lab2/Lab 2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "This project was developed by Peter Chen, Rocky Duan, Pieter Abbeel for the Berkeley Deep RL Bootcamp, August 2017.\n",
    "Bootcamp website with slides and lecture videos: https://sites.google.com/view/deep-rl-bootcamp/.\n",
    "\n",
    "Code adapted from Stanford CS231N materials: http://cs231n.stanford.edu/\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "# note to properly run this lab, you should execute all code blocks sequentially\n",
    "import chainer\n",
    "import chainer.functions as F\n",
    "import chainer.links as L\n",
    "from chainer import training\n",
    "from chainer.training import extensions\n",
    "\n",
    "from collections import namedtuple, defaultdict, deque\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to Chainer\n",
    "\n",
    "Chainer can be understood as Numpy plus the ability to record the computation graph of numerical operations to enable Automatic Differentiation. (Chainer actually also offers many other things; for example, a Numpy equivalent library that runs on GPU, but we will ignore them for now)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's illustrate how Chainer works by a simple 1D regression task.\n",
    "\n",
    "Suppose we have observations from the following model $y = w x + b + \\epsilon$ where $\\epsilon \\sim \\mathcal{N}(0, 0.1)$ and the task is to estimate the linear model parameters $w, b$ from data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDlLwFxHpIAV/EZEO+j9sMvbCn0GLpQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4d22cdf390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# first generate some observations\n",
    "true_a = 1.3\n",
    "true_b = 0.4\n",
    "data_x = (np.arange(100) / 99.0 - .5).astype(np.float32) # Chainer assumes all the cpu computation is done in float32\n",
    "data_y = (data_x * true_a + true_b + np.random.randn(*data_x.shape) * 0.1).astype(np.float32)\n",
    "_ = plt.scatter(data_x, data_y, c='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Chainer provides an abstraction called `Link` that describe some computation and keeps track of parameters for it. For instance, a `Linear` link describes a linear map on input and keeps track of `w` and bias `b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w: variable W([[ 0.26301852]])\n",
      "b: variable b([ 0.])\n",
      "Operations on chainer.Variable: variable([[ 123.26301575]]), type: <class 'chainer.variable.Variable'>\n",
      "numpy arrays: [[ 0.26301852]] [[ 123.26301575]]\n"
     ]
    }
   ],
   "source": [
    "model = L.Linear(in_size=1, out_size=1) # input is 1D data and output is also 1D data\n",
    "\n",
    "# Chainer will randomly initialize `w` and `b` for us.\n",
    "# we can take a look at their values\n",
    "print(\"w:\", model.W)\n",
    "print(\"b:\", model.b)\n",
    "\n",
    "# model.W and model.b have type `chainer.Variable`, \n",
    "#   which is a wrapper around Numpy array\n",
    "assert isinstance(model.W, chainer.Variable)\n",
    "\n",
    "# operations that involve `chainer.Variable` will produce\n",
