{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `numpy` Neural Networks: Weight Regularization & Dropout\n",
    "\n",
    "So we've gotten a lot better at training. Now we need to avoid over training! We'll check out two techniques for this: weight regularization and dropout. First, generating the data and the most training functions from the previous notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've pushed the activations, cost functions, and model initialization functions to `common.py`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from common import *  # bad form but I know what's in there, only funcs from previous notebooks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a much smaller dataset to demonstrate overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DLGhpYkHzPJ5/9Shnd7VNn6GsmEbldZcEpRIISgoTI8EQHxf8dsJ/XHUVmuGt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116de5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_samples = 100\n",
    "\n",
    "np.random.seed(1234)\n",
    "X0 = np.random.normal(loc=[0, 0], scale=[2, 0.5], size=(int(n_samples / 2), 2))\n",
    "X11 = np.random.normal(loc=[1, 2], scale=[0.5, 1], size=(int(n_samples / 4), 2))\n",
    "X12 = np.random.normal(loc=[0, -2], scale=[0.5, 1], size=(int(n_samples / 4), 2))\n",
    "X1 = np.vstack([X11, X12])\n",
    "X = np.vstack([X0, X1])\n",
    "\n",
    "# rescale between -1 and 1\n",
    "X = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))\n",
    "X = 2*X - 1\n",
    "\n",
    "y0 = np.zeros(shape=(int(n_samples / 2), 1))\n",
    "y1 = np.ones(shape=(int(n_samples / 2), 1))\n",
    "yhat = np.vstack([y0, y1])\n",
    "\n",
    "# shuffle the data\n",
    "inds = np.random.permutation(np.arange(n_samples))\n",
    "X = X[inds]\n",
    "yhat = yhat[inds]\n",
    "\n",
    "X0 = X[(yhat==0).reshape(-1)]\n",
    "X1 = X[(yhat==1).reshape(-1)]\n",
    "\n",
    "plt.scatter(*X0.T, label='0', alpha=0.4); plt.scatter(*X1.T, label='1', alpha=0.4)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forwardn(x0, w, b):\n",
    "    n_layers = len(w)\n",
    "    x_prev = x0\n",
    "    for l in range(1, n_layers):\n",
    "        x_l = relu(np.dot(x_prev, w[l]) + b[l].T)  # output of a hidden layer\n",
    "        x_prev = x_l\n",
    "    return sig(np.dot(x_prev, w[n_layers]) + b[n_layers].T)  # output of output layer\n",
    "\n",
    "def backward_mom(X0, w, b, y, yhat, dw, db, alpha, beta):\n",
    "    n_layers = len(w)\n",
    "    batch_size = len(yhat)\n",
    "    z = {}\n",
    "    x = {0:X0}\n",
    "    delta = {}\n",
    "\n",
    "    # x and z values for calculating derivatives\n",
    "    for l in range(1, n_layers+1):\n",
    "        z[l] = np.matmul(x[l-1], w[l]) + b[l].T\n",
    "        x[l] = relu(z[l])\n",
    "            \n",
    "    # deltas and updates\n",
    "    for l in range(n_layers, 0, -1):  # start with last layer and move backward\n",
    "        if l == n_layers:  # base case\n",
    "            delta[l] = (dJ_dy(y, yhat) * dsig_dz(z[n_layers])).T\n",
    "        else:  # recursive case\n",
    "            delta[l] =  np.matmul(w[l+1], delta[l+1]) * drelu_dz(z[l]).T\n",
    "            \n",
    "        # Updates from backprop\n",
    "        dw_new = np.matmul(delta[l], x[l-1]).T / batch_size\n",
    "        db_new = delta[l].mean(axis=1, keepdims=True)\n",
    "        \n",
    "        # Exp. weighted average\n",
    "        dw[l] = beta*dw[l] + (1-beta)*dw_new\n",
    "        db[l] = beta*db[l] + (1-beta)*db_new\n",
    "        \n",
    "        # update weights and biases\n",
    "        w[l] -= alpha * dw[l]\n",
    "        b[l] -= alpha * db[l]\n",
    "    \n",
    "    return w, b, dw, db\n",
    "\n",
    "def train_dec(X, yhat, shape, alpha, n_epoch, batch_size, beta, gamma):\n",
    "    n_samples = X.shape[0]\n",
    "    n_input = X.shape[1]\n",
    "    \n",
    "    # keep track of performance during training\n",
    "    costs = np.zeros(shape=(n_epoch,1))\n",
    "\n",
    "    # random nonzero initialization\n",
    "    w,b = init_model(shape, seed=1234)\n",
    "\n",
