NeuralNetworkReLU.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural Network with ReLU for Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.04153939 -1.11792545]]\n",
      "(1, 2)\n",
      "0.0415393929984\n",
      "-1.11792544511\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "Wh = np.random.randn(1, 2) #/np.sqrt(1)\n",
    "print (Wh)\n",
    "print (Wh.shape)\n",
    "print (np.max(Wh))\n",
    "print (np.min(Wh))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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",
    "        #print  (\"Weights: \",self.Wh,self.Wo)\n",
    "        \n",
    "        # Initialize Biases\n",
    "        # Small positive value to avoid Relu units dying too quickly\n",
    "        # http://cs231n.github.io/neural-networks-2/\n",
    "        self.Bh = np.full((1, hiddenLayerSize), 0.2)\n",
    "        self.Bo = np.full((1, outputLayerSize), 0.2)\n",
    "        #print (\"Biases: \",self.Bh,self.Bo)\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",
    "        # Logging\n",
    "        self.log_interval = 1000\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 relu(self, z):\n",
    "        return np.maximum(0, z)\n",
    "    \n",
    "    def relu_grad(self,z):\n",
    "        #dr/dz = 1(z>0)\n",
    "        grad = np.copy(z)\n",
    "        grad[z <= 0] = 0\n",
    "        grad[z > 0] = 1\n",
    "        return grad\n",
    "    \n",
    "    def cost(self, output, y):\n",
    "        cost = np.sum((output-y)**2) / 2.0\n",
    "        return cost\n",
    "    \n",
    "    def cost_grad(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.relu(self.Zh)\n",
    "        self.Zo = np.dot(self.Ah, self.Wo) + self.Bo\n",
    "        self.Ao = self.Zo #Last layer is linear -no activation\n",
    "        return self.Ao\n",
    "    \n",
    "    def backprop(self, X, output, y):\n",
    "        err_output = self.cost_grad(output, y) #last layer is linear, no gradient needed\n",
    "        err_hidden = np.dot(err_output, self.Wo.T) * self.relu_grad(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(output, y)\n",
    "        return cost\n",
    "\n",
    "    def train(self, X, y, epochs, lr, log_interval):\n",
    "        self.log_interval=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)\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)\n",
    "#             self.log(\"Weights:\" + str(self.Wh) + str(self.Wo), epoch)\n",
    "            #self.log(\"Ao\" + str(self.Ao), epoch)\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):\n",
    "        if epoch == 1 or epoch % self.log_interval == 0:\n",
    "            print(msg)        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Ik8VyTGMGdeHy0zvx2LQ1vD6vwHcciVKV1bX88I2vND0cg5J8B5DoZ2Y8ds1A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\n4XSKbbjPmAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115b55e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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y/wUjNIQlIglJIZKA3lu6gZ++vIBxA7vyhwtHka6zsEQkQenTKcHMXb2Va5+f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\nIiIiEjOFiIiIxOz/A4/oyUtDO2GuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115cd8e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def quadratic(x):\n",
    "    return x**2 + x + 3\n",
    "\n",
    "def get_quadratic_data(start,end,step_size=1):\n",
    "    X = np.array([i for i in np.arange(start,end,step_size)], 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,step_size=1):\n",
    "    X = np.array([i for i in np.arange(start,end,step_size)], 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",
    "\n",
    "qX, qy = get_quadratic_data(-6,6)\n",
    "graph(qX,qy)\n",
    "\n",
    "cX, cy = get_cubic_data(-6,6,.1)\n",
    "graph(cX,cy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "epochs = 5\n",
    "for epoch in range(epochs):\n",
    "    print (epoch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(2)\n",
    "X,y = get_quadratic_data(-20,21)\n",
    "X,y = get_cubic_data(-20,21)\n",
    "\n",
    "#ReLU needs more starting neurons b/c some will \"die\" \n",
    "nn = NeuralNetwork(1,6,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 ---------------\n",
      "Cost:14.05471\n",
      "\n",
      "Epoch 10000 ---------------\n",
      "Cost:0.10074\n",
      "\n",
      "Epoch 20000 ---------------\n",
      "Cost:0.09512\n",
      "\n",
      "Epoch 30000 ---------------\n",
      "Cost:0.09174\n",
      "\n",
      "Epoch 40000 ---------------\n",
      "Cost:0.08827\n",
      "\n",
      "Epoch 50000 ---------------\n",
      "Cost:0.0846\n",
      "\n",
      "Epoch 60000 ---------------\n",
      "Cost:0.08071\n",
      "\n",
      "Epoch 70000 ---------------\n",
      "Cost:0.0766\n",
      "\n",
      "Epoch 80000 ---------------\n",
      "Cost:0.07232\n",
      "\n",
      "Epoch 90000 ---------------\n",
      "Cost:0.06793\n",
      "\n",
      "Epoch 100000 ---------------\n",
      "Cost:0.06348\n",
      "\n",
      "Epoch 110000 ---------------\n",
      "Cost:0.05901\n",
      "\n",
      "Epoch 120000 ---------------\n",
      "Cost:0.05452\n",
