n",
    "    X_test = random.randn(NT, 3)\n",
    "    Y_test = np.array([g(x) for x in X_test])\n",
    "    errors.append(calc_error(w, X_test, Y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 386,
       "width": 1192
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(20,6))\n",
    "plt.plot(NT_list, errors)\n",
    "plt.xticks(NT_list, [str(s) for s in NT_list])\n",
    "plt.title('Testing error for lambda=1e-5 and lambda_k=1')\n",
    "plt.xlabel(\"NT\")\n",
    "plt.ylabel(\"Testing Error\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try different initializations, different choices of $\\lambda$ & $\\lambda_k$, test on different $N_T$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Training & Tuning**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d774b6ac8d6a4d4b9123c080086b9c5f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda', max=5.0, style=ProgressStyle(description_width='…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bc9ee61af458444b965d1e935db34602",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f2697f58e793429b9800aa8ea25d3693",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "216de59f7dc94ffab0e2f1185c1e615d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  after removing the cwd from sys.path.\n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: overflow encountered in exp\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "aa64579e573141e298b943cd7f0a0044",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "621e7238a3934823b8fdfdaededcf7e5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from tqdm import notebook  # For loading bar visualization \n",
    "\n",
    "lambs = [1e-9, 1e-7, 1e-5, 1e-3, 1e-1]\n",
    "lambks = [1e-6, 1e-4, 1e-2, 1, 1e2]\n",
    "train_errors = np.zeros((5, 5))\n",
    "\n",
    "ws = []  # To store the best weight for each permutation of (lambda, lambda_k)\n",
    "for i,lamb in notebook.tqdm(enumerate(lambs), total=len(lambs), desc='lambda'):\n",
    "    \n",
    "    wss = []  # To store the best weight for each lambda_k\n",
    "    for j,lambk in notebook.tqdm(enumerate(lambks), total=len(lambks), desc='lambda_k'):\n",
    "        \n",
    "        # For each permutation of (lambda, lambda_k), \n",
    "        # I performed three trials with three initializations of w\n",
    "        avg_train_error = 0  # Average error over three trials\n",
    "        min_train_error = 100000\n",
    "        best_w = None  # To store the best weight for each trial\n",
    "        for _ in range(3):\n",
    "            w_initial = random.randn(16)\n",
    "            w, _ = LM(X, Y, w_initial, lamb, lambk, 600)  # Run LM algorithm\n",
    "            temp = calc_error(w, X, Y)  # Training error for this trial\n",
    "            if temp < min_test_error:\n",
    "                best_w = w  # Store the best w among three trials\n",
    "                min_train_error = temp\n",
    "            avg_train_error += temp\n",
    "        \n",
    "        wss.append(best_w)\n",
    "        train_errors[i,j] = avg_train_error / 3  # Average over three trials\n",
    "    ws.append(wss)\n",
    "ws = np.array(ws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best weights after tuning regularization parameters: \n",
      "[-1.26630243e+02  4.68676768e-03 -5.19749477e-02 -7.85426137e-03\n",
      " -1.10956017e-01  7.12899571e+01  1.21802999e-01 -7.27544926e-02\n",
      "  1.27533059e-03  7.16264274e-01 -5.17522579e+01  1.43069443e-01\n",
      "  9.64391942e-02  1.08571561e-03  6.78192026e-01 -2.72481468e+01]\n",
      "The best lambda giving the lowest training error:  1e-07\n",
      "The best lambda_k giving the lowest training error:  0.01\n"
     ]
    }
   ],
   "source": [
    "best_train_error = np.where(train_errors == train_errors.min())\n",
    "best_w = ws[best_train_error[0][0], best_train_error[1][0]]\n",
    "best_lambda = lambs[best_train_error[0][0]]\n",
    "best_lambdak = lambks[best_train_error[1][0]]\n",
    "print(\"The best weights after tuning regularization parameters: \")\n",
    "print(best_w)\n",
    "print(\"The best lambda giving the lowest training error: \", best_lambda)\n",
    "print(\"The best lambda_k giving the lowest training error: \", best_lambdak)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns  # merely for training error visualization\n",
    "\n",
    "def plotErrors(errors, cmap=None):\n",
    "    fig = plt.figure(figsize=(10,8))\n",
    "    ax = fig.add_subplot(111)\n",
    "    sns.heatmap(errors, annot=True, ax = ax, fmt='g', xticklabels=lambks, yticklabels=lambs, cmap=cmap)\n",
    "    ax.set_xlabel('lambda_k')\n",
    "    ax.set_ylabel('lambda')\n",