    "    # initialize dw and db to zero\n",
    "    dw = {l:np.zeros_like(wl) for l,wl in w.items()}\n",
    "    db = {l:np.zeros_like(bl) for l,bl in b.items()}\n",
    "    \n",
    "    alph = alpha\n",
    "    \n",
    "    for epoch in range(n_epoch):\n",
    "        for i in range(0, n_samples, batch_size):\n",
    "            X_batch = X[i:i+batch_size,:]\n",
    "            yh = yhat[i:i+batch_size]\n",
    "            \n",
    "            y = forwardn(X_batch, w, b)  # prediction for mini-batch\n",
    "            w, b, dw, db = backward_mom(X_batch, w, b, y, yh, dw, db, alph, beta)  # take step\n",
    "        \n",
    "        # Decay the learning rate\n",
    "        alph *= (1 - gamma)\n",
    "        \n",
    "        # ### Some niceness to see our progress\n",
    "        # Calculate total cost after epoch\n",
    "        predictions = forwardn(X, w, b)  # predictions for entire set\n",
    "        costs[epoch] = np.mean(J(predictions, yhat))  # mean cost per sample\n",
    "        # report progress\n",
    "        accuracy = np.mean(predictions.round() == yhat)  # current accuracy on entire set\n",
    "        print('\\rTraining accuracy after epoch {}: {:.4%}'.format(epoch, accuracy), end='')\n",
    "            \n",
    "    print()    \n",
    "    return w, b, costs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do demonstrate overfitting, we train an unnecessarily large network for thousands of epochs to solve this tiny problem. We use learning rate decay and momentum to really get close to the minimum, and speed things up by using mini-batches. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy after epoch 1999: 97.0000%\n",
      "CPU times: user 6.71 s, sys: 860 ms, total: 7.57 s\n",
      "Wall time: 7.07 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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A4/b1A5J2ApuP8uZzgF0jWM5IcV3Dc7zWBcdvba5reCZiXUtCCHOzFhq3cD8W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\nTUAOdzOzCej/A5yILfZ2uP/KAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112f3ecf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch_size = 16\n",
    "shape = (2,64,128,1)\n",
    "alpha = 0.1\n",
    "gamma = 0.0005\n",
    "beta = 0.9\n",
    "n_epoch = 2000\n",
    "%time w, b, costs = train_dec(X, yhat, shape, alpha, n_epoch, batch_size, beta, gamma)\n",
    "plt.plot(costs)\n",
    "plt.title('Mean cost per sample after each epoch');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TzufD3K64mxXZoiSzMegWKn7Qt6FWqSqhYto/g0Pn6o2M3yEjQ7BAtYeFXoRL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nLMyvbVPdemvgLz/Q4KRlMwHr4UCRCUse0o+/8/IKmK9KuAhArQKkQrg9YhuaTiR686iU///Cbe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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112e67630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(-1.25,1.25,500)\n",
    "x2 = np.linspace(-1.25,1.25,500)\n",
    "fun_map = np.empty((x1.size, x2.size))\n",
    "for n,i in enumerate(x1):\n",
    "    for m,j in enumerate(x2):\n",
    "        fun_map[m,n] = forwardn([i,-j], w, b)\n",
    "\n",
    "X0 = X[(yhat==0).reshape(-1)]\n",
    "X1 = X[(yhat==1).reshape(-1)]\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.imshow(fun_map, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n",
    "           vmin=0, vmax=1, aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.contour(x1, -x2, fun_map, levels=[0.5], colors=['r'], linewidths=2)\n",
    "plt.scatter(*X0.T, label='0', alpha=1); plt.scatter(*X1.T, label='1', alpha=1)\n",
    "plt.xlim([x1.min(),x1.max()]); plt.ylim([x2.min(),x2.max()]);\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the red decision boundary, we see quite a bit of distortion caused by individual datapoints close to the boundary. In particular the \"wiggly\" form along the top of the lower boundary is a sure sign of overfitting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weight Regularization\n",
    "\n",
