07_theano_simple_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center> Simple function regression </center>\n",
    "\n",
    "## Neural Network Scratch\n",
    "\n",
    "<img src=\"images/regr.png\" width = \"50%\">\n",
    "\n",
    "* Why 2 hidden layers? No idea, it just works better this way. I guess playing with learning rate, sample size and training steps would allow to run the same with just one hidden layer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import theano\n",
    "import theano.tensor as T\n",
    "import theano.tensor.nnet as nnet\n",
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "rng = numpy.random # random number generator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### NET ###\n",
    "\n",
    "N = 1000            # number learning of samples\n",
    "nTrainSteps = 10000 # number of training steps\n",
    "alpha = 0.1         # learning rate\n",
    "nTestSamples = 1000 # number of testing samples\n",
    "\n",
    "### FUNCTION ###\n",
    "\n",
    "def f (x): # function to find\n",
    "  return x**2\n",
    "\n",
    "# xrange for f(x)\n",
    "\n",
    "minX = -5\n",
    "maxX = 10\n",
    "\n",
    "xFactor = max(abs(minX), abs(maxX)) # to convert from [-minX, maxX] to [-1,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate training sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def randomX(n, a = minX, b = maxX): # n random number in the range [a,b]\n",
    "    return ((b - a) * rng.sample(n) + a)\n",
    "\n",
    "# generate training sample\n",
    "\n",
    "X = randomX (N)       # random points [minX,maxX]\n",
    "Y = [f(x) for x in X] # value of f\n",
    "\n",
    "# normalize training sample\n",
    "\n",
    "Xn = [(x) / xFactor for x in X] # [-1, 1] -> for efficiency (sigmoid(-100) ~ sigmoid(1000))\n",
    "\n",
    "minY = min(Y) # minimum f(x) in the given x range\n",
    "maxY = max(Y) # maximum f(x) in the given x range\n",
    "\n",
    "def scale (x, a = minY, b = maxY): # scale from [a, b] to [0, 1] range\n",
    "    return (x - a) / (b - a)\n",
    "\n",
    "def scaleBack (x, a = minY, b = maxY): # scale from [0, 1] to [a, b]\n",
    "    return (b - a) * x + a\n",
    "\n",
    "Yn = [scale(y) for y in Y] # [minY, maxY] -> [0, 1], beacuse sigmoid in [0,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot training sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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9bbPL+hqgiEgxsyxoa4NI3lhWBr/4hbsxiYhIas55rf9i1F/kpNcaVBYiItIn4XA0sQaY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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0780f70410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, plots = plt.subplots(1,2) # create a 1x2 grid of plots\n",
    "\n",
    "fig.set_size_inches((2, 1) * fig.get_size_inches()) # double horizontal size of figure\n",
    "\n",
    "# training sample\n",
    "\n",
    "plots[0].set_title('Training sample')\n",
    "plots[0].set_xlabel('x')\n",
    "plots[0].set_ylabel('y')\n",
    "\n",
    "plots[0].plot(X, Y, 'b.')\n",
    "\n",
    "# normalized training sample\n",
    "\n",
    "plots[1].set_title('Normalized training sample')\n",
    "plots[1].set_xlabel('x')\n",
    "plots[1].set_ylabel('y')\n",
    "\n",
    "plots[1].plot(Xn, Yn, 'g.')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "###### SYMBOLIC VARIABLES ###\n",
    "\n",
    "x = T.vector('x') # input\n",
    "y = T.scalar('y') # expected value\n",
    "\n",
    "w1 = theano.shared(rng.rand(2,2), name = 'w1') # first hidden layer's weights (including bias)\n",
    "w2 = theano.shared(rng.rand(3,2), name = 'w2') # second hidden layer's weights (including bias)\n",
    "w3 = theano.shared(rng.rand(3), name = 'w3')   # output layer's weights (including bias)\n",
    "\n",
    "### EXPRESSION GRAPH ###\n",
    "\n",
    "def layer (x, w):\n",
    "    b = numpy.array([1])      # bias term\n",
    "    xb = T.concatenate([x,b]) # input x with bias added\n",
    "    return nnet.sigmoid(T.dot(w.T,xb))\n",
    "\n",
    "hiddenLayer  = layer (x, w1)                  # hidden layer 1\n",
    "hiddenLayer2 = layer (hiddenLayer, w2)        # hidden layer 2\n",
    "outputLayer  = T.sum(layer(hiddenLayer2, w3)) # output layer\n",
    "\n",
    "cost = (outputLayer - y)**2                   # cost function\n",
    "\n",
    "def gradient (c, w):                 # cost function, weights\n",
    "    return w - alpha * T.grad (c, w) # update weights\n",
    "\n",
    "### COMPILE ###\n",
    "\n",
    "train = theano.function(inputs = [x,y],\n",
    "                        outputs = cost,\n",
    "                        updates = [(w1, gradient(cost, w1)),\n",
    "                                   (w2, gradient(cost, w2)),\n",
    "                                   (w3, gradient(cost, w3))])\n",
    "\n",
    "predict = theano.function(inputs=[x], outputs=outputLayer)\n",
    "\n",
    "### TRAIN ###\n",
    "\n",
    "for i in range (nTrainSteps):\n",
    "    for j in range(N):\n",
    "        c = train([Xn[j]], Yn[j]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dWaow64PtjB9vdygRJ3H5MjRuzK7ctWi2ZwTLlqsopHcqDPG8vWH6dLJ8OIgF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\nRERERERERERERERERERExLn8P1unx2LCZSlxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0780d75290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# prepare testing sample\n",
    "\n",
    "test = (randomX(nTestSamples)) # random x values\n",
    "test.sort()                    # sorted x values\n",
    "\n",
    "expected  = [f(t) for t in test]                              # expexted values for test points\n",
    "predicted = [scaleBack(predict([t / xFactor])) for t in test] # predicited values for test points\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.plot(test, expected, 'b', label = 'Expected')\n",
    "plt.plot(test, predicted, 'r', label = 'Predicted')\n",
    "\n",
    "plt.legend(loc=2) # legend in upper left corner\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "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": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}