    "    ax.set_title('Training Errors')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xIQrmiIiIiIiIiIi4EM2ZIyIiIiIiIpLXaWnyPEU9c0REREREREREXIiCOSIiIiIiIiIiLkTDrERERERERETyusSE3K6B5CD1zBERERERERERcSEK5oiIiIiIiIiIuBANsxIRERERERHJ67SaVZ6injkuJDCwFD98/xkHIjcScz6CPeFr+OzTtwkI8L/h5TRsUIcZ00Zz/Og2zp3Zw6aN8+n9wlPky5f2EgoMLMXAAb357dfv2Ll9BZdjD3Ll8iEqVCifbvndHv8fkyf9xM7tKzh9cidno3ezdcsSvh3xMZUrV8iRcylXrgxXLh9K92/c2OE5ci6pjzf0myGE71zFhXN7OXZkG6tWzODFvs9kmve/qHTpkgwd/iE7d6/i+KntbPlnKUM+eoOAgII3rBx3d3ee7dmNYSM+YvmqGZw4vYOzF/by2OMPZXqcRx69j0VLpnDo6BYOHNrMzDnjaNe+pdNjdOwUxtBhQ1i9bg4HD2/myPFtrFo7m9fe6Iuvr0+Gx2nYqA5jxg1j157VHD+1nV17VjN12kjahrXIsG4z54wj8sBGjp74hy3bljBy9NdUqFg+TdqixYrwzruvsnrdHKKO/M2+/RtYunwavfv0yLRu/3WBgaX4/rtPidy3gfPn9hK+azWffvpWttrkay2nQYPaTJs2mqNHtnEmejcbN8znhReedNomN2lSn19+/oq/Ni3gyOGtnDu7h127VjFl8s+0bNnYafl16tzGe+8OYPr0MRzYv4nLcVFE7F2fbn0KFw7giSceYeKEH9m+fQVnz+zhxPHtLF40hW7dHsYYkyZPmTKl+Prr91mxfAYH9m/i/Lm9RO7bwKKFk3nssYdwd3f+e1NwcBDfffspe/es48L5CA7s38SY0UMJDU3/XtG0aQOmTh3JkcNbOX9uLzt2rOCjjwbh739t7YvYuJcsQuBHfQhdPYqqO6ZSedlPlBzUg3wFs95mFOzQmFKDnyH494+45e8JVI+YSZnP+6eb3rN8aYo+cz/lx75P6IpfqLpzKlXWjSHouzfwaXBruvk8ypYg8MPeyXlC146hzFcv4xlSJt08xsuT4n0fpdKCb6m6YwpV1o2l7Dev4lXBeZ4Sr3ZLqdf2yVTZ9CsVZnxFsd6P4Bbgl7ZOpYpS6p3nCJnyGaFrx1B1x1RCV48i+PePCHigDbi7ZfDOSXpKly7JsBEfsWvPak6c3sHW7cv48ONB2XqOuNZy6tW/nUlTfmb/wU0cPfEPq9bOpmevJ5y2yQDly5dl6PAP2b5rBSejd7I7Yi0/j/yKSpVDnKYf8d3HnIuJSPcvvXzt2rXkj+mj2BG+kmMnt/P3tiWMGjOUevVqpUnr7u7Ocz27Mfzbj1mxeiYno3dyLiYiw2ei+g1q8857r7Jk2R9ERK7nxOkdbPlnKd8MG0JISLl08wEEBQXy+Zfv8ve2JRw/tYPIAxtZtGQKz/d+MsN8IpLCWJaV23VwCe6egbn6RoWElGP50mmUKFGMadPnsmvXHurWqUXLlo3ZuWsPzZrfw+nT0TeknE6dwpj4+w/ExsYxYeJ0ok+f4c6ObakSWpFJk2fy8COOwYm77mrHlEk/k5iYyL59ByhcOIBChQIIvaUxe/dGOq3X/D8nULJUcf76ayvHjp4gMTGRqlUr07ZtcxISErj/gSeZ++fi6zqXcuXKsHf3Wjb//Q/Tp89NU4dt/+xiypRZ130uAGFtmzNxwo+4u7sxa/YCdu+OwMfHh9DKFShQwJvmLe9NN++N5OOZP1eOm5ng4CDmLZxI8eJFmTljPrvD91K7Tk2aNW9IePhewto8RPTpMzlejr+/HwcObQbg2LETXL4cT9mypXmh10BGj5qQ7nHee38gL/R5iqioI0z7Yw6enh7cf39HChcpxEv93+KH78Ykp61UOYQNm+Zz4UIMy5etYdfOPfj4FqB162aEVCjH7vAIwto+xOlTaf/9vvRKLwa92Y+TJ08xd85ijh09TpGihalRoyrLl63hzUEfOaT38vJk1JihdLijNeHhe1myeCUXzsdQslQJGjWqwysvv8Ofc1P+HQUFBbJwyRSKFy/KsmVr2LxpK175vWjVqgmVKoewdesO2rS8n9jYuEzf+5vtUnzu1ikkpBxLl/xBiRLFmD59Lrt27aVOndto2bIxu3btoXmLezidhWs2O+V06hTG7799T2xsHBMnzuB09Bk63tmG0NCKTJ48k0cefdYh/aA3+tG9+6OsX/8XUYeOcDHmImXLBtKxY1v8/Hz54IMveevtTx3yfPrpW/R+4SkuX77Mzp17qFGjKlFRRwipUNfpefTo0YVhQz/k8OGjLF26moMHD1G8eFHuuacDAQH+TJkyK829olmzhkye9BPr1v/Fvn0HiD59hsJFCtEurCVBQYEsWbKKDnc8QkJCymSNt91WnfnzJuDvX5BFi1fw11/bKFumFPfc04HLl+Np3+ER1q3b5HCc7t0fZfiwD7ly5Qp//DGHg1FHqFWrOq1aNiE8fC/NW9zDKSf//m6WTYG35dqxs8MzqCQhkz7BvWghzs1bTVxEFN41KuPbqCZxew8S8eArJJw5n2k5FWZ+jXfVEBIuXCT+6CnyVyzLmT8WE9XvM6fpy3z1CgGdmhEbvp+LG7aTcPYCniGBFGxdH+PuxuG3v+P0qBkOefJXq0Dw+A9w8/Phwqq/ubRtDx6lilGwXUOs+CtEdn2DS5t3OeQxnu6UH/s+PnWqcXFLODGrt+BRqij+HZpgxV9hX+fXuPR3uEOeqjunEvvPXuL2HOTKqTPk886Pd61QCtSoTPzRU0Tc35/4IyeT0/vUv5Wg723HvnzwGAlnzuMW4Idvi9p4li7OhdVbiHzsDUhwnV/QGx3bnqvHDw4OYv6iSfb7/zzCwyOoXacGzZs3InzXXsLaPJilNjk75dxxZxvGjh9ObGwcUybPIjr6DB06tKZyaAWmTpnN412fd0hf87ZqzJw9Hn9/P5YsWcXfm7dRJrAUne5ux+XL8dzdsSvr1292yDPiu4/p3OUBhg/7hbNnzqWp93ffjU7zHPH2u6/yYr9nOHXyNDNnzufUqWhCQspxx52tcXd355ke/fn9t2nJ6f39/Th4+G/A8Zno+Z4D0n0m2h2xlqJFC7N2zSY2b97GlStXqFevFg0a1uHChRju6fQY69b9lSZf6zZNGTt+BO7ubsyds5g9e/bh61OASpVD8Pb2pl3bzH9Uu1HOxUSk/fUhD4ldN9Flvvznr/dgnv4scoKCOVmU28Gc2TPHERbWgj5932DY8F+St3/68WD69n2a774fQ6/nB+R4OX5+vuzasRJ/fz+aNb+HjZu2AODl5cWCeRNo2LAOj3Z5jgkTpifnCQwsRXD5svy9ZTvnz19g4fyJNG/eKMMAiJeXF3Fxab+ctWndlLlzfmP7jnBq1HTs9XCt55IUzBk1egJPPvVipu9Vds8lODiITRvmEx19lnYdHmb37giH/e7u7ly5ciVLx89p/9ZgzpQ/fqF1m2a8/NLbfP/t6OTt7w95jedfeJKffxrPi30G5Xg5Hh4eNG/RiK1btnPs2AkGvNabga/1yTCYU6/+7cxfOJGIvftp2fweztgfqoKCAlm6fBoFfApQ9/a2HDhwCIBSpUpwZ8c2jB83hYsXLzkce+z44bTv0Irvvh3NKy+97XCce+7twKgxQ1m8aAVdHu3JhQsxDvudXUeffv4WPZ7uymefDOfddz7n6vb96jxJ6T94/0s+GvJN8vZ8+fLxx/RRNG/RiGd6vMRvv05N/03PJbkdzJk5cyxhbVvQ98VBDE/V/nz88Zv07fM03/8whuefH5jj5fj5+bJj+wr8/f1o3uJeNqVqk+f9+TsNG9ahS5eeTJiY0ian176WLl2StWvmULRoYYJD6nL06PHkfTVrVMUYwz/bw4mPj+dyXFSGwZwWLRrh41OA2bMXOlx3JUoUY+WKmQQFBfK//z3N1D9mJ+/z8PDgypUrTq/T2bPG06JFIx599FkmTZ6ZvG/d2rncdlt1Xnr5Lb7++sfk7fXr386ihZOJjDxIzdtaJV/nJUoUI3zXatzd3Wje4l42bEj5gtSv37N8OOQNRo+ewFM9+jk9r5vB1YI55Ua+g1+z2zn81recHp3y2ZR8/SmKPnkPp8fP4fAbwzItx6fBrcQfPcXlyMP41L+V4F+HZBjMCbi/NbE79hG73fGeWqBedcqPfhcsCG/WnSsnUr7QVpjxFd7VKnDkvR849XPKl1bvWlUI+e1DLkcdY3e7nnAlJWBY9LkHKfny45ydvYKDL3wE9uvTr019yn0/iNjw/ezp8HzydgDj6YF1OT5NnYv370rxXv/j1NhZHHlzREp6D3esKwkOZQDg7kb5Ue/i27AGB57/kHOzV2T6Pv5b5HYwZ+q0kbb7f/+3+C7V/f+DD1/n+Ree5Kcfx/NinzdyvBw/P182b11EwYJ+hLV+iL/+2grYflyZOXsc9RvU5onHezN5Usq/leWrZlCzZjUGvvoew4b+nLy9Xr1azJn3G/sjo6hXp53D/TopmFP9lqbJzxcZKV6iKLt2r+bkydM0rH8HJ0+cSt7XtFkDZs0Zz759B6hZvUXydg8PD1q0bMSWLds5dvQEA1/rw8DX+2QYzOnb7xl+Gz/V4f4B0P+lngx++yX++WcXDet1cNhXvnxZVq6ZxZkz57i7Y1f27NnnsD83n5NBwZx/EwVzMqdhVi4gODiIsLAW7Nt3gOEjRjrse+udT7lwIYYune+nQAHvHC/n/vvupHjxovw+YXpyIAcgLi6ONwd/DMCzTz/mUNahQ0dYsXId589fyPI5OvuiAbBg4XKio89Q8aphTTn1nmQmO+fy5qD++Pn58vwLA9MEcoBcvUH9G5UvX5bWbZqxP/KgQ48WgCHvf8WFCzH87+F7Mv0ss1NOfHw8C+Yv5dixE1mub/cnHwXg00+GJQdyAA4cOMQPP4wlf34vOnd9IHn7kSPH+PGHcQ6BnKRjf/ap7eG+SdP6DvuMMbz9zivExFzkye4vpgnkQNrrKDg4iO5PPsrGDX/zztufpfmC7CxP+fJBAMyZtdBhe2JiYnIPnqJFCzt5F/7bgoODCGvbgn2RBxhxVfvzzjufceFCDJ0fzWKbfI3l3GdvkydMmJ4cyAFbGzr4LVub/PRVbXJ67evhw0dZs2Yjbm5uBAcHOez7e8t2Nv/9D/Hxab+gOrNkySpmzVqQ5ro7duwEP/xg+/fYrHlDh33x8fHpXqfTZ/wJQMWKwcnbg4ODuO226hw7doJvvvnJIc/atZuYMWMelSqF0K5di+Tt7du3wts7P9On/+kQyAH44ovvOH78JA8/fA+FCgVk6Tz/6zzKlsCv2e1cPniU02Mce7Ie/3IcCTGXCLinJcbbK9OyYtZs5XLk4Swf+8zkhWkCOQAX123j4tqt5PPyoEDtWxzq6l2tAldORnPql+kOeS79tZNzC9biFRyIX7PaDvsKP2r74nn