    "To help reduce overtraining, one approach is to penalize the size of the model's weights in the cost function. Large weights can lead to very sharp derivatives, or to over-reliance on one feature. To do this, we define a new cost function, which contains an extra term. There are a few different ways of doing this, but most commonly one can minimize either the sum of the absolute value of the weights ($L_1$ regularization) or the sum of their squares ($L_2$ regularization). We will do $L_2$ regularization, penalizing the sum-of-squares of all the weights. The amount of regularization is controlled by the new parameter $\\lambda$:\n",
    "\n",
    "$$ J_{reg}(y,\\hat y, w, \\lambda) = J(y,\\hat y) + \\frac{\\lambda}{2} \\sum_{\\ell,i,j} (w^\\ell_{ij})^2 $$\n",
    "\n",
    "Note that the partial derivative with respect to $y$ remains unchanged, but since there is now an explicit $w$ dependence, we will need to incorporate this into $dw$. In matrix notation,\n",
    "\n",
    "$$ \\frac{\\partial J_{reg}}{\\partial y} = \\frac{\\partial J}{\\partial y} $$\n",
    "\n",
    "$$ \\frac{\\partial J_{reg}}{\\partial w^\\ell} = \\lambda w^\\ell$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Jreg(y, yhat, w, lam):\n",
    "    eps = 1e-6\n",
    "    cost_term = -(yhat*np.log(y+eps) + (1-yhat)*np.log(1-y+eps)) # Same as J\n",
    "    reg_term = 0.5*lam*sum([(w[l]**2).sum() for l in w])  # Weight regularization\n",
    "    return cost_term + reg_term\n",
    "\n",
    "def dJreg_dy(y, yhat, w, lam):  # Same as dJ_dy, just redefine to match parameters of Jreg\n",
    "    eps = 1e-8\n",
    "    return (1-yhat)/(1-y+eps) - yhat/(y+eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y     :    0.000    0.250    0.500    0.750    1.000\n",
      "y_hat :    1.000    1.000    1.000    1.000    1.000\n",
      "\n",
      "J     :   18.421    1.386    0.693    0.288   -0.000\n",
      "J_reg :   25.096   12.667   11.974   11.568   11.280\n"
     ]
    }
   ],
   "source": [
    "y = np.linspace(0,1, num=5)\n",
    "yh = np.ones(5)\n",
    "print('y     :', *[f'{i:>8.3f}' for i in y])\n",
    "print('y_hat :', *[f'{i:>8.3f}' for i in yh])\n",
    "print()\n",
    "print('J     :', *[f'{i:>8.3f}' for i in J(y,yh).T])\n",
    "print('J_reg :', *[f'{i:>8.3f}' for i in Jreg(y, yh, w, 0.01).T])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that $J_{reg}$ will always have a higher value than $J$ since we have added an extra non-negative term. This means that the cost functions are not directly comparable to each other!\n",
    "\n",
    "We define a new training function that utilizes the new cost function and takes `lam` as a parameter, and train a new model with the same settings as before, but adding weight regularization with $\\lambda = 0.01$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward_reg(X0, w, b, y, yhat, dw, db, alpha, beta, lam):\n",
    "    n_layers = len(w)\n",
    "    batch_size = len(yhat)\n",
    "    z = {}\n",
    "    x = {0:X0}\n",
    "    delta = {}\n",
    "\n",
    "    # x and z values for calculating derivatives\n",
    "    for l in range(1, n_layers+1):\n",
    "        z[l] = np.matmul(x[l-1], w[l]) + b[l].T\n",
    "        x[l] = relu(z[l])\n",
    "            \n",
    "    # deltas and updates\n",
    "    for l in range(n_layers, 0, -1):  # start with last layer and move backward\n",
    "        if l == n_layers:  # base case\n",
    "            delta[l] = (dJreg_dy(y, yhat, w, lam) * dsig_dz(z[n_layers])).T\n",
    "        else:  # recursive case\n",
    "            delta[l] =  np.matmul(w[l+1], delta[l+1]) * drelu_dz(z[l]).T\n",
    "            \n",
    "        # dw_new now with extra term from explicit w dependence!\n",
    "        dw_new = (np.matmul(delta[l], x[l-1]).T / batch_size) + lam*w[l]  \n",
    "        db_new = delta[l].mean(axis=1, keepdims=True)\n",
    "        \n",
    "        # Exp. weighted average\n",
    "        dw[l] = beta*dw[l] + (1-beta)*dw_new\n",
    "        db[l] = beta*db[l] + (1-beta)*db_new\n",
    "        \n",
    "        # update weights and biases\n",
    "        w[l] -= alpha * dw[l]\n",
    "        b[l] -= alpha * db[l]\n",
    "    \n",
    "    return w, b, dw, db\n",
    "\n",
    "def train_reg(X, yhat, shape, alpha, n_epoch, batch_size, beta, gamma, lam):\n",
