NeuralNetworkSigmoid.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural Network with Sigmoid for Regression\n",
    "\n",
    "Three-layer neural network for regression tasks using Sigmoid activation function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class NeuralNetwork():\n",
    "    def __init__(self, inputLayerSize, hiddenLayerSize, outputLayerSize):\n",
    "        self.inputLayerSize = inputLayerSize \n",
    "        self.hiddenLayerSize = hiddenLayerSize \n",
    "        self.outputLayerSize = outputLayerSize \n",
    "        \n",
    "        # Initialize Weights\n",
    "        self.Wh = np.random.randn(inputLayerSize, hiddenLayerSize)/np.sqrt(inputLayerSize)\n",
    "        self.Wo = np.random.randn(hiddenLayerSize, outputLayerSize)/np.sqrt(hiddenLayerSize)\n",
    "        \n",
    "        # Initialize Biases\n",
    "        self.Bh = np.zeros((1, hiddenLayerSize))\n",
    "        self.Bo = np.zeros((1, outputLayerSize))\n",
    "        \n",
    "        # Normalized Data Range\n",
    "        self.minNorm = 0\n",
    "        self.maxNorm = 1\n",
    "        \n",
    "        # Weighted Inputs\n",
    "        self.Zh = None\n",
    "        self.Zo = None\n",
    "        \n",
    "        # Activations\n",
    "        self.Ah = None\n",
    "        self.Ao = None\n",
    "        \n",
    "    def normalize(self, X, newMin, newMax):\n",
    "        curMin = np.amin(X, axis=0)\n",
    "        curMax = np.amax(X, axis=0)\n",
    "        curRange = (curMax - curMin)  \n",
    "        newRange = (newMax - newMin)\n",
    "        return (((X - curMin) * newRange) / curRange) + newMin\n",
    "\n",
    "    def denormalize(self, normalized, oldMin, oldMax):\n",
    "        return self.normalize(normalized, oldMin, oldMax)\n",
    "\n",
    "    def sigmoid(self, z):\n",
    "        return 1/(1+np.exp(-z))\n",
    "    \n",
    "    def sigmoidGradient(self,z):\n",
    "        #http://mathworld.wolfram.com/SigmoidFunction.html\n",
    "        #Z = WeightedInput to the CurrentLayer\n",
    "        #We could alternatively pass in the Activation value\n",
    "        #At which point the formula would become Activation*(1-Activation)\n",
    "        #np.exp(-z)/((1+np.exp(-z))**2)\n",
    "        return self.sigmoid(z)*(1-self.sigmoid(z))\n",
    "    \n",
    "    def cost(self, X, y):\n",
    "        output = self.feed_forward(X)\n",
    "        cost = np.sum((output-y)**2) / 2.0\n",
    "        return cost\n",
    "    \n",
    "    def costGradient(self, output, y):\n",
    "        return output - y\n",
    "    \n",
    "    def dCdW(self, layer_input, layer_error):\n",
    "        #Derivative of Cost with respect to any weight in the network\n",
    "        return np.dot(layer_input.T, layer_error)\n",
    "            \n",
    "    def dCdB(self, curLayerError):\n",
    "        #Derivative of Cost with respect to the Bias of any neuron in the network\n",
    "        '''\n",
    "        CurLayerError has one row for each observation in our training set.\n",
    "        This is fine for dCdW because the matrix multiplication takes\n",
    "        care of transforming the output into dimensions that\n",
    "        equal our weight dimensions (so we can subtract).\n",
    "        However bias isn't multiplied by anything so we're stuck with \n",
    "        the dimensions of the output error. To fix this take the sum of\n",
    "        all the output errors across observations (we could also take the average\n",
    "        but our learning rate will handle scaling this value appropriately).\n",
    "        The operation below sums all the values in a matrix on the row axis (0).\n",
    "        It's essentially like summing all the rows into a single row. The column\n",
    "        dimensions remain unchanged.\n",
    "        '''\n",
    "        return np.sum(curLayerError, axis=0, keepdims=True)\n",
    "    \n",
    "    def feed_forward(self, X):\n",
    "        self.Zh = np.dot(X, self.Wh) + self.Bh\n",
    "        self.Ah = self.sigmoid(self.Zh)\n",
    "        self.Zo = np.dot(self.Ah, self.Wo) + self.Bo\n",
    "        self.Ao = self.sigmoid(self.Zo) #network output\n",
    "        return self.Ao\n",
    "    \n",
    "    def backprop(self, X, output, y):\n",
    "        err_output = self.costGradient(output, y) * self.sigmoidGradient(self.Zo)\n",
    "        err_hidden = np.dot(err_output, self.Wo.T) * self.sigmoidGradient(self.Zh)\n",
    "        \n",
    "        # Weight Gradients\n",