0w18cgi3nF6wlZt028lcuh0/96g55nAVyAM7NsgVjvMqXdkwffyVtIAfgSgLn569xmkfSl3T/j4w8yPdX3f8/eO9LLlyI4eFHsv4ccS3l3H1vB4oVK8rkSTOTAzkAcXGXefedzwF48qnODseoWbMax4+fZPiwlAA+wLp1fzFr5gIqVgqmTdtm1/YmXCWobCBubm5sWL/ZIZADsHzZGs6dO5/m/h4fH8/8eUs5djTrz0Rffv5dmkAOwBeff8vFi5eoVi2UwoUd29eBr/fBz8+Xfn0GpQnkgJ6Tb7jERNf5k0wpmOMCWrawzWkwf8GyNA++Fy7EsGrVenx8CtCgfm1n2a+rnKT5FP6c5zjECWDZ8jXExFykYcM6eHp6XvuJZUHjRnUpVCiArdt2Omy/nvekdKkS9HiqCwNefYEeT3Xh1ltvSZMmu9zd3bn/vjs5duwEs+cspG6d2+jTuwf9+z3LnXe0wcPDI8eOlVckfcFbtGiF089y7ZqN+PgUoK6T8d03opzM69sAgAXzl6XZN3/eUoe6ZOaK/YtywlUPLvUb3E754CDmz1vCmeizhLVrQd8Xn+bZnt3Srf/9D3bCzc2N8eOnULCgLw/972769X+Wbk88nO649Z07dgMQdtVcP8YY2obZhjguW7o6S/sZ9q8AACAASURBVOfyX9LC3v4sSK/9WW1rf+rXvz3Hy0lq++bNW5KmvOXL19rb5NpZapOLFStC3bq3ERsbS3j43kzTZ1e8/frO6gN6vnz5aG+/Jrdu25G8vUSJYgDs3x/lNAi0b98BAFq2bJK8raQ9T9K+1CzLYv/+KDw9PWl6VUBVnPNtWBOAC8v/ShOMSIy5xMWNO8hXID8FalW5qfWy7D1rrFQ9bNyLFQLgctRxp4GTyweOAuDTuGbyNs9ypfAMLE5cRBTxUcfS5Dm/dKMtT8OaafY549e6HgCxOyOzlJ58+fBtUefa8kjK/X/h8px5jriGcprb8zh7Jli5Yh0xMRep3+D25Da5uL1NOpBOOxYZaWurWqQzn1nbsBb07fcML/R5ijvtQ2Wd2bs3kri4OGrXqUnhIoUc9jVqXJeCBf1Ysnil07w5wbKs5DY/9VBZd3d37r6nA8ePn+TPPxdTu3YNej3fnd59e9C+fSs9J4tcI61m5QJC7RMAO+vlAbB7zz7CwlpQqVIIixan3yU3O+UkTT68OzxtnoSEBPZFHqB6tSqEhASxc+eerJ9UOu67706qVwvF2zs/lSqF0KF9K06diqbPVV1jr+c9adu2OW3bNnfYtmTJKp54sg8HD2b9V0JnqlcPpUABb9as2cj4cSN46MG7HPbv3x/F/x5+mg0b/76u4+QllSrZJu3bszvtrzNgeyBp3aYZFSuWZ+mSVTe8nIwUKOBNYGApzp+/4LQ3T9LQu9S9CTLS5bEHgbQPgbffXgOA48dPsmzldKpXd/xitGLFWh7r8jynTp5Olcc2Aah/QT82b11MkSIpv7glJiby04/jeOWld0hM9UvHl19+T7sOLRn0Zj+aNWvA35v/wcPTg1atm1CieDFe6DWQLVtyt+v8v1HlTNqfPXsiCWtruyYXZ/CwnJ1yKtsnuQx3kichIYHIyANUS6dNvv32Gtx5Rxvc3d0IDCxFx45hFCzoS98XB92wOWPc3Nzo0tnWU81ZAAqgSJFC9HzuCYwxFC1WmNatm1GpYjC//jqVWbMWJKc7dcp2vQcFBTotJ6l3UWhoxeRtJ+3nVb582TTpjTGUK2eb0Da0ckXgz2s7uf8gzxDbex+3z/m98nLkYWh2O17BpYlZdXPucx6li+HTqCaJF2OJWbcteXtCtK3npEdgcaf5PINKAuCVaiLkLJ0f4BXsvNdMkafuxc3Hm3x+BfC+tRI+datxacc+Tnw70Wl6t0IFKfJYRzDgVtgf3ya18CpfmjPTlnB+0bqMTltSSZr811kvD4C9e5Lu/8EZP0dko5yMnj0SEhLYv/8gVauGUj64LOG79ibPa1M2nXYsqcds5XQmNP7iq3cdXp87d563B3/KD9879iSKjj7L4EEf88GHr7N+45/MnDGf06fPEBwcxB13tmHRwuX06Z35sLPsuve+OyhY0I91azdx9mzKHFpVq1WmQAFv1q37i19Gfc39D3R0yHfgwCEe69zLoeepiKTPpYM5xrY8xq1AFaAQkAAcB9ZblnUkN+uWkwr621ZCOHs27YRnYGvIgUxn689OOUkrfZw953wyw3P2BjrA/9pWb0nP/ffdyf8eujv5dfjuCLp27eUwxAuydy4XL17ivfe/YNq0uUTYf6WtcestvDmoPy1bNmbe3AnUrts2zXCYa1G8WFEAmjVrwKVLsTzVox/Tpv+Jr28Bej7XjZdf6sWM6WOoXqN5rk64+W+S9FmeS+8aO2cb4pbZqjM5VU6GxyiYyTHs/x78/dOuXnK1Dne05onujxAVdYSvvvzeYV+xYkUA25Cu/ZFR3NWxKxvWb6ZsUCDvf/Aabdo2Y9SYb+jYoXOaPK+90Zcli1fxxutDOLA/itp1avLlV+/R4+munDx5mg8/+Do5z8kTp2jT8n6GjfiITne1o3mLRoAt+DNq5O8sWZy9oFde55/c/qR3HdjapYBMrrXslJN0/aZ3DZ5NvgbTHrt27RoMGpQyN8y5c+fp0aM/48ZPzrCe1+P99wdSvXoVZs9ZyPz5S52mKVq0sEO9EhMT+ezzbxk06EOHdLt37yM8fC+VK1egV6/uDBuWMtdE3bq16NQpDIBCqVYBmz9/CfHx8dx1Vztuv72GwxeE3r2fonhxW5tdqFDO3MPyOjc/22pViefTDv0ESLBvz1fQeW+BnGY83Snz5Uvk8/Lk6JCfSTyXUq/L+w4TFxGFV0gZCj/eyWFyZO+alSnYxtYby80/pa7Xe35Fe9yHR7GUXhDnl2wg6pUvSTjt/FnFrVBBivd5NPm1lZjIie8nc+zT0U7Ti3PJ9+Z02tKkZ1j/zJ6Ts1FOVp8LktrxPXv2sTvctvrUs889zrcjRiWnrVOnJnd2bGNLf9VqhitXrmfen0tYv24zJ06cpFSpEnS8K4wBA3vz2RdvEx8fz8hffnPIM3zYL+zfH8XwER/xRPdHkrfv3RPJuLGT0wy/yinlypXhk88GEx8fz2sDP3DYl/Ss0qRJPS5diqXnc68ya8Y8fHx86PFMV17s9wyTpvxEndphTheGkBygpcnzFJccZmWM8TLGvAkcBv4CfgWGA98BU4EoY8xCY4zzmRrTL3djen85fhI5KGnJ1+udzDo75eTUsZN07tITd89AChUJpWmzu4ncd4BlS//gsa7XNqu9s3qdOHGKt97+lL82b+Ps2XOcPXuO5SvW0v6OR1i7dhOVKgXzZPdH0ysyS9zcbMuJuru78/obQxg56neio89w8OBhBr72AVOmzqJYsSI89WTnTEqSJEkzn1339Z1D5WRFZoeoV/92fvz5C2JiLtK1c0+HuXcg5ToyxvBYl14sXbKKmJiL7Nyxm86PPEtU1BGaNm3g0NU7Kc/Royfo/Miz7NgeTkzMRZYtXc1jXXqRkJBAr+e7O3RhDgoKZPafv1G1aij339udMqVqUimkPv36vsmDD93F4mVTk3suSNaltD83v5yM8vzww1g8vcrgV7ACNWq2YNToCfzyy1cMHTrk+iqajl69utPvxWfZuXM3TzzRJ910u3btxdOrDPm9g6hQsR4vvfw2Tz35KIsWTk4zl03PXgOIjY3li8/fYfbs8QwZ8gZjRg9l0cJJ7LAPG0zdpf/AgUO8/faneHp6snTJVMaMHsqQIW8we/Z4Pvl4cHLPs9R5JPuSl6C/GYtr5MtHmc/641OnGmdmLOPkD1PSJDn8+jAS4y5TevAzlB/9LiUGPEGZr14m+LePiN1z0JboGlaMMmR8frvqd2VbSEd21OvC/mffxzOoJBVnfEX+ahWcpr8cEcW2kI5sq3gXu5o8wdH3fqTwI+0J+e0jhyCTXJ9/23Nyn96vExsbx8efDuaPGaN59/0B/DzyK+bM+y25R+XVbdLY0ROZOmU2UVGHiYu7TGTkQYZ+/RNPPWFb0OPNwf3TLIPe58WnGTNuGOPGTaZGteaUKFqVpo07ERl5gJ9++ZJ33nv12t+ETBQtVoTJU3+hWLGivPryu6xb67i6YOrn5LcHf8LY0ROJjj5LVNRhBg/6iGl/zKVosSJ0e+LhHK+bSF7kcsEcY4wXMB94CygOJK31aIB/gN+BA0BLYKUxpmsuVDNHncvgl1Ygebxser/uXk85ST1f/As672ngZ/916uw55786Zdf58xdYvWYDd9/bjV3hexk29AMCA0sl78+p9wRsN8yffh4PcN3zJkRHn03+/z+mpV3+PGlb3bqutXrJjZT0WRbM5BpL71evnC4nw2Ocy/gYmfUOAqhbrxaTptiWu7//3u5s2pi2K/GZM7brKHLfQbZdNV9UbGwcixbYhmXVrlMzTZ6F85elWUp827ad7I+MomBBP0JDU75UDP/uY6pXr0LXzj1ZMH8p589f4Pjxk/zy86+8+87nlChRjFcH9k73XP6rzmbSA8vPfn1k1i5mp5ykNjndazD5Ok//2HFxcezcuYf+/Qfz/Q9jeLpHV+67984M63qtnn32cb74/B22b99F27CHiI7OfEngxMREDh48zNChP9Gr1wAaNKjN4MEvOaRZtmw1jRt3YtKkGdxa/RZeeL47derexpAhX/PW258AcOLESYc8H38yjPsf6M7q1Rtp374VPZ/rRqEAf7p06cncuYsAOH5VHnEuuWeKvQfL1fL5FgDS79mSY/Llo8wX/fG/sylnZy4jqt+nTpPFrN3K3nv7cXbWcvJXKU+RbndRoEZlTgz7neOf24alXDmVcm1men5+WTu/hJNnOD9vNZGPDcItoCBlPs1ktbTEROIPn+DUyOkcfn0YBW6vQvEXu2ScR5Il35vTaUsL2p8J0+txcz3lZPZckPKcnJJnxfK1tGx+L1Mmz6J69So817MbtWvX4JOPhvGefdLkE1nsNTN37iIOHTpC0WJFqHJLpeTtTZrW5933BjB71kJeG/A+kZEHuXQplr83/8OjDz/LoUNHeKH3U06HoGZX0WJFmDl7LJVDK/DKS2/z4w9j06Q5k+o5ecb0eWn2z7RPfl+7do0cq5dIXuZywRzgFaAJMBTwtyyrBOAPfAPcAvxoWVYw0B5bz52fjDHV0yssNcuyaqf3d2NOJWt22SemTBqXe7VK9vk50pt34XrKSZoUs5KTsbtubm4Elw8iPj6eiIi0k0vmhPj4eBYvWom3t7fDJKA59Z4kOXHSdtP0KVDgeqqbXC9I+XKdWtJNzDv/v3OJ8NyQ9BlVrOR8npkK9pXM9uyJvCnlZOTixUscOnQEPz/f5MlYnR/D+Xj7ho3qMOWPX7Asi3vv7sbaNc47/SWdS3rDCJN68njn90qVZ18meWzXXn5v27Xn6+tD06YNOH0qmn/+2ZUm/XL7xMe31cpS8/mfEp5J+1OxYnkg8/YnO+WE2+cvq+wkj5ubG+WvsU3+80/b5PZZnbQ7K1544Um+/up9tm3bSduwh65ptbgkc+31at6sQZp9W7ft4NHOz1E2qBa+fiHccksTPhjyFbfXsj38b9iQdq6WGTPmEdbuIYoVr4p/QEUaNrqTCROn06BBnXTzSFqXI2xLIqc3Z4ynfQWm9OacyRFu+Sj71csEdGrOmWlLONj30wx718TtjOTgCx+xs15Xtle5l/CWPTgx9De8b7XNrXRpy+7ktDl9fvGHTxC35wD5Q8vhVihrQ3zPL90AgE/9W7OUXlLmdUxvvroK9rY0vXvz9ZST0bOHm5sb5cqVJT4+nsh9Bx32/bNtJ90ee4GKwfUoWqgKNW9tyccfDaVWLdvn7uyHnvSctM+f55Nqla32HVoBsHxZ2kUMLl2KZeOGLbi5uVGjZrUsHycjJUoWY/ac8VSpUol+fd90GD6WWur7mbPnlTP2ua68vfWcLJIVrhjMeQRYa1lWb8uyLgBYlnXBsqw+wAZgkH3bPKA1cAV4ObcqmxOWLLXNW9G2TbOULsx2vr4+NGpUl4sXL7FmbcajwbJTTtKkm+3CHFe7AWjWtAE+PgVYvXoDly9fvvYTy6LSgbZJClOvhJJT70mSBvZAUYSTFU+uRXT0Gf7abJuAsXq1tKt5VKsWCkDk/qjrOk5esnyZbRnWVq2aOP0s6zeozcWLl1i/7q+bUk5mli21HcfZsqFtw5rb06R9eGrWvCGTpvxMwpUE7r3rMTas35wmTZKVK9cTHx9PSIXyTld2uKVqZcA2hCRJ0mSMSftS8/T0JMQeaDpgv/Y8PG3l+hX0dXqMovZx7fHpLLn7X7bU3v60Sa/9aWhrf9Ze1b08J8pZvMTWJoeFtUhTXtOm9e1t8sYst8mlS6dtX6/HS/178tmnb7N58zbahj2Y5V+XrxaYXK+sDX/y9PSkc5f7SUhIYMLE6ZlnAEJDK9C4cV0i9u1nTTqBVXEUs8b2BdO3aS246prN5+NNgdq3kHgplot/7XSW/boZD3eChg3E/86mRE9eSFS/z7K1fK3xdCfg3lZYCQmcnZkyAf3l/Ue4fOg4XiFl8ChTIk0+v+a23/ZiVmc9+OdRwjYZvZXFoXweJYpcU3pJdf9v3TRnniOuoZyl9vu9s2eCxk3q4eNTgLVrNmWpTfb09OThR+8lISGByZNmZpoebD2CKleuQGJiIvsPpDxbetlXz7p6+fEkSdtz4vm9dOmSzJn7G5VDK9C39xtOe+QkiY4+y99//wNAVSfPK7dUs23bv/9Qmn2SQ3J7uXEtTZ6jXDGYEwykt2TTSqBO0gvLsvYCM7ANuXJZERH7mTdvCcHBQfR8rpvDvrfefAlfXx/GjJ2UPHGvu7s7oaEV0ixHfK3lAEyeMosTJ07xv4fuovbtKV0evby8eOftVwD49vvrm6ivcOFCaVbrSXLnHW245+72nD9/gWX2m2x2z6Ve3VpOv7S2bNGYPr17ADB+fNox99dqxIiRALz7zqt4eaX0nAgMLJV8nAkTpl33cfKKffsOsHDBMsqVL0uPZxxHRQ58vQ++vj789utUh+u7UuWQ5JVrsltOdv38k21I3ksv93KYYDsoKJAePboQGxvHuDGTHPK0atWE3yf+QFxcHHd17MqmTVszPMbpU9FMmTyLgICCvDrwBYd9LVs2pnWbppw5c44FqSaUnT9vKfsi9tO6TVNaXrWk6SsDnicgoCDLl6/h+HHbcJLo02fYuXM3Hh4evDLgeYf0Xl6evPRKL4Bsr/yVl0VE7Gfe/CUElw/iuavanzff7I+vrw9jx2WxTb6GcgCm2Nvkhx66K3nVM7C1yW+/ZWuTv7+qTW7atEGaLyYAISHlGPCqbRjdnDkLr+1NcOK1gX344IPX2Ljxb9q1fzjTSd7r1q3l9NdXH58CfPb5207rVaCAd5p5Idzd3Rn6zQcElw/iu+/HEBGx32G/s6V7ixUrwuhRQ3Fzc+P11z64KXNp5QWXDxzl/LJNeJYtSeGujkPzivftjJuPN2emLsa6ZB/q6e6GZ0iZ5JWjrofxdCfo29cpGNaQ07//yaFXvsx0bh7j7QVXXS+4u1H63V54li3J6XFzkpcoT3J6/BwASg54wiFg5demPj71qhMbvp+YtSmrZnmGlMG9qOPcTraDG4r374p70ULEbNjuMDmzd83KmFQ9K5PkK5CfUm8+DcD5xeszPDdJkXT/L1++LE9fdf9/7Y2++Pr68Ov4rD9HZLUcgGlT53DyxCnuf6Bjcq8asN1HB71pG17304/jHMpKrx374qt3KV++LD/9MI59qX5cLF6iaJr7B9jayhHffYy3d36WLF7J8WMpw0VXrbJdP926P0KpUo6BybZhzWnQsDaXLsWmmdPmWpUpU5o5f/5KcEgQvXoOSDMJszM/fGcb4jjorZfw8vJM3l66dEl6Pd8dgMmTZjjNKyKOjKs9wBhjooGplmV1d7LvZ+BBy7L8Um17H+hvWdZ19ddz9wzM1TcqJKQcy5dOo0SJYkybPpedO3dTr+7ttGzZmF3he2na7G5On7Y9OJcrV4a9u9cSGXmQipUbZLucJHfd1Y4Jv31PbGwcv0+YRnT0GTp2DKNKaEUmTZ7Jw488k6a+P/34RfL/twtrQcmSxZkydRbn7ePMf/55PCvtN5qaNauxcf08Nm7awvbt4Rw+fAR/f39uq1mNBg1qc/nyZR5/og8Tr/q19VrPZeH8iVStGsrSZas5FGVb7OzWW2+hVasmALw5+GM+GPLVdZ0L2Ca7mzjhB+65uwO7wvcyb94SfHwKcPdd7SlSpBBff/Mj/foPdvo532g+nv/ObqvBwUHMWziR4sWLMnPGfMJ37aFO3dto1rwhu8MjaNvmQaJP2+Y1CAoKZOv2ZezfH0WNas2zXU6SF/s9QyX7EtG31riFGjWqsmb1xuRlxtes3sDoURMc8rz3wUBe6P0UUVFHmPbHHDw9Pbjv/jspUqQwL/V/K/lBBWxdr1esmom3d36m/TGH7dvDnb4HqVeZAlvPmHnzJ1ChYnlWrlzHpg1bKBtUmo6dwrAsi6e6v8gfU+c45GnQsDZTp43C09ODmTPmcfDAYWrVvpUmTepz4sQp2rV9iL2phpm1aNGICZN/xMvLi/Xr/mLt2k14e+enTdvmtnZkTyStW92f5j37N7gUH5d5ohsoJKQcS5f8QYkSxZg+fS47d+6hbt1atGzZmPDwvTRrfjen7e9buXJl2B2+hsjIg1QObZjtcpLcdVc7fvv1O2Jj45gwYbq9TW5LaGhFJk+eySOPPuuQ/vixfzhz5hzr1//FwajDuLu7UyGkHGFhLfDw8GDosJ/p1+9NhzyhoRV4+aVeya8fe+whYmIuMnlyyq/Frw54Nzlg07XLA/z005dcuXKFYcN/cTo3ReT+g4wZk7JE86SJP9KsWUOWL1/DgYOHuXTxEmXKlKZduxYUKhTAqlXrubNjZ2JiLibnueOO1nw74hMWLVpBVNRh/Ar60r59K4LLBzFr9gIefvgZ4uIcr40PP3yDdmEtWLNmEydPnrIvy96WgAB/3nrrE6ft/s20KdC15lDzDCpJyKRPcC9aiHPzVhO3NwrvmpXxbVSTuIgoIh54mYQzts/fI7A4oct/5nLUMcKbPelQjl/bBhRsa3tGcS9WCL/mtbm8/wgx622/2idEn+PokJQVywI/7kOhB9py5dRZTo+bBU6eymLWbCVmbUqw3K9VXUoP6U3Mys3EHzlJPl9v/FrUwbNsSc4tWsfBnkOwrup9aDzdKT/2A3zqVOXilnBiVv2NR+li+HdoghV/hX2dX+PS3ynteJEn7qLkgO7ErP+Hy/uPkHDmPO5FA/CpVx3PcqWIP36ayC6vE7cnZZhN0Lev49PgVmLWbiP+8AkSY+PwKFUUv+Z1cPP3JWbDdvZ3e5PEi7HZ/JRuvkbHtufq8YODg5i/aJL9/j+PXbv2UqduTZo3b2S7/7d+ILktDQoKZNuO5ezfH8WtVZtlu5wkd3Zsy5hxw4iNjWPypJlER5/hjjvaUDm0AlOnzObxro4/mLRv34pvhg9hyeKVREUdoaCfL23btaB8+bLMnbOIrp17EheX0mOmSdP6zJ77K2vXbGTXrr2cOHGK0qVL0LJVE0qWLM6+iP3c2aEzUVEpw/+MMUydPopWrZpw7tx5Zs6Yx7FjJwkNrUD7Dq3Ily8fr778DiOGj3So24v9n01eFv3WGlXtz0Qbkp+JVq9yfCba8s9Sypcvy6ZNW/lzziKnn824sZMcehIbYxg7fjid7mrH7vAIFi5YRgGfAnTs2JbCRQoxYvgvvPryu07LuhnOxUSk/fUjD4ldOc5lvvznb9w5T38WOcEVgzmLgNpADcuy9qfaXg7YAvxjWVajVNuHYwvwpJ3g4hrkdjAHbNHvtwa/RLuwFhQpUogjR44zbfpc3n3vC4fJJTMK5lxLOak1aliHgQN606BBbfLn92LP3khGjvydb4b+RKKTbnBXLmfcPbL7ky8yeoztZhAQ4E//fs/StEl9KlQoT5EihYiPv8KBg4dYtmwN3wz9MXl2/+s5lye6Pcw9d3egWrVQihYtjIeHO8eOnWTN2o0MH/4LK1auc3qMazmXJG5ubvR8rhuPP/4/KlcKITExkS1btvPt96NzpPdPdv1bgzlg67n02ht9adO2GYULB3D06AlmzZzPR0O+dphYOqNgzrWUk2TmnHE0bZr230mScWMn0/PZV9Jsf+TR+3j6ma6EVqlIYmIif//9D19/+QN/zl3skK5J0/rMmjM+0/P390272kmhQv689EovOnUKo1TpElw4H8Pq1Rv4/LNv0x2mFVqlIgMG9qZpswb4+/tx/Pgp5s9bwscfDuXw4aNp0lerFkrvvj1o3KQ+JUoUJSEhkcjIA8yeuYCvvvw+S5OI54bcDuYAlClTisFvvkRYqvZn+ow/ec9Jm5xeMOdaykmtYcM6DBjQmwb1byd//vzs3RvJyFG/MXToz2na5Oeff5I2bZpRrWooxYoVwc0tH8eOnWT9+r/4+ZdfnS4Z3qxZQxbMn5hme2qVKjdgv33Y3qA3+jksL+7M0qWraRv2YPLrDh1a8fD/7qVOnZoUL16UAgW8iY4+y9ZtO5g0aSYjR/6WZkWXSpWCee/dgdSpcxvFixfh0qVYtmzZwajRvzN27CSnPWw6dGhF3z7PUK1aKAEBBYmOPsvq1Rv46usfWJlOu38zuVowB8CjVFGKv9gZ32a1cQvw48qJaM7NW8OJr8eTcPZCSroMgjnF+zzqsCz31a7OEzx+CD4NMp5H5vhX4zn+VUp76xlcmhIvP06BGpVxKxKAFRdH7I59RE9awJkpi9Lt2WO8PCn23AP439UCj1LFSLxwkZi1Wzn+5TiHoAyAV+VyFO7cgQK1q+JRsghuBX1JvBRL3L5DXFi8gVMjpzu8JwC+LesQcFcLvGtUwr1oAPnye5Fw9gKxuyI5O2s50RPnX9MqW/8GuR3MAdv9//VBL151/5/Hhx+kfY5IL5hzLeWkVr9BbV5+pRd169Uif34vIiL2M3b0REYMH5mmTa5YMZjBb79M7To1KFasCJcuxbFt6w7Gjp3Er+OmpGnHAgNL8fKrvbi9dg3KBJbCP6AgFy/Gsmd3BLNmzufbEaO4cCHtpNzu7u48/UxX7n+gI6FVKtrb2DNs3LCFb0eMZNHCtAMdZs0ZT1Mnc5UlGTd2Es89k/JMdC4m87kp72j/CCuWr3XY5ubmxtPPdKVz1weoWDGYxMREtm3dwU8/juP333K393qeD+YsH5Pr32mzKn/Trnn6s8gJrhjMuReYDEQDPwD7sA29egooBDxpWdbIVOnXApcty2p6Pcf9NwRzRK7XvzmYI3It/g3BHJGc4IrBHJGr/RuCOSI5QcGcfw8FczLnntsVuFaWZU21D516jZSJjZM+6G+vCuT4AfuxzZsjIiIiIiIiIuLyXC6YA2BZ1iBjzGTgXqAkcBKYaVnW6qvSnQceyoUqioiIiIiIiPxrWJZWystLXDKYA2BZ1mYg/bV9RURERERERETyIFdcmlxERERERERE5D/LZXvmGGN8gAeAVkBlIADbQpVngXBgITDFsqwL6RYiIiIiIiIiyFtAEgAAIABJREFUIuJiXDKYY4zphG0lq2KkTH6cWn2gC/CRMaaHZVkzb2b9RERERERERP5VEhNzuwaSg1wumGOMaQhMARKAscAcYDe2HjkGKAhUAu7ANvnxFGNMU8uy1uZOjUVEREREREREco7LBXOAN4BLQEvLsjamk2Yj8Jsx5htgkT1Pp5tUPxERERERERGRG8YVgzkNgN8zCOQksyxrvTFmAnDPja+WiIiIiIiIyL+UpWFWeYkrrmblDZy+hvQngfw3qC4iIiIiIiIiIjeVKwZzdgOdjDGemSU0xnhhG16154bXSkRERERERETkJnDFYM4vQBVggTGmmTEmzTkYY/IZY5oDC4BQ4OebXEcRERERERERkRvCFefM+RpoDNwPLAYuGmMisK1mBeAPhAAFsK1uNQn4JhfqKSIiIiIiIvLvoKXJ8xSXC+ZYlpUIPGiMeQR4DmgI3HpVsgRgBTDCsqzfbnIVRURERERERET+z959x1VZ/n8cf1+C4N4zDfcoG5aa4gIHaK6GlZqj4ajMWaZpamZZ2fo11Cy/5c6dKe69c6el5kJxbxQXIMr9++MAcuAARwHxnF7Px4MHD+77vsatF4f7fM51fa5043LBnFiWZU2RNCUmd05Z2WbkSLYZOgcty7qRYZ0DAAAAAABIJy4bzIkVE7TZk9H9AAAAAADgvsXW5G7FFRMgJ8kY85gxpkNG9wMAAAAAACC9uFUwR9Jzsu12BQAAAAAA4JZcfpkVAAAAAABIAbtZuRV3m5kDAAAAAADg1gjmAAAAAAAAuBB3C+aESTqa0Z0AAAAAAABIL26VM8eyrG8lfZvR/QAAAAAA4L7C1uRuxd1m5gAAAAAAALg1lw/mGGMyGWO6G2M2GmPCjDE34517whgzyhhTPiP7CAAAAAAAkFZcepmVMcZL0kJJ/pJCJV2RlCPeJYclvS7pnKQP73X/AAAAAAC4L7A1uVtx9Zk570mqJ+kjSYUl/S/+ScuyLklaI6nRve8aAAAAAABA2nP1YE5bSestyxpqWVa0JMvBNYcl+dzbbgEAAAAAAKQPVw/mlJK0MYVrQiXluwd9AQAAAAAASHcunTNHUrikPClc4yPp0j3oCwAAAAAA9ydy5rgVV5+Zs0NSYEwi5ESMMblly5ez+Z72CgAAAAAAIJ24ejBnjKQHJU02xuSKf8IYk0fSOEl5JY2+910DAAAAAABIey69zMqyrCnGmIaSXpPUQtJFSTLGbJVUSZK3pJGWZS3IuF4CAAAAAJDBLJZZuRNXn5kjy7I6Snpd0h5JBSUZSU9KOiipo2VZ3TOwewAAAAAAAGnKpWfmxLIsa5ykccaYrLItqwqzLOtaxvYKAAAAAAAg7blFMCeWZVnhsu1wBQAAAAAAYrGblVtx+WVWKTHGfGmMCc7ofgAAAAAAAKQFtw/mSCogqWRGdwIAAAAAACAt/BeCOQAAAAAAAG7D5XLmGGMm3GGRmunSEQAAAAAAXAVbk7sVlwvmSGonyZJtC3JnWenUFwAAAAAAgHvKFYM5VyQdl9TVyevflxSYft0BAAAAAAC4d1wxmLNT0uOWZa125mJjzKvp2x0AAAAAAO5zbE3uVlwxAfIOSTmMMWUyuiMAAAAAAAD3mivOzFktqY6k4pKCnbj+D0kh6dkhAAAAAACAe8XlgjmWZc2SNOsOrp8jaU769QgAAAAAAODecblgDgAAAAAAuENsTe5WXDFnDgAAAAAAwH8WwRwAAAAAAAAXwjIrAAAAAADcHVuTuxVm5gAAAAAAALgQgjkAAAAAAAAuhGVWAAAAAAC4O5ZZuRVm5gAAAAAAALgQgjkAAAAAAAAuhGAOAAAAAACACyFnDgAAAAAA7s6yMroHSEPMzAEAAAAAAG7HGFPcGPOrMeakMSbSGBNijPnWGJPXyfL5jTGdjDGzjTEHjTHhxpgwY8w6Y0xHY0ySMRVjTE1jzAJjTKgx5rox5m9jTC9jjEda3BszcwAAAAAAgFsxxpSRtEFSIUlzJO2V9JSknpIaG2NqWZZ1IYVqXpT0o6RTklZKOiqpsKTnJf1P0tPGmBcty37akzHmGUmzJEVImiYpVFJzSf8nqVZMvalCMAcAAAAAAHf339uafJRsgZwelmX9EHvQGPONpN6Shkl6M4U69ktqIWm+ZVlx/4DGmAGSNktqKVtgZ1a8c7kkjZF0S5K/ZVlbY44PkrRC0gvGmNaWZU1Nzc2xzAoAAAAAALgNY0xpSYGSQiSNTHD6Q0nXJLU3xmRPrh7LslZYlhUUP5ATc/y0pNExP/onKPaCpIKSpsYGcmLKREgaGPPjW07fTBII5gAAAAAAAHdSP+b7EgeBmCuS1kvKJqlGKtqIivl+M4m2Fzkos0bSdUk1jTHeqWibZVYAAAAAAOD+YYzZltQ5y7KqOFFFhZjv+5M4f0C2mTvlJS2/s95JxhhPSR1ifkwYtEmybcuybhpjDkuqJKm0pH/vtO1YBHMAAAAAAHB3/62cObljvoclcT72eJ67rP9zSY9IWmBZ1uJ73LYkgjkAAAAAAOA+4uTsm9QwsU3dcUFjekh6V7bdsdrfy7bjI2cOAAAAAABwJ7GzX3IncT5XguucYox5W9J3kvZIqmdZVui9ajshZuYAAAAAAODurP/UMqt9Md/LJ3G+XMz3pHLqJGKM6SXp/yTtktTAsqyzybRdNaZtu9w/Mbl2SsmWNPmQs207wswcAAAAAADgTlbGfA80xtjFPYwxOSXVkhQuaaMzlRlj+skWyNkh24ycpAI5krQi5ntjB+fqyraL1gbLsiKdaTspBHMAAAAAAIDbsCwrWNISSSUlvZ3g9EeSskuaYFnWNUkyxmQ2xlQ0xpRJWJcxZpBsCY+3yTYj53wKzc+UdF5Sa2NM1Xj1ZJH0ScyPP97xTSXAMisAAAAAANzdf2s3K0nqKmmDpO+NMQ1k2wa8uqR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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 495,
       "width": 569
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot training errors in a heatmap \n",
    "# To better visualize different permutation of lambda and lambda_k\n",
    "plotErrors(train_errors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Test the best regularization parameter on test sets with different size**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [],
   "source": [
    "# NT from 50 to 300 with a step size of 50\n",
    "NT_list = [50 + 50 * n for n in range(6)]  \n",
    "\n",
    "errors = []\n",
    "for NT in NT_list:\n",
    "    X_test = random.randn(NT, 3)\n",
    "    Y_test = np.array([g(x) for x in X_test])\n",
    "    errors.append(calc_error(best_w, X_test, Y_test))  # Use the best weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 494,