    "    n_samples = X.shape[0]\n",
    "    n_input = X.shape[1]\n",
    "    \n",
    "    # keep track of performance during training\n",
    "    costs = np.zeros(shape=(n_epoch,1))\n",
    "\n",
    "    # random nonzero initialization\n",
    "    w,b = init_model(shape, seed=(1234))\n",
    "    \n",
    "    # initialize dw and db to zero\n",
    "    dw = {l:np.zeros_like(wl) for l,wl in w.items()}\n",
    "    db = {l:np.zeros_like(bl) for l,bl in b.items()}\n",
    "    \n",
    "    alph = alpha\n",
    "\n",
    "    for epoch in range(n_epoch):\n",
    "        for i in range(0, n_samples, batch_size):\n",
    "            X_batch = X[i:i+batch_size,:]\n",
    "            yh = yhat[i:i+batch_size]\n",
    "            \n",
    "            y = forwardn(X_batch, w, b)  # prediction for mini-batch\n",
    "            w, b, dw, db = backward_reg(X_batch, w, b, y, yh, dw, db, alph, beta, lam)  # take step\n",
    "            \n",
    "        # Decay the learning rate\n",
    "        alph *= (1 - gamma)\n",
    "        \n",
    "        # ### Some niceness to see our progress\n",
    "        # Calculate total cost after epoch\n",
    "        predictions = forwardn(X, w, b)  # predictions for entire set\n",
    "        costs[epoch] = np.mean(Jreg(predictions, yhat, w, lam))  # mean cost per sample\n",
    "        # report progress\n",
    "        accuracy = np.mean(predictions.round() == yhat)  # current accuracy on entire set\n",
    "        print('\\rTraining accuracy after epoch {}: {:.4%}'.format(epoch, accuracy), end='')\n",
    "            \n",
    "    print()    \n",
    "    return w, b, costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy after epoch 1999: 91.0000%\n",
      "CPU times: user 6.92 s, sys: 871 ms, total: 7.79 s\n",
      "Wall time: 7.31 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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XUkZEZJqIrBKRj0RkRPOEm2DDL4LMdjD/z35HYowxCRXPlnsI+JmqDgHGANeI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\ncCnDlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114b65470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch_size = 16\n",
    "shape = (2,64,128,1)\n",
    "alpha = 0.1\n",
    "gamma = 0.0005\n",
    "beta = 0.9\n",
    "n_epoch = 2000\n",
    "lam = 0.003\n",
    "%time w_reg, b_reg, costs_reg = train_reg(X, yhat, shape, alpha, n_epoch, batch_size, beta, gamma, lam)\n",
    "plt.plot(costs, label='GD')\n",
    "plt.plot(costs_reg, label='GD with weight regularization')\n",
    "plt.legend()\n",
    "plt.title('Mean cost per sample after each epoch');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oFyhDhL4plcWEQ/lUrKFWMMYjm4vYrXMDzYUSACU/YFVrGz1hEyh4cfo7s6ZCpVxVSZKa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\npjanpTarRaGsn0UUKVGkREiJo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nyca/wUFwBPj+DxjQduBd4bTQu9AmivaDM7GghXYTkC\nROQtwFXAVOAnIrLBGHOOiMwCrjXGvLGviOJRPOxG40rgRhG5FNgGXAQQjZF/yBhzGbAEuFpEQqwI\nv9IY4wRLPwxXdLajmkE+zh8VkQuAIvZxfv+oHXADIiI3AK8GpojIDuBvAB/AGPNNbNrqG4FNQDfw\ngdE5UseR4pJuHQ6Hw+FwjHlcS8jhcDgcDseYxwkWh8PhcDgcYx4nWBwOh8PhcIx5nGBxOBwOh8Mx\n5nGCxeFwOBwOx5jHCRaHw+FwOBxjHidYHA6Hw+FwjHmcYHE4HA6HwzHm+f/DXxJfRBfVXwAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113093128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vDiYsu0jE4esv1xHcFh4+ul/1bbbclm223HZUj5lfqCssY4QYO+BKQmvWAeGJ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\nRFviApCSt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DqBleQcBY3fA10LGd1+OX3P7V2w6gpA/73fy3hYgGo+oirOTFTAcmHEfMi0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\nFkEQBEEQxh4pWARBEARBGHv+H6xiNpFZdao7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11309f1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fun_map_reg = np.empty((x1.size, x2.size))\n",
    "for n,i in enumerate(x1):\n",
    "    for m,j in enumerate(x2):\n",
    "        fun_map_reg[m,n] = forwardn([i,-j], w_reg, b_reg)\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.imshow(fun_map, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n",