    "        dCdWh = self.dCdW(X, err_hidden)\n",
    "        dCdWo = self.dCdW(self.Ah, err_output)\n",
    "        \n",
    "        # Bias Gradients\n",
    "        dCdBh = self.dCdB(err_hidden)\n",
    "        dCdBo = self.dCdB(err_output)\n",
    "\n",
    "        return dCdWh, dCdWo, dCdBh, dCdBo\n",
    "    \n",
    "    def update_weights(self, X, y, lr):\n",
    "        output = self.feed_forward(X)\n",
    "        dCdWh, dCdWo, dCdBh, dCdBo = self.backprop(X, output, y)\n",
    "        \n",
    "        # Update Weights\n",
    "        self.Wh -= lr * dCdWh\n",
    "        self.Wo -= lr * dCdWo\n",
    "        \n",
    "        # Update Biases\n",
    "        self.Bh -= lr * dCdBh\n",
    "        self.Bo -= lr * dCdBo\n",
    "    \n",
    "        cost = self.cost(X, y)\n",
    "        return cost\n",
    "\n",
    "    def train(self, X, y, epochs, lr, log_interval):\n",
    "        X = self.normalize(X, self.minNorm, self.maxNorm)\n",
    "        y = self.normalize(y, self.minNorm, self.maxNorm)\n",
    "        cost_history = []\n",
    "        for epoch in range(1,epochs+1):\n",
    "            self.log(\"Epoch %d ---------------\" % epoch, epoch, log_interval)\n",
    "            cost = self.update_weights(X, y, lr)\n",
    "            cost_history.append(cost)\n",
    "            msg = \"Cost:\" + str(round(cost,5)) + \"\\n\"\n",
    "            self.log(msg, epoch, log_interval)\n",
    "        return cost_history\n",
    "    \n",
    "    def predict(self, X, y_min, y_max):\n",
    "        normalized_input = self.normalize(X, self.minNorm, self.maxNorm)\n",
    "        output = self.feed_forward(normalized_input)\n",
    "        denormalized_output = self.denormalize(output, y_min, y_max)\n",
    "        return denormalized_output\n",
    "    \n",
    "    def log(self, msg, epoch, log_interval):\n",
    "        if epoch % log_interval == 0:\n",
    "            print(msg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def graph(x, y, xlabel=\"X\", ylabel=\"Y\", title=\"X vs Y\"):\n",
    "    plt.plot(x, y)\n",
    "    plt.title(title)\n",
    "    plt.xlabel(xlabel)\n",
    "    plt.ylabel(ylabel)\n",
    "    plt.show()\n",
    "    \n",
    "def graph_error(error_history):\n",
    "    iterations = [i for i in range(1,len(error_history)+1)]\n",
    "    plt.plot(iterations, error_history)\n",
    "    plt.title('Error Rate')\n",
    "    plt.xlabel('Training Iterations')\n",
    "    plt.ylabel('Mean Squared Error')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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2o5kVmllheXl5TEIu2riLucu3cdMZR9Mtp3VMnkNEJNFlxOqBzWwB0NQ3zXe5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\nREQkYioRERGJmEpEREQi9v8BkyaZzBwMKmIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c9e12e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ik8VyTGMGdeHy0zvx2LQ1vD6vwHcciVKV1bX88I2vND0cg5J8B5DoZ2Y8ds1A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\n4XSKbbjPmAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1034b8940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def quadratic(x):\n",
    "    return x**2 + x + 3\n",
    "\n",
    "def get_quadratic_data(start,end):\n",
    "    X = np.array([i for i in range(start,end)], dtype=\"float64\")    \n",
    "    X.shape = (len(X),1)\n",
    "    \n",
    "    y = np.array([quadratic(X[i]) for i in range(len(X))], dtype=\"float64\")\n",
    "    y.shape = (len(y),1)\n",
    "    \n",
    "    return X, y\n",
    "\n",
    "def cubic(x):\n",
    "    return x**3 + x**2 - x - 1\n",
    "\n",
    "def get_cubic_data(start,end):\n",
    "    X = np.array([i for i in range(start,end)], dtype=\"float64\")    \n",
    "    X.shape = (len(X),1)\n",
    "    \n",
    "    y = np.array([cubic(X[i]) for i in range(len(X))], dtype=\"float64\")\n",
    "    y.shape = (len(y),1)\n",
    "    \n",
    "    return X, y\n",
    "\n",
    "cX, cy = get_cubic_data(-6,6)\n",
    "graph(cX,cy)\n",
    "\n",
    "qX, qy = get_quadratic_data(-6,6)\n",
    "graph(qX,qy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X,y = get_quadratic_data(-20,21)\n",
    "#X,y = get_cubic_data(-5,6)\n",
    "nn = NeuralNetwork(1,2,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 5000 ---------------\n",
      "Cost:0.02902\n",
      "\n",
      "Epoch 10000 ---------------\n",
      "Cost:0.02791\n",
      "\n",
      "Epoch 15000 ---------------\n",
      "Cost:0.02735\n",
      "\n",
      "Epoch 20000 ---------------\n",
      "Cost:0.02689\n",
      "\n",
