Demo Notebook for the TA Session from 30.10.2015

Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.array([1, 2, 3, 2, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f423c9d7ef0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f423ea628d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.random.randn(100)\n",
    "y = np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f423a97f4a8>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gCF5WSWxxcY+mpvZKWpJ0h6TP6vTpv9fKyi7Nz+/um8Svu267pPdIKr4k0iv5rKzs2jRG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\nEjgARIoEDgCR+n8pjnf7ct6coQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f423ca2f160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markup\n",
    "other text\n",
    "\n",
    "$x_i = 12$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nr_inputs = 2\n",
    "nr_examples = 10\n",
    "\n",
    "X = np.random.randn(nr_inputs, nr_examples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f423a853240>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pVEScjoiXJd0r6cZB+yzbOP6PpqbejWNd1NQbahqtYc3xf1zS0TavXyLpzKb1p/PXAAAV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\nGIIfABLzf2jaeA1/t1k0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f423a895320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[0], X[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nr_hid = 5\n",
    "\n",
    "W = np.random.randn(nr_inputs, nr_hid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H = np.dot(X.T, W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 5)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.54452406, -0.5537587 , -0.92271437,  0.96583749,  0.37911714],\n",
       "       [-0.46361784,  0.91916244,  0.12191831, -0.94046617, -0.86199782],\n",
       "       [ 0.05754065, -0.95565177,  0.95636015,  0.31133529,  0.93597057],\n",
       "       [-0.78171908,  0.90999548,  0.97818869, -0.99823641, -0.80032524],\n",
       "       [-0.49866617,  0.32188822,  0.93460688, -0.94690781, -0.15162181],\n",
       "       [-0.81700905, -0.22364497,  0.99979299, -0.99880042,  0.47936414],\n",
       "       [ 0.61247239, -0.58751963, -0.95930993,  0.98239383,  0.39391214],\n",
       "       [-0.75303432,  0.83243437,  0.98236399, -0.9970919 , -0.67370374],\n",
       "       [ 0.20072429,  0.96086947, -0.99463016,  0.47837135, -0.95024969],\n",
       "       [-0.14326874, -0.3438382 ,  0.73788608, -0.41585964,  0.34992547]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tanh(H)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bias = np.array([0, 1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 5)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5,)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bias.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "bias = bias.reshape(5, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 5)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.6105641 , -0.50190986,  0.05760428, -1.04977555, -0.54752928,\n",
       "        -1.14775518,  0.71286842, -0.97992704,  0.20348713, -0.14426123],\n",
       "       [ 0.3762138 ,  2.58360119, -0.89320304,  2.52749813,  1.33375216,\n",
       "         0.77251029,  0.32613026,  2.19601277,  2.95712014,  0.64156114],\n",
       "       [ 0.39300744,  2.12252783,  3.90143507,  4.25375404,  3.69362115,\n",
       "         6.58789325,  0.06281821,  4.3610512 , -0.9587077 ,  2.94582278],\n",
       "       [ 5.02627236,  1.25793063,  3.32202334, -0.51633502,  1.19901612,\n",
       "        -0.70916693,  5.36190539, -0.26597367,  3.5208702 ,  2.55732457],\n",
       "       [ 4.39902819,  2.69893208,  5.70451065,  2.90048361,  3.8472    ,\n",
       "         4.52215839,  4.4164223 ,  3.18250575,  2.16565199,  4.36535883]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.T + bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x, w):\n",
    "    return np.dot(x, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.random.randn(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = np.random.randn(5, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.24408677,  1.17294168,  1.69420828])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def E(h):\n",
    "    return np.sum(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e= E(f(x, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "epsilon = 1e-5\n",
    "w2 = w.copy()\n",
    "w2[0,0] = w[0, 0] + epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e2 = E(f(x, w2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47638558524631941"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(e2 - e)/ epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gradient = np.zeros((5, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gradient[0, 0] = (e2 - e)/ epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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