       "width": 900
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(15,8))\n",
    "plt.plot(NT_list, errors)\n",
    "plt.xticks(NT_list, [str(s) for s in NT_list])\n",
    "plt.title('Testing error for the best weights found with lambda=1e-7 and lambda_k=1e-2')\n",
    "plt.xlabel(\"NT\")\n",
    "plt.ylabel(\"Testing Error\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Testing Error:  0.0017187574459052715\n"
     ]
    }
   ],
   "source": [
    "print(\"Average Testing Error: \", sum(errors)/len(errors))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary & Comments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**To reiterate**:   \n",
    "$\\lambda$ is the regularization constant for the weight itself, to prevent the weights from blowing up.   \n",
    "$\\lambda_k$ is the regularization coefficient to control how big of a jump the algorithm make from one iteration to the next.   \n",
    "$\\lambda$ is constant across one run of the LM algorithm while $\\lambda_k$ is updated during each iteration in a run of the LM algorithm.    \n",
    "\n",
    "**Error Metrics**  \n",
    "I used Mean Squared Error (MSE) to evaluate the trained neural network. It's defined as $$ \\frac{1}{N} \\sum_{n=1}^{N} \\left( f_w(x^{(n)}) - y^{(n)} \\right)^2 $$ And it's defined as function calc_error at the very top of this section.   \n",
    "\n",
    "**Training Method**  \n",
    "I tried $\\lambda$ from $10^{-9}$ to $10^{-1}$ with a multiplication step of $100$, along with $\\lambda_k$ from $10^{-6}$ to $10^2$ with a multiplication step of $100$. In addition, I performed three trials per permutation of $\\lambda$ and $\\lambda_k$ because I initialized the starting weights using random numbers of normal distribution. To avoid bias, three trials of random initializations were conducted every permutation and the training error was averaged over three trials, such that the training is more reasonable since it won't be affected by a single \"bad\" starting point. \n",
    "  \n",
    "I also tried warm starting to start the LM algorithm at the solution of the previously solved problem, i.e. the minimzer w of the previous run of the LM algorithm. However, the training errors were close to each other for different permutations of $\\lambda$ and $\\lambda_k$, which was not ideal to tune and pick the best regularization parameters. Although warming start greatly reduce the number of iterations required to converge, it didn't provide much helpful insight into our parameter tuning.  \n",
    "  \n",
    "In short, as above I have conducted a tuning of our regularization parameters with $5*5*3=75$ iterations, with $25$ permutations of $(\\lambda, \\lambda_k)$ and three random initialization trials for each.   \n",
    "\n",
    "**Training Results**  \n",
    "I have found that the lowest training error $0.001066$ was given by $\\lambda = 10^{-7}, \\lambda_k=10^{-2}$. I also stored the best weights among the three trials with that initialization of $\\lambda$ and $\\lambda_k$.   \n",
    "Additionally, In the heatmap drawn, we can find a trend that smaller $\\lambda$ and larger $\\lambda_k$ give smaller training errors, while larger $\\lambda$ and smaller $\\lambda_k$ give bigger training errors.     \n",
    "  \n",
    "**Testing**  \n",
    "Since I found the best weights, I just evaluate our simple neural network with the best weights found on test sets with different sizes, i.e. $N_T$. I tested it on $6$ different $N_T$, from $50$ to $300$ with a step size of $50$. The testing errors versus $N_T$ has been plotted. Finally, I averaged over six errors and gave the final testing error: $0.001718757$.    \n",
    "  \n",
    "**Comments on my results**  \n",
    "I believe I have conducted a thorough tuning of different initializations of $\\lambda$ and $\\lambda_k$. I tried five different $\\lambda$ with another five different $\\lambda_k$. Plus, to avoid bias when randomly initializing the starting weights, I performed three trials per permutation. I also tried warm starting but the result did not help much with finding the best parameters. I tested the best weights found on six sets of test points with different $N_T$, as required. Finally the average testing error of the best weights is $0.00172$, a little higher than the training error $0.001066$, which is reasonable and intuitive. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Different Non-linear Function $g_2(x)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The non-linear function I chose is: $$g_2(\\textbf{x}^{(n)})=\\left(x_1^{(n)}\\right)^2+x_2^{(n)}+x_3^{(n)}$$\n",
    "$$y^{(n)} = g_2(\\textbf{x}^{(n)}), n = 1,2,\\dots, N$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Code Re-use**  \n",
    "Since I implemented my LM algorithm by modular programming, i.e. with independent, interchangeable modules, I can re-use most of my code without modifications. For example, my $f_w(x)$, $r_n(w)$, $l(w)$ are all independent of the non-linear function $g(x)$ to approximate. The only thing I need to take care of besides just copying and pasting is to find a reasonable max_iteration and threshold for the \"small residual\" stopping criterium. Therefore, below I will first try a few initializations of $\\lambda$ on $g_2$, and observe a few things:  \n",