      "Epoch 25000 ---------------\n",
      "Cost:0.0265\n",
      "\n",
      "Epoch 30000 ---------------\n",
      "Cost:0.02617\n",
      "\n",
      "Epoch 35000 ---------------\n",
      "Cost:0.02589\n",
      "\n",
      "Epoch 40000 ---------------\n",
      "Cost:0.02565\n",
      "\n",
      "Epoch 45000 ---------------\n",
      "Cost:0.02544\n",
      "\n",
      "Epoch 50000 ---------------\n",
      "Cost:0.02526\n",
      "\n",
      "Epoch 55000 ---------------\n",
      "Cost:0.02509\n",
      "\n",
      "Epoch 60000 ---------------\n",
      "Cost:0.02495\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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gmAmh5B6GmdmgIj2MDwFHANuAS4GngY80M6h2USmJAScMMzOgQQ9DUhn4VET8BfCxsQmp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\n/k9HTi8aswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10329a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cost_hist = nn.train(X, y, epochs=60000, lr=.1, log_interval=5000)\n",
    "graph_error(cost_hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "start,end = (-20,20)\n",
    "\n",
    "#Quadratic\n",
    "X,y = get_quadratic_data(start,end)\n",
    "output = nn.predict(X,y_min=0,y_max=quadratic(max(abs(start), abs(end))))\n",
    "\n",
    "#Cubic\n",
    "#X,y = get_cubic_data(start, end)\n",
    "#output = nn.predict(X,y_min=cubic(start), y_max=cubic(end))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EcB5HNhqdsDEPXLJrztajbE3J4qUbOxLawM+EcK5FCr3J6vv7kdf1HnpbdjF3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\nXggh3Nz/AxkNX1cmSQTIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c1dc8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,y)\n",
    "plt.plot(X,output)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scikit-Learn Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 566,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#https://scikit-neuralnetwork.readthedocs.io/en/latest/module_mlp.html#regressor\n",
    "from sknn.mlp import Regressor\n",
    "from sknn.mlp import Layer\n",
    "hiddenLayer = Layer(\"Sigmoid\", units=3)\n",
    "outputLayer = Layer(\"Linear\", units=1)\n",
    "nn = Regressor([hiddenLayer, outputLayer],learning_rule='sgd',learning_rate=.01,\n",
    "               batch_size=5,loss_type=\"mse\",debug=False,verbose=False,regularize=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 567,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initializing neural network with 2 layers, 1 inputs and 1 outputs.\n",
      "  - Dense: Sigmoid    Units:  3   \n",
      "  - Dense: Linear     Units:  1   \n",
      "\n",
      "Training on dataset of 11 samples with 22 total size.\n",
      "  - Early termination after 10 stable iterations.\n",
      "    1          2.627e+02                 N/A            0.0s\n",
      "    2          1.888e+02                 N/A            0.0s\n",
      "    3          4.005e+02                 N/A            0.0s\n",
      "    4          1.629e+02                 N/A            0.0s\n",
      "    5          1.195e+02                 N/A            0.0s\n",
      "    6          1.068e+02                 N/A            0.0s\n",
      "    7          1.007e+02                 N/A            0.0s\n",
      "    8          9.278e+01                 N/A            0.0s\n",
      "    9          8.761e+01                 N/A            0.0s\n",
      "   10          8.427e+01                 N/A            0.0s\n",
      "   11          8.442e+01                 N/A            0.0s\n",
      "   12          8.229e+01                 N/A            0.0s\n",
      "   13          9.281e+01                 N/A            0.0s\n",
      "   14          8.711e+01                 N/A            0.0s\n",
      "   15          7.144e+01                 N/A            0.0s\n",
      "   16          7.299e+01                 N/A            0.0s\n",
      "   17          7.634e+01                 N/A            0.0s\n",
      "   18          7.074e+01                 N/A            0.0s\n",
      "   19          6.719e+01                 N/A            0.0s\n",
      "   20          7.516e+01                 N/A            0.0s\n",
      "   21          1.709e+02                 N/A            0.0s\n",
      "   22          1.550e+02                 N/A            0.0s\n",
      "   23          1.422e+02                 N/A            0.0s\n",
      "   24          6.296e+01                 N/A            0.0s\n",
      "   25          6.647e+01                 N/A            0.0s\n",