    "#   `chainer.Variable` and this records the computation graph\n",
    "var_result = model.W + 123 # some random computation\n",
    "print(\"Operations on chainer.Variable: %s, type: %s\" % (var_result, type(var_result)))\n",
    "\n",
    "# the underlying numpy array can be accessed by `data` attribute\n",
    "print(\"numpy arrays:\", model.W.data, var_result.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEICAYAAAC3Y/QeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nqT0JcgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4d22ccff60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A chainer link is a callable object. calling it performs the\n",
    "#   forward computation. (in this case, it performs Wx + b)\n",
    "model_y = model(data_x[:, None]) # chainer's link usually assumes input is [Batch Size, Input Dimension]\n",
    "# `model_y` is a chainer variable so we use `.data` to access its numpy array for plotting\n",
    "\n",
    "# we can plot the model's current fit in red. it should be terrible because we haven't trained it yet\n",
    "_ = plt.plot(data_x, model_y.data[:,0], c='r')\n",
    "_ = plt.scatter(data_x, data_y, c='b')\n",
    "_ = plt.title(\"Initial model\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss variable(0.2617785334587097)\n",
      "dloss/dW [[-0.16712697]]\n"
     ]
    }
   ],
   "source": [
    "# now let's walk through how to perform forward computation\n",
    "#  and use AD to get gradients\n",
    "\n",
    "# first we clear the gradients that are stored in the model\n",
    "model.cleargrads()\n",
    "# as we have seen we can perform forward computation by calling the link\n",
    "model_y = model(data_x[:, None])\n",
    "\n",
    "# remember that `model_y` is a chainer variable. to operate on chainer variable\n",
    "#    we will use functions from chainer.functions to operate on those objects.\n",
    "loss = F.mean(F.square(model_y - data_y[:, None]))\n",
    "# `loss` is a scalar chainer variable\n",
    "assert isinstance(loss, chainer.Variable)\n",
    "print(\"loss\", loss)\n",
    "# calculating gradients d loss /d params is as simple as\n",
    "loss.backward()\n",
    "\n",
    "# we can inspect the gradient of loss with respect to W\n",
    "print(\"dloss/dW\", model.W.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we know how to calculate gradients, we can code up a simple loop to perform gradient descent to train this model:\n",
    "\n",
    "(Hint: if you run into weird problems, maybe the state has been messed up and you can try re-runing all the code blocks from the beginning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itr 0 loss: variable(0.20220519602298737)\n",
      "Itr 25 loss: variable(0.021838046610355377)\n",
      "Itr 50 loss: variable(0.01632477529346943)\n",
      "Itr 75 loss: variable(0.013986889272928238)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEICAYAAABfz4NwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4d209ad240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEICAYAAAC3Y/QeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4d20a24630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now we can perform gradient descent to improve this model\n",