    "           vmin=0, vmax=1, aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.scatter(*X0.T, label='0', alpha=1); plt.scatter(*X1.T, label='1', alpha=1)\n",
    "plt.legend()\n",
    "plt.contour(x1, -x2, fun_map, levels=[0.5], colors=['r'], label='Decision boundary', linewidths=2)\n",
    "plt.title('Decision function GD')\n",
    "plt.show();\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.imshow(fun_map_reg, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n",
    "           vmin=0, vmax=1, aspect='auto')\n",
    "plt.colorbar();\n",
    "plt.contour(x1, -x2, fun_map_reg, levels=[0.5], colors=['r'], label='Decision boundary', linewidths=2)\n",
    "plt.title('Decision Function GD with weight regularization');\n",
    "plt.scatter(*X0.T, label='0', alpha=1); plt.scatter(*X1.T, label='1', alpha=1)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that regularizing the weights has had all the expected effects:\n",
    "\n",
    "* The cost function remains higher in value than its unregularized counterpart (not a concern because it is actually a different function)\n",
    "* The gradients are much less steep than in the unregularized model\n",
    "\n",
    "The less shallower gradients also cause the \"wiggles\" in the bottom part of the heatmap, which are a result of overfitting our small dataset, to blur and smooth out, which is exactly what we were hoping to see.\n",
    "\n",
    "It remains to be seen if the weights are also indeed lower than the unregularized weights. We plot them all on a scatter plot to investigate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Mz5IkSVJLhmdJkiSpJcOzJEmS1JLhWZIkSWrJ8CxJkiS1ZHiWJEmSWjI8S5Ik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\nz5IkSVJLhmdJkiSppf8HS50yrhJVhvoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112f86be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_w = np.hstack([w[l].reshape(-1) for l in w])\n",
    "all_w_reg = np.hstack([w_reg[l].reshape(-1) for l in w_reg])\n",
    "\n",
    "plt.figure(figsize=(12,5))\n",
    "plt.hist(all_w, label='Unregularized', alpha=0.6, bins=50, range=(-2,2))\n",
    "plt.hist(all_w_reg, label='Regularized', alpha=0.6, bins=50, range=(-2,2))\n",
    "plt.title('Distributions of learned weights'); plt.xlabel('weight');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distributions of learned weights is very different. With regularization, the distribution is very sharply peaked around zero. This suggests that our model is actually much larger than necessary, since many of the connections are redundant, and with the incentive to get rid of them, the model can do so while still maintaining reasonable accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dropout\n",
    "\n",
    "Dropout, introduced in [this paper](https://www.cs.toronto.edu/~hinton/absps/JMLRdropout.pdf), takes a different approach to regularization. The basic idea is, at each training step, to randomly remove a portion of the units in the network and only update the remaining connections via backprop. Some reasoning behind doing this is:\n",
    "\n",
    "* It's possible that several units can learn \"bad\" features that compensate for each other to still produce an okay result. This situation is very brittle and although it may work on the training set, on a test set it's unlikely that the specific conditions required to balance these bad units will still be present, leading to poor generalization. Dropout ensures that units can't depend on each other since there is always a good chance that each unit might disappear. \n",
    "\n",
    "* Ideally we would like to make an ensemble of all possible networks and average over their predictions, weighted by their accuracy. This is clearly not feasible for computational reasons. Using dropout, we instead sample a lot of different sub-networks and train those, and average over them when making predictions.\n",
    "\n",
    "When making predictions, we don't do dropout, but use all of our connections. This has the effect of averaging over all the random sub-networks that we trained using dropout.\n",
    "\n",