      "   26          6.442e+01                 N/A            0.0s\n",
      "   27          5.833e+01                 N/A            0.0s\n",
      "   28          5.061e+01                 N/A            0.0s\n",
      "   29          5.019e+01                 N/A            0.0s\n",
      "   30          5.747e+01                 N/A            0.0s\n",
      "   31          5.611e+01                 N/A            0.0s\n",
      "   32          4.843e+01                 N/A            0.0s\n",
      "   33          6.221e+01                 N/A            0.0s\n",
      "   34          5.781e+01                 N/A            0.0s\n",
      "   35          4.570e+01                 N/A            0.0s\n",
      "   36          5.173e+01                 N/A            0.0s\n",
      "   37          4.440e+01                 N/A            0.0s\n",
      "   38          5.600e+01                 N/A            0.0s\n",
      "   39          5.333e+01                 N/A            0.0s\n",
      "   40          4.295e+01                 N/A            0.0s\n",
      "   41          5.181e+01                 N/A            0.0s\n",
      "   42          5.059e+01                 N/A            0.0s\n",
      "   43          4.624e+01                 N/A            0.0s\n",
      "   44          4.030e+01                 N/A            0.0s\n",
      "   45          9.718e+01                 N/A            0.0s\n",
      "   46          4.924e+01                 N/A            0.0s\n",
      "   47          4.890e+01                 N/A            0.0s\n",
      "   48          4.784e+01                 N/A            0.0s\n",
      "   49          4.478e+01                 N/A            0.0s\n",
      "   50          4.700e+01                 N/A            0.0s\n",
      "   51          4.528e+01                 N/A            0.0s\n",
      "   52          8.711e+01                 N/A            0.0s\n",
      "   53          3.798e+01                 N/A            0.0s\n",
      "   54          4.023e+01                 N/A            0.0s\n",
      "   55          4.376e+01                 N/A            0.0s\n",
      "   56          3.838e+01                 N/A            0.0s\n",
      "   57          4.373e+01                 N/A            0.0s\n",
      "   58          7.347e+01                 N/A            0.0s\n",
      "   59          3.321e+01                 N/A            0.0s\n",
      "   60          4.240e+01                 N/A            0.0s\n",
      "   61          4.024e+01                 N/A            0.0s\n",
      "   62          3.528e+01                 N/A            0.0s\n",
      "   63          3.152e+01                 N/A            0.0s\n",
      "   64          3.995e+01                 N/A            0.0s\n",
      "   65          3.376e+01                 N/A            0.0s\n",
      "   66          3.619e+01                 N/A            0.0s\n",
      "   67          3.752e+01                 N/A            0.0s\n",
      "   68          3.303e+01                 N/A            0.0s\n",
      "   69          2.920e+01                 N/A            0.0s\n",
      "   70          3.396e+01                 N/A            0.0s\n",
      "   71          3.250e+01                 N/A            0.0s\n",
      "   72          2.825e+01                 N/A            0.0s\n",
      "   73          3.340e+01                 N/A            0.0s\n",
      "   74          2.900e+01                 N/A            0.0s\n",
      "   75          3.038e+01                 N/A            0.0s\n",
      "   76          3.128e+01                 N/A            0.0s\n",
      "   77          6.048e+01                 N/A            0.0s\n",
      "   78          3.458e+01                 N/A            0.0s\n",
      "   79          2.685e+01                 N/A            0.0s\n",
      "   80          2.603e+01                 N/A            0.0s\n",
      "   81          3.046e+01                 N/A            0.0s\n",
      "   82          2.664e+01                 N/A            0.0s\n",
      "   83          5.829e+01                 N/A            0.0s\n",
      "   84          2.607e+01                 N/A            0.0s\n",
      "   85          2.506e+01                 N/A            0.0s\n",
      "   86          5.443e+01                 N/A            0.0s\n",
      "   87          3.378e+01                 N/A            0.0s\n",
      "   88          3.192e+01                 N/A            0.0s\n",