    "model = L.Linear(in_size=1, out_size=1)\n",
    "losses = []\n",
    "\n",
    "lr = 0.1\n",
    "\n",
    "for i in range(100):\n",
    "    model.cleargrads()\n",
    "    loss = F.mean(F.square(model(data_x[:, None]) - data_y[:, None]))\n",
    "    losses.append(float(loss.data))\n",
    "    ## *** YOUR CODE HERE TO PERFORM GRADIENT DESCENT ***\n",
    "    ## Hint: you could access gradients with model.W.grad, model.b.grad\n",
    "    ## Hint2: you could write data into a parameter with model.W.data[:] = some_numpy_array\n",
    "    ## Hint3: if your model doesn't learn, remember to try different learning rates\n",
    "    loss.backward()\n",
    "    model.W.data -= lr*model.W.grad\n",
    "    model.b.data -= lr*model.b.grad\n",
    "    \n",
    "    if i % 25 == 0:\n",
    "        print(\"Itr\", i, \"loss:\", loss)\n",
    "plt.plot(np.array(losses))\n",
    "plt.title(\"Learning curve\")\n",
    "plt.figure()\n",
    "plt.plot(data_x, model(data_x[:, None])[:,0].data, c='r')\n",
    "plt.scatter(data_x, data_y, c='b')\n",
    "_ = plt.title(\"Trained model fitness\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train your first deep model\n",
    "\n",
    "Now we have learned the basics of Chainer. We can use it to train a deep model to classify MNIST digits. We will train a model on the MNIST dataset because the dataset is small.\n",
    "\n",
    "First we load the data and see what the images look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading from http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz...\n",
      "Downloading from http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz...\n",
      "Downloading from http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz...\n",
      "Downloading from http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz...\n",
      "train[i][0] is the ith image that's flattened, and has shape: (784,)\n",
      "train[i][1] is the ith image's label, such as: 3\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAEICAYAAACQ6CLfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4d20b0b400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAEICAYAAACQ6CLfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAADuFJREFUeJzt3X+s1fV9x/HnC0RQKpUrjlGQ2iLtQpoUmxu1qW1xbp3a\nbtgZiWxVmjmpqWYzcUuNy6LrtoQ0bZ3bOrfrdKLr7LpRA9lIV0rWmnab9WqpYukK2kuFXsQfdaBW\nhMt7f5wvzRXv+d7LOd9zvof7fj2Sk/s93/f3e75vTnjd74/POferiMDM8plSdwNmVg+H3ywph98s\nKYffLCmH3ywph98sKYc/MUnfkPS73V7XeoPDPwlIGpL0K3X30Yykv5X00qjHAUn76+4ruxPqbsAm\nv4i4Frj2yHNJ9wCHa2vIAO/5JzVJsyX9m6RnJf20mF5w1GKLJH1H0j5J6yX1jVr/PEn/JelFSd+T\ntKyCnmYClwFr230ta4/DP7lNAf4BeCuwEPgZ8NdHLXMV8DvAPOAQ8JcAkuYD/w78GdAH/AGwTtLp\nR29E0sLiF8TCCfR0GfAs8GAr/yCrjsM/iUXE8xGxLiJeiYj9wJ8DHzxqsfsiYmtEvAz8MbBC0lTg\nY8DGiNgYEYcjYhMwCFwyxnZ+HBGnRsSPJ9DWKuDe8JdKaufwT2KSTpb0d5J2StpHY297ahHuI54e\nNb0TmAbMoXG0cHmxR39R0ovA+TSOEFrtZyGwDLi31dew6viC3+R2I/BO4NyI2CNpKfBdQKOWOWPU\n9ELgIPAcjV8K90XENRX2cyXw7Yh4qsLXtBZ5zz95TJM0Y9TjBOAUGuf5LxYX8m4ZY72PSVoi6WTg\n08C/RsQI8I/Ar0v6NUlTi9dcNsYFw2NxFXBPG+tbhRz+yWMjjaAfedwK/AVwEo09+f8AXx1jvfto\nBHIPMAP4PYCIeBpYDtxM4wLd08AfMsb/meKC30tlF/wkvRdYAPxLK/84q5583cUsJ+/5zZJy+M2S\ncvjNknL4zZLq6jj/iZoeM5jZzU2apfIqL/NaHND4S7YZfkkXAbcDU4G/j4g1ZcvPYCbn6sJ2Nmlm\nJR6KzRNetuXD/uIjol8ALgaWACslLWn19cysu9o55z8H2BERT0XEa8CXaHwoxMyOA+2Efz6v/1LI\nrmLe60haLWlQ0uBBDrSxOTOrUsev9kfEQET0R0T/NKZ3enNmNkHthH83r/9G2IJinpkdB9oJ/8PA\nYklvk3QicAWwoZq2zKzTWh7qi4hDkq4H/oPGUN/dEfFEZZ2ZWUe1Nc4fERtpfJXUzI4z/nivWVIO\nv1lSDr9ZUg6/WVIOv1lSDr9ZUg6/WVIOv1lSDr9ZUg6/WVIOv1lSDr9ZUg6/WVIOv1lSDr9ZUg6/\nWVIOv1lSDr9ZUg6/WVIOv1lSDr9ZUg6/WVIOv1lSDr9ZUg6/WVIOv1lSDr9ZUg6/WVIOv1lSDr9Z\nUm3dolvSELAfGAEORUR/FU2ZWee1Ff7CBRHxXAWvY2Zd5MN+s6TaDX8AX5P0iKTVYy0gabWkQUmD\nBznQ5ubMrCrtHvafHxG7Jf0CsEnSDyLiwdELRMQAMAAwS33R5vbMrCJt7fkjYnfxcy/wAHBOFU2Z\nWee1HH5JMyWdcmQa+BCwtarGzKyz2jnsnws8IOnI6/xTRHy1kq7MrONaDn9EPAW8u8JezKyLPNRn\nlpTDb5aUw2+WlMNvlpTDb5ZUFV/sseNZY6i2qamLziyt/+i355XWP/Dh7zatrTztodJ1P/ORy0rr\nI9u2l9atnPf8Zkk5/GZJOfxmSTn8Zkk5/GZJOfxmSTn8Zkl5nH8SmPqORU1rQ5fPLV33/cubj8MD\n/M38dS31NBHDI6+U1rW/vG7t8Z7fLCmH3ywph98sKYffLCmH3ywph98sKYffLCmP8/eAw+cvLa2/\n8Kny8e6vL72naW3WlBml6657eXZpffGma0rrOuFwaf2HF9zVtPZb264sXfekXT8qrVt7vOc3S8rh\nN0vK4TdLyuE3S8rhN0vK4TdLyuE3S8rj/BV45TfPLa3fsOb+0vr7T/p2af20KSeV1n/pm59sWnvL\n/SeWrjvzmz8orS/e90hp/fAHzy6tc0Hz0u5t5X9r4Cw8zt9J4+75Jd0taa+kraPm9UnaJGl78bP8\nkyJm1nMmcth/D3DRUfNuAjZHxGJgc/HczI4j44Y/Ih4EXjhq9nJgbTG9Fri04r7MrMNaPeefGxHD\nxfQeoOnJm6TVwGqAGZzc4ubMrGptX+2PiACipD4QEf0R0T+N6e1uzswq0mr4n5E0D6D4ube6lsys\nG1oN/wZgVTG9ClhfTTtm1i3jnvNLuh9YBsyRtAu4BVgDfFnS1cBOYEUnm+x1r8wp/x36V0O/XFr/\n9Cvl4/gnrj+1tP72td9pXjw8UrpuebWzpr6qGrdu44Y/IlY2KV1YcS9m1kX+eK9ZUg6/WVIOv1lS\nDr9ZUg6/WVL+Sm8F5gz8d/kCA+XlX6yula6b/id7Wl73rNueLK3XOQyZgff8Zkk5/GZJOfxmSTn8\nZkk5/GZJOfxmSTn8Zkl5nN/acl6f/7z28cp7frOkHH6zpBx+s6QcfrOkHH6zpBx+s6QcfrOkPM5v\nHXXz3vc0rR1+/uhbQFo3ec9vlpTDb5aUw2+WlMNvlpTDb5aUw2+WlMNvlpTH+a3U1HcsKq1fN/u+\n0vrFj1/VtPbmQzta6smqMe6eX9LdkvZK2jpq3q2SdkvaUjwu6WybZla1iRz23wNcNMb82yJiafHY\nWG1bZtZp44Y/Ih4E/DlMs0mmnQt+10t6rDgtmN1sIUmrJQ1KGjzIgTY2Z2ZVajX8dwCLgKXAMPC5\nZgtGxEBE9EdE/zSmt7g5M6taS+GPiGciYiQiDgN3AudU25aZdVpL4Zc0b9TTjwJbmy1rZr1p3HF+\nSfcDy4A5knYBtwDLJC0FAhgCPtHBHq1GQ5fPLa3PmjKjtD79jr4q27EKjRv+iFg5xuy7OtCLmXWR\nP95rlpTDb5aUw2+WlMNvlpTDb5aUv9JrpWac+3xp/RAjpfWZO37atFa+pnWa9/xmSTn8Zkk5/GZJ\nOfxmSTn8Zkk5/GZJOfxmSXmc30q96/Th0vqa595dWh/Ztr3KdqxC3vObJeXwmyXl8Jsl5fCbJeXw\nmyXl8Jsl5fCbJeXwmyXl8Jsl5fCbJeXwmyXl8Jsl5fCbJeXwmyXl8JslNZFbdJ8B3AvMpXFL7oGI\nuF1SH/DPwJk0btO9IiKa/5F260lT55xWWv/sgg2l9U8OLR9nC88dY0fWLRPZ8x8CboyIJcB5wHWS\nlgA3AZsjYjGwuXhuZseJccMfEcMR8WgxvR/YBswHlgNri8XWApd2qkkzq94xnfNLOhM4G3gImBsR\nR/7G0x4apwVmdpyYcPglvQlYB9wQEftG1yIiaFwPGGu91ZIGJQ0e5EBbzZpZdSYUfknTaAT/ixHx\nlWL2M5LmFfV5wN6x1o2IgYjoj4j+aUyvomczq8C44Zck4C5gW0R8flRpA7CqmF4FrK++PTPrlIn8\n6e73AVcCj0vaUsy7GVgDfFnS1cBOYEVnWrROGr7inaX106acVFp/+s7FpfVTPdTXs8YNf0R8C1CT\n8oXVtmNm3eJP+Jkl5fCbJeXwmyXl8Jsl5fCbJeXwmyXlW3Qn9+bf+Elb68/a+WpFnVi3ec9vlpTD\nb5aUw2+WlMNvlpTDb5aUw2+WlMNvlpTH+a3Uk4d+Vlqf9pP/K62PVNmMVcp7frOkHH6zpBx+s6Qc\nfrOkHH6zpBx+s6QcfrOkPM6f3BULHi6tbznwltL6yPanqmzHush7frOkHH6zpBx+s6QcfrOkHH6z\npBx+s6QcfrOkxh3nl3QGcC8wFwhgICJul3QrcA3wbLHozRGxsVONWmuG/vS9pfVrT72jtH7WNz5e\nWl/ElmNtyXrERD7kcwi4MSIelXQK8IikTUXttoj4bOfaM7NOGTf8ETEMDBfT+yVtA+Z3ujEz66xj\nOueXdCZwNvBQMet6SY9JulvS7CbrrJY0KGnwIAfaatbMqjPh8Et6E7AOuCEi9gF3AIuApTSODD43\n1noRMRAR/RHRP43pFbRsZlWYUPglTaMR/C9GxFcAIuKZiBiJiMPAncA5nWvTzKo2bvglCbgL2BYR\nnx81f96oxT4KbK2+PTPrlIlc7X8fcCXwuKQj4zo3AyslLaUx/DcEfKIjHVpbDvYdbmv9uQ/4VG2y\nmsjV/m8BGqPkMX2z45g/4WeWlMNvlpTDb5aUw2+WlMNvlpTDb5aUIqJrG5ulvjhXF3Zte2bZPBSb\n2RcvjDU0/wbe85sl5fCbJeXwmyXl8Jsl5fCbJeXwmyXl8Jsl1dVxfknPAjtHzZoDPNe1Bo5Nr/bW\nq32Be2tVlb29NSJOn8iCXQ3/GzYuDUZEf20NlOjV3nq1L3BvraqrNx/2myXl8JslVXf4B2refple\n7a1X+wL31qpaeqv1nN/M6lP3nt/MauLwmyVVS/glXSTpfyXtkHRTHT00I2lI0uOStkgarLmXuyXt\nlbR11Lw+SZskbS9+jnmPxJp6u1XS7uK92yLpkpp6O0PSf0r6vqQnJP1+Mb/W966kr1ret66f80ua\nCvwQ+FVgF/AwsDIivt/VRpqQNAT0R0TtHwiR9AHgJeDeiHhXMe8zwAsRsab4xTk7Ij7VI73dCrxU\n923bi7tJzRt9W3ngUuDj1PjelfS1ghretzr2/OcAOyLiqYh4DfgSsLyGPnpeRDwIvHDU7OXA2mJ6\nLY3/PF3XpLeeEBHDEfFoMb0fOHJb+Vrfu5K+alFH+OcDT496vosa34AxBPA1SY9IWl13M2OYGxHD\nxfQeYG6dzYxh3Nu2d9NRt5XvmfeuldvdV80X/N7o/Ih4D3AxcF1xeNuTonHO1ktjtRO6bXu3jHFb\n+Z+r871r9Xb3Vasj/LuBM0Y9X1DM6wkRsbv4uRd4gN679fgzR+6QXPzcW3M/P9dLt20f67by9MB7\n10u3u68j/A8DiyW9TdKJwBXAhhr6eANJM4sLMUiaCXyI3rv1+AZgVTG9ClhfYy+v0yu3bW92W3lq\nfu967nb3EdH1B3AJjSv+TwJ/VEcPTfp6O/C94vFE3b0B99M4DDxI49rI1cBpwGZgO/B1oK+HersP\neBx4jEbQ5tXU2/k0DukfA7YUj0vqfu9K+qrlffPHe82S8gU/s6QcfrOkHH6zpBx+s6QcfrOkHH6z\npBx+s6T+Hx9jbUzs60hCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4d20c37160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train, test = chainer.datasets.get_mnist()\n",
    "# use train[data_point_index] to access data\n",
    "print(\"train[i][0] is the ith image that's flattened, and has shape:\", train[12][0].shape)\n",
    "print(\"train[i][1] is the ith image's label, such as:\", train[12][1])\n",
    "# here we visualize two of them\n",
    "plt.imshow(train[12][0].reshape([28, 28,]))\n",
    "plt.title(\"Label: %s\" % train[12][1])\n",
    "plt.figure()\n",
    "plt.imshow(train[42][0].reshape([28, 28,]))\n",
    "_ = plt.title(\"Label: %s\" % train[42][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will provide some boilerplate code and train a linear classifier as an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy: 0.0625; loss: 2.32046127319\n",
      "accuracy: 0.82; loss: 0.67633217454\n",
      "accuracy: 0.9025; loss: 0.431563625932\n",
      "accuracy: 0.8725; loss: 0.436200680137\n",
      "accuracy: 0.8875; loss: 0.416910642982\n",
      "accuracy: 0.9125; loss: 0.324158379734\n",
      "accuracy: 0.9025; loss: 0.37119664818\n",
      "accuracy: 0.8925; loss: 0.398179800808\n",
      "accuracy: 0.92; loss: 0.327991143167\n",
      "accuracy: 0.915; loss: 0.294581488669\n",
      "accuracy: 0.915; loss: 0.251825500131\n",
      "accuracy: 0.9325; loss: 0.28893787384\n",
      "accuracy: 0.9125; loss: 0.343733860552\n",
      "accuracy: 0.92; loss: 0.315376929939\n",
      "accuracy: 0.9475; loss: 0.244635521173\n",
      "accuracy: 0.9325; loss: 0.255046423227\n",
      "accuracy: 0.92; loss: 0.273771564662\n",
      "accuracy: 0.935; loss: 0.303561233878\n",
      "accuracy: 0.9125; loss: 0.336780593395\n",