    "- Check if our simple neural network $f_w(x)$ is able to handle the complexity of the new non-linear function $g_2$  \n",
    "    - i.e. see if the LM algorithm is able to converge with a reasonably small \"small residual\" value  \n",
    "- If it's able to fit $g_2$, empirically choose the new \"small residual\" threshold for the LM algorithm ($0.5$ for $g$ before)  \n",
    "- If it's able to fit $g_2$, empirically choose a number of maximum iteration for the LM algorithm ($1000$ for $g$ before)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Different Non-linear function to approximate\n",
    "def g2(x):\n",
    "    return x[0]**2 + x[1] + x[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 500\n",
    "X2 = random.randn(N, 3)\n",
    "Y2 = np.array([g2(x) for x in X2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_initial = random.randn(16)\n",
    "w, losses = LM(X2, Y2, w_initial, 1e-5, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 395
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Training loss curve')\n",
    "plt.xlabel('iteration')\n",
    "plt.ylabel('loss')\n",
    "plt.plot(losses)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try different initializations & effect on final model training loss error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_initial = random.randn(16)\n",
    "w2, losses2 = LM(X2, Y2, w_initial, 1e-6, 1)\n",
    "w_initial = random.randn(16)\n",
    "w3, losses3 = LM(X2, Y2, w_initial, 1e-7, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 386,
       "width": 618
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title('Training loss curve for different lambda but same lambda_k=1 on g2(x)')\n",
    "plt.xlabel('iteration')\n",
    "plt.ylabel('loss')\n",
    "plt.xlim(0, 55)\n",
    "plt.plot(losses)\n",
    "plt.plot(losses2)\n",
    "plt.plot(losses3)\n",
    "plt.legend(['lambda=1e-5', 'lambda=1e-6', 'lambda=1e-7'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observation**  \n",
    "Using the threshold 0.5 as I used for $g(x)$, the LM algorithm successfully converged for $g_2(x)$ as well and actually faster. Therefore, I will decrease the max_iteration argument to $200$ and keep the same thresh argument in my LM algorithm when varying different $\\lambda$ and $\\lambda_k$ below. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try different initializations, different choices of $\\lambda$ & $\\lambda_k$, test on different $N_T$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Training & Tuning**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3d8d64f4a2504123aff81a7305d79a0b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda', max=5.0, style=ProgressStyle(description_width='…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0c4cf3536cbe4e2b98259dffba736656",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b25b9feebe5b40848f9128812b4e17cf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a708e08ba72349b0ab5b1c0e762704e5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: overflow encountered in exp\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "682d52b005304aafab43e8d23650271b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e949b9ff1aaa406eaf6467f622592d7d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, description='lambda_k', max=5.0, style=ProgressStyle(description_width…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from tqdm import notebook  # For loading bar visualization \n",
    "\n",
    "lambs = [1e-9, 1e-7, 1e-5, 1e-3, 1e-1]\n",
    "lambks = [1e-6, 1e-4, 1e-2, 1, 1e2]\n",
    "train_errors2 = np.zeros((5, 5))\n",
    "\n",
    "ws2 = []  # To store the best weight for each permutation of (lambda, lambda_k)\n",
    "for i,lamb in notebook.tqdm(enumerate(lambs), total=len(lambs), desc='lambda'):\n",
    "    \n",
    "    wss = []  # To store the best weight for each lambda_k\n",
    "    for j,lambk in notebook.tqdm(enumerate(lambks), total=len(lambks), desc='lambda_k'):\n",
    "        \n",
    "        # For each permutation of (lambda, lambda_k), \n",
    "        # I performed three trials with three initializations of w\n",
    "        avg_train_error = 0  # Average error over three trials\n",
    "        min_train_error = 100000\n",
    "        best_w = None  # To store the best weight for each trial\n",
    "        for _ in range(3):\n",
    "            w_initial = random.randn(16)\n",
    "            \n",
    "            # Run LM algorithm with a smaller max iteration (explained above)\n",
    "            w, _ = LM(X2, Y2, w_initial, lamb, lambk, 200)  \n",
    "            temp = calc_error(w, X2, Y2)  # Training error for this trial\n",
    "            if temp < min_test_error:\n",
    "                best_w = w  # Store the best w among three trials\n",
    "                min_train_error = temp\n",