    "When implementing dropout it's important to pay attention to scaling issues. Call the fraction of units for each that we keep $p^\\ell$. In other words, for layer $\\ell$, each unit is dropped (output multiplied by zero) with probability $1-p^\\ell$. Since we drop a bunch of the units, the average magnitude of the input to the following layer, $z^{\\ell+1}$, will be reduced by the same amount, simply because a bunch of the input terms will be zero. For this reason, it is important to multiply each layer's output $x^\\ell$ by $1/p^\\ell$. Otherwise, the weights will be learned with the expectation that $z^\\ell$ has a particular scale, and at prediction time (when we keep all the units), $z^\\ell$ will get contributions from all the units and so will be much larger.\n",
    "\n",
    "To implement this practically, we first write a function to make a random mask for each layer. It takes two variables: the `shape` of the network, and the probability of keeping a unit for each layer, a tuple which we will call `p`. It outputs an array that we can use to multiply $x^\\ell$. The elements of the mask have value `1/p[i]` with probability `p[i]`, and otherwise zero. Since each layer is a different size, we take the same approach as with `w`  and `b` and store it in a dictionary. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_mask(p, shape):\n",
    "    mask = {}\n",
    "    for layer, size in enumerate(shape):\n",
    "        # 1 with prob b[layer] = binomial(1 trial, probability p[layer])\n",
    "        # then divide by p[layer] for scaling\n",
    "        mask[layer] = np.random.binomial(1, p[layer], size=(1, size)) / p[layer]\n",
    "        \n",
    "    return mask"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to keep all the input data and the output, so the first and last elements of `p` are always 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: array([[1., 1.]]),\n",
       " 1: array([[2., 0., 0., 2., 0.]]),\n",
       " 2: array([[0., 5., 0., 0., 0., 0., 0., 5., 0., 0.]]),\n",
       " 3: array([[1.]])}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_mask(p=(1,0.5,0.2,1), shape=(2,5,10,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During training, we need to generate a new mask at each update step, but apply the same mask for both the forward and the backward pass, so we call `make_mask` inside the training loop. Then we pass the `mask` to both the forward and the backward functions.\n",
    "\n",
    "In the forward pass, we multiply the output of each layer by the corresponding mask. In the backward pass, we only update those weights that correspond to units that were not dropped out. Practically, we set up a vector `keep_units` for every mask containing the indices of all the non-zero units in the mask, and then only update the values in `db`, `dw`, `b` and `w` at those indices.\n",
    "\n",
    "To track our costs, we make predictions based on a mask where $p=1$ for every layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_drop(x0, w, b, mask):\n",
    "    n_layers = len(w)\n",
    "    x_prev = x0 * mask[0]\n",
    "    \n",
    "    for l in range(1, n_layers):\n",
    "        x_l = relu(np.dot(x_prev, w[l]) + b[l].T)  # output of a hidden layer\n",
    "        x_l = np.multiply(x_l, mask[l])\n",
    "        x_prev = x_l\n",
    "        \n",
    "    out = sig(np.dot(x_prev, w[n_layers]) + b[n_layers].T)\n",
    "    out = out * mask[n_layers]\n",
    "    \n",
    "    return out\n",
    "\n",
    "\n",
    "def backward_drop(X0, w, b, y, yhat, dw, db, alpha, beta, lam, mask):\n",
    "    n_layers = len(w)\n",
    "    batch_size = len(yhat)\n",
    "    z = {}\n",
    "    x = {0:X0 * mask[0]}\n",
    "    delta = {}\n",
    "    \n",
    "    # x and z values for calculating derivatives\n",
    "    for l in range(1, n_layers):\n",
    "        z[l] = np.matmul(x[l-1], w[l]) + b[l].T\n",
    "        x[l] = relu(z[l]) * mask[l]\n",
    "        \n",
    "    z[n_layers] = np.matmul(x[n_layers-1], w[n_layers]) + b[n_layers].T\n",
    "            \n",
    "    # deltas and updates\n",
    "    for l in range(n_layers, 0, -1):  # start with last layer and move backward\n",