      "accuracy: 0.935; loss: 0.288008983731\n",
      "accuracy: 0.94; loss: 0.228321945965\n",
      "accuracy: 0.9075; loss: 0.318285391927\n",
      "accuracy: 0.9375; loss: 0.268234203756\n",
      "accuracy: 0.9175; loss: 0.29458026439\n",
      "accuracy: 0.9175; loss: 0.291807190478\n",
      "accuracy: 0.9125; loss: 0.301603880227\n"
     ]
    }
   ],
   "source": [
    "def run(model, batchsize=16, num_epochs=2):\n",
    "    \n",
    "    optimizer = chainer.optimizers.Adam() # we will use chainer's Adam implementation instead of writing our own gradient based optimization\n",
    "    optimizer.setup(model)\n",
    "    \n",
    "    stats = defaultdict(lambda: deque(maxlen=25))\n",
    "    for epoch in range(num_epochs):\n",
    "        train_iter = chainer.iterators.SerialIterator(train, batchsize, repeat=False, shuffle=True)\n",
    "        test_iter = chainer.iterators.SerialIterator(test, batchsize, repeat=False, shuffle=False)\n",
    "        \n",
    "        for itr, batch in enumerate(train_iter):\n",
    "            xs = np.concatenate([datum[0][None, :] for datum in batch])\n",
    "            ys = np.array([datum[1] for datum in batch])\n",
    "\n",
    "            logits = model(xs)\n",
    "\n",
    "            loss = F.softmax_cross_entropy(logits, ys)\n",
    "            model.cleargrads()\n",
    "            loss.backward()\n",
    "            optimizer.update()\n",
    "            \n",
    "            # calculate stats\n",
    "            stats[\"loss\"].append(float(loss.data))\n",
    "            stats[\"accuracy\"].append(float((logits.data.argmax(1) == ys).sum() / batchsize))\n",
    "            if itr % 300 == 0:\n",
    "                print(\"; \".join(\"%s: %s\" % (k, np.mean(vs)) for k, vs in stats.items()))\n",
    "\n",
    "# try a simple linear model\n",
    "run(L.Linear(None, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will try to improve performance by training an MLP instead. A partial implementation is provided for you to fill in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy: 0.0625; loss: 2.31594276428\n",
      "accuracy: 0.9175; loss: 0.266508683562\n",
      "accuracy: 0.9325; loss: 0.19411064744\n",
      "accuracy: 0.9275; loss: 0.25324193716\n",
      "accuracy: 0.9325; loss: 0.209913341105\n",
      "accuracy: 0.945; loss: 0.177825641036\n",
      "accuracy: 0.9575; loss: 0.141109347939\n",
      "accuracy: 0.9475; loss: 0.15408366859\n",
      "accuracy: 0.97; loss: 0.117115167677\n",
      "accuracy: 0.9575; loss: 0.0909008306265\n",
      "accuracy: 0.97; loss: 0.111247750521\n",
      "accuracy: 0.955; loss: 0.137013470531\n",
      "accuracy: 0.9725; loss: 0.0714947903156\n",
      "accuracy: 0.9625; loss: 0.113363589048\n",
      "accuracy: 0.98; loss: 0.0709389805794\n",
      "accuracy: 0.975; loss: 0.0889854925871\n",
      "accuracy: 0.985; loss: 0.0516876414418\n",
      "accuracy: 0.9675; loss: 0.138806474209\n",
      "accuracy: 0.955; loss: 0.124097278714\n",
      "accuracy: 0.97; loss: 0.0737819629908\n",
      "accuracy: 0.9725; loss: 0.0771839380264\n",