      "   89          2.894e+01                 N/A            0.0s\n",
      "   90          3.032e+01                 N/A            0.0s\n",
      "   91          2.422e+01                 N/A            0.0s\n",
      "   92          5.453e+01                 N/A            0.0s\n",
      "   93          2.415e+01                 N/A            0.0s\n",
      "   94          2.237e+01                 N/A            0.0s\n",
      "   95          2.246e+01                 N/A            0.0s\n",
      "   96          2.256e+01                 N/A            0.0s\n",
      "   97          2.922e+01                 N/A            0.0s\n",
      "   98          2.818e+01                 N/A            0.0s\n",
      "   99          2.210e+01                 N/A            0.0s\n",
      "  100          4.746e+01                 N/A            0.0s\n",
      "  101          2.420e+01                 N/A            0.0s\n",
      "  102          2.427e+01                 N/A            0.0s\n",
      "  103          4.913e+01                 N/A            0.0s\n",
      "  104          2.860e+01                 N/A            0.0s\n",
      "  105          2.106e+01                 N/A            0.0s\n",
      "  106          2.649e+01                 N/A            0.0s\n",
      "  107          2.391e+01                 N/A            0.0s\n",
      "  108          4.811e+01                 N/A            0.0s\n",
      "  109          4.064e+01                 N/A            0.0s\n",
      "  110          4.534e+01                 N/A            0.0s\n",
      "  111          2.182e+01                 N/A            0.0s\n",
      "  112          2.605e+01                 N/A            0.0s\n",
      "  113          1.871e+01                 N/A            0.0s\n",
      "  114          2.601e+01                 N/A            0.0s\n",
      "  115          1.845e+01                 N/A            0.0s\n",
      "  116          2.397e+01                 N/A            0.0s\n",
      "  117          2.009e+01                 N/A            0.0s\n",
      "  118          4.231e+01                 N/A            0.0s\n",
      "  119          2.040e+01                 N/A            0.0s\n",
      "  120          2.390e+01                 N/A            0.0s\n",
      "  121          1.916e+01                 N/A            0.0s\n",
      "  122          2.240e+01                 N/A            0.0s\n",
      "  123          1.715e+01                 N/A            0.0s\n",
      "  124          1.813e+01                 N/A            0.0s\n",
      "  125          1.841e+01                 N/A            0.0s\n",
      "  126          2.177e+01                 N/A            0.0s\n",
      "  127          3.380e+01                 N/A            0.0s\n",
      "  128          1.827e+01                 N/A            0.0s\n",
      "  129          1.589e+01                 N/A            0.0s\n",
      "  130          1.525e+01                 N/A            0.0s\n",
      "  131          2.096e+01                 N/A            0.0s\n",
      "  132          3.114e+01                 N/A            0.0s\n",
      "  133          1.997e+01                 N/A            0.0s\n",
      "  134          1.726e+01                 N/A            0.0s\n",
      "  135          2.039e+01                 N/A            0.0s\n",
      "  136          3.725e+01                 N/A            0.0s\n",
      "  137          2.054e+01                 N/A            0.0s\n",
      "  138          1.466e+01                 N/A            0.0s\n",
      "  139          2.852e+01                 N/A            0.0s\n",
      "  140          1.969e+01                 N/A            0.0s\n",
      "  141          1.896e+01                 N/A            0.0s\n",
      "  142          1.551e+01                 N/A            0.0s\n",
      "  143          1.338e+01                 N/A            0.0s\n",
      "  144          2.661e+01                 N/A            0.0s\n",
      "  145          1.827e+01                 N/A            0.0s\n",
      "  146          3.478e+01                 N/A            0.0s\n",
      "  147          2.541e+01                 N/A            0.0s\n",
      "  148          1.898e+01                 N/A            0.0s\n",
      "  149          1.768e+01                 N/A            0.0s\n",
      "  150          2.395e+01                 N/A            0.0s\n",
      "  151          1.893e+01                 N/A            0.0s\n",
      "  152          1.266e+01                 N/A            0.0s\n",