    "        if l == n_layers:  # base case\n",
    "            delta[l] = (dJreg_dy(y, yhat, w, lam) * dsig_dz(z[n_layers])).T\n",
    "        else:  # recursive case\n",
    "            delta[l] =  np.matmul(w[l+1], delta[l+1]) * drelu_dz(z[l]).T\n",
    "        \n",
    "        # for indexing only the units that were part of the network\n",
    "        keep_units = mask[l].nonzero()[1]\n",
    "        \n",
    "        # Explicit w dependence\n",
    "        dw_new = (np.matmul(delta[l], x[l-1]).T / batch_size) + lam*w[l]  \n",
    "        db_new = delta[l].mean(axis=1, keepdims=True)\n",
    "        \n",
    "        # update steps for relevant units\n",
    "        dw[l][:, keep_units] = beta*dw[l][:, keep_units] + (1-beta)*dw_new[:, keep_units]\n",
    "        db[l][keep_units] = beta*db[l][keep_units] + (1-beta)*db_new[keep_units]\n",
    "        \n",
    "        # update weights and biases for relevant units\n",
    "        w[l][:, keep_units] -= alpha * dw[l][:, keep_units]\n",
    "        b[l][keep_units] -= alpha * db[l][keep_units]\n",
    "    \n",
    "    return w, b, dw, db\n",
    "\n",
    "\n",
    "def train_drop(X, yhat, shape, alpha, n_epoch, batch_size, beta, lam, p):\n",
    "    n_samples = X.shape[0]\n",
    "    n_input = X.shape[1]\n",
    "    \n",
    "    # keep track of performance during training\n",
    "    costs = np.zeros(shape=(n_epoch,1))\n",
    "\n",
    "    # random nonzero initialization\n",
    "    w,b = init_model(shape)\n",
    "    \n",
    "    # initialize dw and db\n",
    "    dw = {l:np.zeros_like(wl) for l,wl in w.items()}\n",
    "    db = {l:np.zeros_like(bl) for l,bl in b.items()}\n",
    "    \n",
    "    # mask of p=1 (for test time)\n",
    "    p1_mask = make_mask(np.ones_like(shape), shape)\n",
    "    \n",
    "    alph = alpha\n",
    "    \n",
    "    for epoch in range(n_epoch):\n",
    "        for i in range(0, n_samples, batch_size):\n",
    "            # make a new mask\n",
    "            mask = make_mask(p, shape)\n",
    "            \n",
    "            X_batch = X[i:i+batch_size,:]\n",
    "            yh = yhat[i:i+batch_size]\n",
    "            \n",
    "            y = forward_drop(X_batch, w, b, mask)  # prediction for mini-batch\n",
    "            w, b, dw, db = backward_drop(X_batch, w, b, y, yh, dw, db, alph, beta, lam, mask)  # take step\n",
    "        \n",
    "        # Decay the learning rate\n",
    "        alph *= (1 - gamma)\n",
    "        \n",
    "        # ### Some niceness to see our progress\n",
    "        # Calculate total cost after epoch\n",
    "        predictions = forward_drop(X, w, b, mask=p1_mask)  # predictions for entire set\n",
    "        costs[epoch] = np.mean(Jreg(predictions, yhat, w, lam))  # mean cost per sample\n",
    "        \n",
    "        # report progress\n",
    "        accuracy = np.mean(predictions.round() == yhat)  # current accuracy on entire set\n",
    "        print('\\rTraining accuracy after epoch {}: {:.4%}'.format(epoch, accuracy), end='')\n",
    "\n",
    "    print()    \n",
    "    return w, b, costs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train a network with dropout and no regularization to see how they compare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy after epoch 1999: 91.0000%\n",
      "CPU times: user 10.3 s, sys: 1.03 s, total: 11.3 s\n",
      "Wall time: 10.9 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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CcfV93szeMrOnzKxfphmZ2RQzW2Rmi7Zs2dKEcLP1uSu5i4ika64Lqn8GBjjn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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114648e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch_size = 16\n",
    "shape = (2,64,128,1)\n",
    "alpha = 0.1\n",
    "gamma = 0.0005\n",
    "beta = 0.9\n",
    "n_epoch = 2000\n",
    "\n",
    "lam = 0\n",
    "p = (1,0.5,0.5,1)\n",
    "\n",
    "%time w_drop, b_drop, costs_drop = train_drop(X, yhat, shape, alpha, n_epoch, batch_size, beta, lam, p)\n",
    "plt.plot(costs, label='Mini-batch GD')\n",
    "plt.plot(costs_drop, label='Mini-batch GD with Dropout')\n",
