A Simple Neural Network with Lasagne/Theano and Keras

simpleNeuralNetwork.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/paul/anaconda/lib/python2.7/site-packages/theano/tensor/signal/downsample.py:5: UserWarning: downsample module has been moved to the pool module.\n",
      "  warnings.warn(\"downsample module has been moved to the pool module.\")\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "import theano\n",
    "import lasagne\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.10.4'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train a Neural Network to predict a function\n",
    "\n",
    "Which should be possible for every function: http://neuralnetworksanddeeplearning.com/chap4.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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64oBgBEoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107ad4d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = lambda x: np.sin(2*x)\n",
    "x = np.linspace(0, 1, 100)\n",
    "y = f(x)\n",
    "plt.plot(x, y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = x.reshape((1, -1))\n",
    "#y = y.reshape((-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 100)\n",
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "print(np.shape(X))\n",
    "print(np.shape(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "input_var = theano.tensor.vector(name='X', dtype=theano.config.floatX)\n",
    "target_var = theano.tensor.scalar(name='y', dtype=theano.config.floatX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Set up the Layers\n",
    "\n",
    "1. Input Layer, size 1\n",
    "2. Hidden Layer, fully connected, size 100\n",
    "3. Output Layer, fully connected, size 1\n",
    "\n",
    "$y=g(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def build_NeuralNetwork(input_var=None):\n",
    "    layer_in = lasagne.layers.InputLayer(\n",
    "                    shape=(1, ),\n",
    "                    input_var=input_var)\n",
    "    layer_hid1 = lasagne.layers.DenseLayer(\n",
    "                    layer_in, num_units=200,\n",
    "                    nonlinearity=lasagne.nonlinearities.rectify,\n",
    "                    W=lasagne.init.Uniform())\n",
    "    layer_out = lasagne.layers.DenseLayer(\n",
    "                    layer_hid1, num_units=1)\n",
    "    return layer_out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "network = build_NeuralNetwork(input_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "initial_W = network.W.get_value()\n",
    "initial_b = network.b.get_value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "prediction = lasagne.layers.get_output(network)\n",
    "loss = lasagne.objectives.squared_error(prediction, target_var)\n",
    "loss = loss.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "params = lasagne.layers.get_all_params(network, trainable=True)\n",
    "updates = lasagne.updates.adagrad(loss, params, learning_rate=1.0, epsilon=1e-06)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Training Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train_fn = theano.function([input_var, target_var], loss, updates=updates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1: Loss 0.592776\n",
      "Epoch 1000: Loss 0.592776\n",
      "Epoch 2000: Loss 0.592776\n",
      "Epoch 3000: Loss 0.592776\n",
      "Epoch 4000: Loss 0.592776\n",
      "Epoch 5000: Loss 0.592776\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(5000):\n",
    "    loss = 0\n",
    "    for i in range(X.size):\n",
    "        \n",
    "        # Train the Network\n",
    "        loss += train_fn(X[:,i], y[i])\n",
    "    \n",
    "    # Outputs\n",
    "    if epoch==0 or epoch%1000==999:\n",
    "        print(\"Epoch %d: Loss %g\" % (epoch + 1, loss/X.size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(0.51)=0.00\n"
     ]
    }
   ],
   "source": [
    "test_prediction = lasagne.layers.get_output(network, deterministic=True)\n",
    "predict_fn = theano.function([input_var], theano.tensor.argmax(test_prediction, axis=1))\n",
    "print(\"f(%.2f)=%.2f\" % (X[:,50], predict_fn(X[:,50])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trained_W = network.W.get_value()\n",
    "trained_b = network.b.get_value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109352790>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/paul/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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SDeTnT2Pr1h1s2bKclJRBeDxna3pxglC3mIjEjcY9V54iGHSUl19IdXUSo0efTGlpJenp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\nEYm6/w89TYcMhGY4HgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109158310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(initial_W, trained_W, c='b', alpha=0.5)\n",
    "plt.scatter(initial_b, trained_b, c='g', alpha=0.5)\n",
    "plt.xlabel('initial')\n",
    "plt.ylabel('trained')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Plot the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_pred = []\n",
    "for i in range(X.size):\n",
    "    y_pred.append(predict_fn(X[:,i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10964cb10>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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APr3QfS/gXPwkcFG3PHk+z8WMun8APga8ZaH7XsCfixXAF4HV3folC933As7FB5h+Dgrg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109158850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# :-(\n",
    "\n",
    "Is not learning at all"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}

simpleNeuralNetworkKeras.ipynb