      "  153          3.273e+01                 N/A            0.0s\n",
      "  154          1.802e+01                 N/A            0.0s\n",
      "  155          2.232e+01                 N/A            0.0s\n",
      "  156          1.401e+01                 N/A            0.0s\n",
      "  157          3.031e+01                 N/A            0.0s\n",
      "  158          1.767e+01                 N/A            0.0s\n",
      "  159          1.641e+01                 N/A            0.0s\n",
      "  160          1.585e+01                 N/A            0.0s\n",
      "  161          1.085e+01                 N/A            0.0s\n",
      "  162          1.096e+01                 N/A            0.0s\n",
      "  163          1.567e+01                 N/A            0.0s\n",
      "  164          1.112e+01                 N/A            0.0s\n",
      "  165          1.096e+01                 N/A            0.0s\n",
      "  166          1.590e+01                 N/A            0.0s\n",
      "  167          1.212e+01                 N/A            0.0s\n",
      "  168          1.080e+01                 N/A            0.0s\n",
      "  169          1.206e+01                 N/A            0.0s\n",
      "  170          1.106e+01                 N/A            0.0s\n",
      "  171          1.098e+01                 N/A            0.0s\n",
      "  172          1.425e+01                 N/A            0.0s\n",
      "  173          1.983e+01                 N/A            0.0s\n",
      "  174          1.415e+01                 N/A            0.0s\n",
      "  175          1.068e+01                 N/A            0.0s\n",
      "  176          1.273e+01                 N/A            0.0s\n",
      "  177          1.059e+01                 N/A            0.0s\n",
      "  178          1.053e+01                 N/A            0.0s\n",
      "  179          1.008e+01                 N/A            0.0s\n",
      "  180          1.347e+01                 N/A            0.0s\n",
      "  181          1.053e+01                 N/A            0.0s\n",
      "  182          1.800e+01                 N/A            0.0s\n",
      "  183          1.495e+01                 N/A            0.0s\n",
      "  184          1.106e+01                 N/A            0.0s\n",
      "  185          2.724e+01                 N/A            0.0s\n",
      "  186          1.214e+01                 N/A            0.0s\n",
      "  187          1.066e+01                 N/A            0.0s\n",
      "  188          9.072e+00                 N/A            0.0s\n",
      "  189          2.534e+01                 N/A            0.0s\n",
      "  190          1.167e+01                 N/A            0.0s\n",
      "  191          1.639e+01                 N/A            0.0s\n",
      "  192          1.365e+01                 N/A            0.0s\n",
      "  193          9.722e+00                 N/A            0.0s\n",
      "  194          8.709e+00                 N/A            0.0s\n",
      "  195          8.399e+00                 N/A            0.0s\n",
      "  196          8.335e+00                 N/A            0.0s\n",
      "  197          1.200e+01                 N/A            0.0s\n",
      "  198          8.542e+00                 N/A            0.0s\n",
      "  199          1.023e+01                 N/A            0.0s\n",
      "  200          9.403e+00                 N/A            0.0s\n",
      "  201          1.282e+01                 N/A            0.0s\n",
      "  202          1.173e+01                 N/A            0.0s\n",
      "  203          8.950e+00                 N/A            0.0s\n",
      "  204          8.754e+00                 N/A            0.0s\n",
      "  205          1.189e+01                 N/A            0.0s\n",
      "  206          8.359e+00                 N/A            0.0s\n",
      "\n",
      "Early termination condition fired at 206 iterations.\n"
     ]
    },
    {
     "data": {
      "image/png": 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toc8AhjpuDwWmOyeOnxKBq8dCTCP46hbI2XvahzetUZmpd3XmsT5Nmbcpgx6v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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4b1e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,y = get_quadratic_data(-5,6)\n",
    "nn.fit(X,y)\n",
    "predictions = nn.predict(X)\n",
    "plt.plot(predictions)\n",
    "plt.plot(y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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