    "plt.legend()\n",
    "plt.title('Mean cost per sample after each epoch');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oFyhDhL4plcWEQ/lUrKFWMMYjm4vYrXMDzYUSACU/YFVrGz1hEyh4cfo7s6ZCpVxVSZKa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\npjanpTarRaGsn0UUKVGkREiJo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nyca/wUFwBPj+DxjQduBd4bTQu9AmivaDM7GghXYTkC\nROQtwFXAVOAnIrLBGHOOiMwCrjXGvLGviOJRPOxG40rgRhG5FNgGXAQQjZF/yBhzGbAEuFpEQqwI\nv9IY4wRLPwxXdLajmkE+zh8VkQuAIvZxfv+oHXADIiI3AK8GpojIDuBvAB/AGPNNbNrqG4FNQDfw\ngdE5UseR4pJuHQ6Hw+FwjHlcS8jhcDgcDseYxwkWh8PhcDgcYx4nWBwOh8PhcIx5nGBxOBwOh8Mx\n5nGCxeFwOBwOx5jHCRaHw+FwOBxjHidYHA6Hw+FwjHmcYHE4HA6HwzHm+f/DXxJfRBfVXwAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113065668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FrBRTQL3FSpObpimfZtof2/j4V3/P9N3teJbFdy9czPdPuwKr2ybe6eN0e9hZ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\n140HPv/1jS3GVVHKQJzOAURIA2kTd2XGDgwtVCiS5ubKYRFCPAF8BtO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mOyC552POP+ju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\nYg4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11653f160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fun_map_drop = np.empty((x1.size, x2.size))\n",
    "for n,i in enumerate(x1):\n",
    "    for m,j in enumerate(x2):\n",
    "        fun_map_drop[m,n] = forward_drop([i,-j], w_drop, b_drop, np.ones_like(shape))\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.imshow(fun_map, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n",
    "           vmin=0, vmax=1, aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.contour(x1, -x2, fun_map, levels=[0.5], colors=['r'], label='Decision boundary', linewidths=2)\n",
    "plt.scatter(*X0.T, label='0', alpha=1); plt.scatter(*X1.T, label='1', alpha=1)\n",
    "plt.legend()\n",
    "plt.title('Decision function GD')\n",
    "plt.show();\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.imshow(fun_map_drop, extent=[x1.min(), x1.max(), x2.min(), x2.max()], \n",
    "           vmin=0, vmax=1, aspect='auto')\n",
    "plt.title('Decision Function GD with dropout')\n",
    "plt.colorbar();\n",
    "plt.contour(x1, -x2, fun_map_drop, levels=[0.5], colors=['r'], linewidths=2);\n",
    "plt.scatter(*X0.T, label='0', alpha=1); plt.scatter(*X1.T, label='1', alpha=1)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much like with weight regularization, dropout causes the wiggles to largely be smoothed out. However, the gradients, especially along the top boundary, aren't nearly as shallow as when we did regularization, suggesting that the weights themselves aren't necessarily smaller. We also still see overfitting looming on the horizon, as a little island of yellow is beginning to surface near the center of the plot where the overfit \"peninsula\" sticks out of the unregularized decision function. Of course, this is not a silver bullet, and with enough epochs, overfitting is not to be completely avoided.\n",
    "\n",
    "We can check our theory about the weights themselves by plotting their histograms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Sk3UYkjPzASDWsvmIdtoncPoG1iVJkiS1jI+lliRJkioMyZIkSVKFIVmSJEmq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\nJFX8f1/eX7I4LZlSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1164a1400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_w_drop = np.hstack([w_drop[l].reshape(-1) for l in w_drop])\n",
    "\n",
    "plt.figure(figsize=(12,5))\n",
    "plt.hist(all_w, label='Unregularized', alpha=0.5, bins=50, range=(-2,2))\n",
    "plt.hist(all_w_drop, label='Dropout', alpha=0.5, bins=50, range=(-2,2))\n",
    "plt.title('Distributions of learned weights'); plt.xlabel('weight');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed the dropout weights are pretty much indistinguishable from the unregularized ones. Dropout has induced a more robust configuration, but has not reduced the magnitudes of the weights themselves. For this reason it's often a good idea to combine dropout with some form of direct weight regularization."
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}