      "accuracy: 0.9825; loss: 0.0438422170281\n",
      "accuracy: 0.9675; loss: 0.0992624759674\n",
      "accuracy: 0.965; loss: 0.122117995024\n",
      "accuracy: 0.9675; loss: 0.115024679601\n",
      "accuracy: 0.9825; loss: 0.073054381609\n"
     ]
    }
   ],
   "source": [
    "class MLP(chainer.Chain):\n",
    "\n",
    "    def __init__(self, n_units, n_out):\n",
    "        super(MLP, self).__init__()\n",
    "        with self.init_scope():\n",
    "            # the size of the inputs to each layer will be inferred\n",
    "            self.l1 = L.Linear(None, n_units)  # n_in -> n_units\n",
    "            self.l2 = L.Linear(None, n_units)  # n_units -> n_units\n",
    "            self.l3 = L.Linear(None, n_out)  # n_units -> n_out\n",
    "\n",
    "    def __call__(self, x):\n",
    "        # *** YOUR CODE HERE TO BUILD AN MLP W/ self.l1, self.l2, self.l3 ***\n",
    "        # \n",
    "        # Hint: you should make use of non-linearities / activation functions\n",
    "        #     https://docs.chainer.org/en/stable/reference/functions.html#activation-functions\n",
    "        x = F.relu(self.l1(x))\n",
    "        x = F.relu(self.l2(x))\n",
    "        x = self.l3(x)\n",
    "        return x\n",
    "run(MLP(200, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next you should try to implement logging test loss and see if the model is overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_loss: 2.28831; accuracy: 0.1875; loss: 2.23641705513; test_accuracy: 0.1232\n",
      "test_loss: 0.314889; accuracy: 0.8825; loss: 0.375114524364; test_accuracy: 0.9061\n",
      "test_loss: 0.220765; accuracy: 0.9425; loss: 0.202896259427; test_accuracy: 0.9315\n",
      "test_loss: 0.207392; accuracy: 0.9425; loss: 0.176324358881; test_accuracy: 0.9352\n",
      "test_loss: 0.221745; accuracy: 0.9525; loss: 0.192280195653; test_accuracy: 0.9293\n",
      "test_loss: 0.165214; accuracy: 0.955; loss: 0.141820861697; test_accuracy: 0.9485\n",
      "test_loss: 0.140204; accuracy: 0.9525; loss: 0.180047000051; test_accuracy: 0.9579\n",
      "test_loss: 0.134326; accuracy: 0.96; loss: 0.147384900451; test_accuracy: 0.9601\n",
      "test_loss: 0.130313; accuracy: 0.955; loss: 0.167229895592; test_accuracy: 0.9609\n",
      "test_loss: 0.120142; accuracy: 0.9625; loss: 0.115275173485; test_accuracy: 0.9624\n",
      "test_loss: 0.105237; accuracy: 0.97; loss: 0.0883056977391; test_accuracy: 0.9661\n",
      "test_loss: 0.128996; accuracy: 0.9625; loss: 0.135939595103; test_accuracy: 0.9601\n",
      "test_loss: 0.113456; accuracy: 0.9675; loss: 0.103017296791; test_accuracy: 0.9653\n",
      "test_loss: 0.105752; accuracy: 0.9675; loss: 0.0749690851569; test_accuracy: 0.9681\n",
      "test_loss: 0.100812; accuracy: 0.975; loss: 0.0744584748149; test_accuracy: 0.9686\n",
      "test_loss: 0.120662; accuracy: 0.9675; loss: 0.0959579020739; test_accuracy: 0.9644\n",
      "test_loss: 0.110436; accuracy: 0.97; loss: 0.0862606954575; test_accuracy: 0.9637\n",
      "test_loss: 0.0958224; accuracy: 0.975; loss: 0.0715580525994; test_accuracy: 0.9686\n",