    "            avg_train_error += temp\n",
    "        \n",
    "        wss.append(best_w)\n",
    "        train_errors2[i,j] = avg_train_error / 3  # Average over three trials\n",
    "    ws2.append(wss)\n",
    "ws2 = np.array(ws2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best weights for the neural network to fit g_2: \n",
      "[ 7.79713407e+00 -5.88474221e-01  2.59440650e-03  4.72935879e-03\n",
      " -1.51180223e+00 -7.59468597e+00 -5.90099612e-01 -1.15932515e-03\n",
      " -6.29932070e-03  1.42725847e+00 -1.08368599e+01  1.11589204e-02\n",
      " -9.29500939e-02 -9.18220129e-02 -1.00025905e-02  1.37522336e+01]\n",
      "The best lambda to fit g_2 with the lowest training error:  1e-09\n",
      "The best lambda_k to fit g_2 with the lowest training error:  0.01\n"
     ]
    }
   ],
   "source": [
    "best_train_error2 = np.where(train_errors2 == train_errors2.min())\n",
    "best_w2 = ws2[best_train_error2[0][0], best_train_error2[1][0]]\n",
    "best_lambda2 = lambs[best_train_error2[0][0]]\n",
    "best_lambdak2 = lambks[best_train_error2[1][0]]\n",
    "print(\"The best weights for the neural network to fit g_2: \")\n",
    "print(best_w2)\n",
    "print(\"The best lambda to fit g_2 with the lowest training error: \", best_lambda2)\n",
    "print(\"The best lambda_k to fit g_2 with the lowest training error: \", best_lambdak2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 495,
       "width": 563
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot training errors in a heatmap \n",
    "# To better visualize different permutation of lambda and lambda_k\n",
    "plotErrors(train_errors2, \"pink\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Test the best regularization parameter on test sets with different size**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [],
   "source": [
    "NT_list = [50 + 50 * n for n in range(6)]\n",
    "errors2 = []\n",
    "for NT in NT_list:\n",
    "    X_test2 = random.randn(NT, 3)\n",
    "    Y_test2 = np.array([g2(x) for x in X_test2])\n",
    "    errors2.append(calc_error(best_w2, X_test2, Y_test2))  # Use the best weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 494,
       "width": 900
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(15,8))\n",
    "plt.plot(NT_list, errors2)\n",
    "plt.xticks(NT_list, [str(s) for s in NT_list])\n",
    "plt.title('Testing error for the best weights found for g_2')\n",
    "plt.xlabel(\"NT\")\n",
    "plt.ylabel(\"Testing Error\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Testing Error:  0.014386148541055098\n"
     ]
    }
   ],
   "source": [
    "print(\"Average Testing Error: \", sum(errors2)/len(errors2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary & Comments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observations**  \n",
    "Compared to $g(\\textbf{x})$, our neural network $f_w(\\textbf{x})$ actually performs better to fit $g_2(\\textbf{x})$ because it uses fewer iterations to converge to the same \"small residual\" threshold. Therefore, it's reasonable to think of $g_2$ as a less complex non-linear function than the original $g$. \n",
    "  \n",
    "**Error Metrics**  \n",
    "Same as before, I used Mean Squared Error (MSE) to evaluate the trained neural network. \n",
    "\n",
    "**Training Method**  \n",
    "Same as before, I have conducted a tuning of our regularization parameters with $5*5*3=75$ iterations, with $25$ permutations of $(\\lambda, \\lambda_k)$, three $3$ initialization trials for each.   \n",
    "\n",
    "**Training Results**  \n",
    "I have found that the lowest training error $0.000884$ was given by $\\lambda = 10^{-9}, \\lambda_k=10^{-2}$. I also stored the best weights among the three trials with that initialization of $\\lambda$ and $\\lambda_k$.   \n",
    "Additionally, In the heatmap drawn, we can find the trend that generally, smaller $\\lambda$ gives smaller training errors, hence better. This is a little different from what we found for $g(\\textbf{x})$.  \n",
    "  \n",
    "**Testing**  \n",
    "Same as before, to evaluate our simple neural network with the best weights found on test sets with different sizes, I tested it on $6$ different $N_T$, from $50$ to $300$ with a step size of $50$. The testing errors versus $N_T$ has been plotted. Finally, I averaged over six errors and gave the final testing error: $0.01438615$.    \n",
    "  \n",
    "**Comments on my results**  \n",
    "I believe I have conducted a thorough tuning of different initializations of $\\lambda$ and $\\lambda_k$ on the new non-linear function $g_2(\\textbf{x})$. Same as before, I tried five different $\\lambda$ with another five different $\\lambda_k$. Plus, to avoid bias when randomly initializing the starting weights, I performed three trials per permutation. I tested the best weights found on six sets of test points with different $N_T$, as required. Finally the average testing error of the best weights is $0.014386$, a little higher than the training error $0.000884$, which is reasonable and intuitive. "
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