09-theano/09.11-net-on-mnist.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Theano 实例：人工神经网络"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "神经网络的模型可以参考 UFLDL 的教程，这里不做过多描述。 \n",
    "\n",
    "http://ufldl.stanford.edu/wiki/index.php/%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using gpu device 1: Tesla K10.G2.8GB (CNMeM is disabled)\n"
     ]
    }
   ],
   "source": [
    "import theano\n",
    "import theano.tensor as T\n",
    "\n",
    "import numpy as np\n",
    "from load import mnist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们在这里使用一个简单的三层神经网络：输入 - 隐层 - 输出。\n",
    "\n",
    "对于网络的激活函数，隐层用 `sigmoid` 函数，输出层用 `softmax` 函数，其模型如下： \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    h & = \\sigma (W_h X) \\\\\n",
    "    o & = \\text{softmax} (W_o h)\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, w_h, w_o):\n",
    "    \"\"\"\n",
    "    input:\n",
    "        X: input data\n",
    "        w_h: hidden unit weights\n",
    "        w_o: output unit weights\n",
    "    output:\n",
    "        Y: probability of y given x\n",
    "    \"\"\"\n",
    "    # 隐层\n",
    "    h = T.nnet.sigmoid(T.dot(X, w_h))\n",
    "    # 输出层\n",
    "    pyx = T.nnet.softmax(T.dot(h, w_o))\n",
    "    return pyx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用随机梯度下降的方法进行训练："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sgd(cost, params, lr=0.05):\n",
    "    \"\"\"\n",
    "    input:\n",
    "        cost: cost function\n",
    "        params: parameters\n",
    "        lr: learning rate\n",
    "    output:\n",
    "        update rules\n",
    "    \"\"\"\n",
    "    grads = T.grad(cost=cost, wrt=params)\n",
    "    updates = []\n",
    "    for p, g in zip(params, grads):\n",
    "        updates.append([p, p - g * lr])\n",
    "    return updates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于 `MNIST` 手写数字的问题，我们使用一个 `784 × 625 × 10` 即输入层大小为 `784`，隐层大小为 `625`，输出层大小为 `10` 的神经网络来模拟，最后的输出表示数字为 `0` 到 `9` 的概率。\n",
    "\n",
    "为了对权重进行更新，我们需要将权重设为 shared 变量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def floatX(X):\n",
    "    return np.asarray(X, dtype=theano.config.floatX)\n",
    "\n",
    "def init_weights(shape):\n",
    "    return theano.shared(floatX(np.random.randn(*shape) * 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "因此变量初始化为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = T.matrix()\n",
    "Y = T.matrix()\n",
    "\n",
    "w_h = init_weights((784, 625))\n",
    "w_o = init_weights((625, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "模型输出为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "py_x = model(X, w_h, w_o)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "预测的结果为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_x = T.argmax(py_x, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "模型的误差函数为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cost = T.mean(T.nnet.categorical_crossentropy(py_x, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "更新规则为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "updates = sgd(cost, [w_h, w_o])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义训练和预测的函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train = theano.function(inputs=[X, Y], outputs=cost, updates=updates, allow_input_downcast=True)\n",
    "predict = theano.function(inputs=[X], outputs=y_x, allow_input_downcast=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "训练："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导入 MNIST 数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "trX, teX, trY, teY = mnist(onehot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "训练 100 轮，正确率为 0.956："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "for i in range(100):\n",
    "    for start, end in zip(range(0, len(trX), 128), range(128, len(trX), 128)):\n",
    "        cost = train(trX[start:end], trY[start:end])\n",
    "    print \"{0:03d}\".format(i), np.mean(np.argmax(teY, axis=1) == predict(teX))"
   ]
  }
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