      "test_loss: 0.0816625; accuracy: 0.98; loss: 0.0677686110139; test_accuracy: 0.9742\n",
      "test_loss: 0.111627; accuracy: 0.965; loss: 0.107404745817; test_accuracy: 0.9653\n",
      "test_loss: 0.0990185; accuracy: 0.9675; loss: 0.0789766716957; test_accuracy: 0.9682\n",
      "test_loss: 0.0937835; accuracy: 0.9675; loss: 0.089258158803; test_accuracy: 0.9709\n",
      "test_loss: 0.0947481; accuracy: 0.9575; loss: 0.134399876297; test_accuracy: 0.9693\n",
      "test_loss: 0.107915; accuracy: 0.96; loss: 0.103552013338; test_accuracy: 0.9673\n",
      "test_loss: 0.10877; accuracy: 0.97; loss: 0.0778160172701; test_accuracy: 0.9654\n",
      "test_loss: 0.0941961; accuracy: 0.9575; loss: 0.154451772571; test_accuracy: 0.9703\n"
     ]
    }
   ],
   "source": [
    "def better_run(model, batchsize=16, num_epochs=2):\n",
    "\n",
    "    optimizer = chainer.optimizers.Adam() # we will use chainer's Adam implementation instead of writing our own gradient based optimization\n",
    "    optimizer.setup(model)\n",
    "    \n",
    "    stats = defaultdict(lambda: deque(maxlen=25))\n",
    "    for epoch in range(num_epochs):\n",
    "        train_iter = chainer.iterators.SerialIterator(train, batchsize, repeat=False, shuffle=True)\n",
    "        for itr, batch in enumerate(train_iter):\n",
    "            xs = np.concatenate([datum[0][None, :] for datum in batch])\n",
    "            ys = np.array([datum[1] for datum in batch])\n",
    "\n",
    "            logits = model(xs)\n",
    "\n",
    "            loss = F.softmax_cross_entropy(logits, ys)\n",
    "            model.cleargrads()\n",
    "            loss.backward()\n",
    "            optimizer.update()\n",
    "            \n",
    "            # calculate stats\n",
    "            stats[\"loss\"].append(float(loss.data))\n",
    "            stats[\"accuracy\"].append(float((logits.data.argmax(1) == ys).sum() / batchsize))\n",
    "            if itr % 300 == 0:\n",
    "                # test_iter = chainer.iterators.SerialIterator(test, batchsize, repeat=False, shuffle=False)\n",
    "                # *** YOUR CODE implement logging of stats on test set ***\n",
    "                xs = np.concatenate([datum[0][None, :] for datum in test])\n",
    "                ys = np.array([datum[1] for datum in test])\n",
    "                logits = model(xs)\n",
    "                stats[\"test_accuracy\"] = F.accuracy(logits, ys).data\n",
    "                stats[\"test_loss\"] = F.softmax_cross_entropy(logits, ys).data\n",
    "                print(\"; \".join(\"%s: %s\" % (k, np.mean(vs)) for k, vs in stats.items()))\n",
    "\n",
    "better_run(MLP(200, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try different variants!\n",
    "\n",
    "- Does using a ConvNet improve performance (reduce overfitting?)\n",
    "- Try changing the learning rate and observe the effect\n",
    "- Does the model train if you give it correlated gradients? (consecutively sample many batches of \"1\", then many batches of \"2\", ... etc"
   ]
  }
 ],
 "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}