      "\n",
      "Epoch 130000 ---------------\n",
      "Cost:0.05013\n",
      "\n",
      "Epoch 140000 ---------------\n",
      "Cost:0.04589\n",
      "\n",
      "Epoch 150000 ---------------\n",
      "Cost:0.04192\n",
      "\n",
      "Epoch 160000 ---------------\n",
      "Cost:0.03829\n",
      "\n",
      "Epoch 170000 ---------------\n",
      "Cost:0.03503\n",
      "\n",
      "Epoch 180000 ---------------\n",
      "Cost:0.03206\n",
      "\n",
      "Epoch 190000 ---------------\n",
      "Cost:0.02934\n",
      "\n",
      "Epoch 200000 ---------------\n",
      "Cost:0.02687\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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5TeDZwApgUyoOwInAzKwCiuwRjAL7dTi/UF/N2MDNzHqgSB/BSuCZZQdSBk9DbWaWr8ge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\nbMA5EZiZDbj/D71w7uwpz6F9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115aa7358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cost_hist = nn.train(X, y, epochs=200000, lr=.0001, log_interval=10000)\n",
    "graph_error(cost_hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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14Yp+bejeqgk9WjemfdMG1nduTDUKqSQBoKofAh96HUedcGSfXzJwp8DO8btu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\nWZIwxhhTLksSxhhjyvX/ATcf7ClSHZYQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117326400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,y)\n",
    "plt.plot(X,output)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How Does Number of Neurons Impact Learning?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1315,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 ---------------\n",
      "Cost:4.68752\n",
      "\n",
      "Epoch 50000 ---------------\n",
      "Cost:0.10273\n",
      "\n",
      "Epoch 100000 ---------------\n",
      "Cost:0.10235\n",
      "\n",
      "Epoch 150000 ---------------\n",
      "Cost:0.10214\n",
      "\n",
      "Epoch 200000 ---------------\n",
      "Cost:0.10201\n",
      "\n",
      "Epoch 1 ---------------\n",
      "Cost:3.21028\n",
      "\n",
      "Epoch 50000 ---------------\n",
      "Cost:0.10587\n",
      "\n",
      "Epoch 100000 ---------------\n",
      "Cost:0.10378\n",
      "\n",
      "Epoch 150000 ---------------\n",
      "Cost:0.10263\n",
      "\n",
      "Epoch 200000 ---------------\n",
      "Cost:0.09994\n",
      "\n",
      "Epoch 1 ---------------\n",
      "Cost:2.2018\n",
      "\n",
      "Epoch 50000 ---------------\n",
      "Cost:0.0644\n",
      "\n",
      "Epoch 100000 ---------------\n",
      "Cost:0.03713\n",
      "\n",
      "Epoch 150000 ---------------\n",
      "Cost:0.02208\n",
      "\n",
      "Epoch 200000 ---------------\n",
      "Cost:0.01395\n",
      "\n",
      "Epoch 1 ---------------\n",
      "Cost:2.73806\n",
      "\n",
      "Epoch 50000 ---------------\n",
      "Cost:0.03478\n",
      "\n",
      "Epoch 100000 ---------------\n",
      "Cost:0.01597\n",
      "\n",
      "Epoch 150000 ---------------\n",
      "Cost:0.00897\n",
      "\n",
      "Epoch 200000 ---------------\n",
      "Cost:0.00588\n",
      "\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(2)\n",
    "\n",
    "epochs = 200000\n",
    "learning_rate = .0001\n",
    "costs = {}\n",
    "cost_histories = {}\n",
    "predictions = {}\n",
    "networks = {}\n",
    "neurons = [3,6,20,100]\n",
    "for n in neurons:\n",
    "    start,end = (-20,21)\n",
    "    X,y = get_cubic_data(start,end)\n",
    "    nn = NeuralNetwork(1,n,1)\n",
    "    networks[n] = nn\n",
    "    cost_histories[n] = nn.train(X, y, epochs=epochs, lr=learning_rate, log_interval=50000)\n",
    "    \n",
    "    X,y = get_cubic_data(-10,10)\n",
    "    predictions[n] = nn.predict(X,y_min=cubic(start), y_max=cubic(end))\n",
    "    costs[n] = math.log(nn.cost(X, predictions[n], y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1316,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4Cgvn/0szFILAOPjGwD9Kc/9xnmr/I3/o3cv+4ZMETIh0y8X2zCquzFzL1Wnl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\nSqUwDQGllEphGgJKKZXC/h+eoh1HxJvtFAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c6599b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(cost_histories[3][300:20000]))\n",
    "plt.plot(np.log(cost_histories[6][300:20000]))\n",
    "plt.plot(np.log(cost_histories[20][300:20000]))\n",
    "plt.plot(np.log(cost_histories[100][300:20000]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1317,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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M7N92jKfv30z/0TRL3jeDq++YR1y/lBeRk9CaQd5VPldg9codrHt6L7VTEnzs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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c5cb748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,predictions[3])\n",
    "plt.plot(X,predictions[6])\n",
    "plt.plot(X,predictions[20])\n",
    "plt.plot(X,predictions[100])\n",
    "plt.plot(X,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scikit-Learn Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1422,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nfsu5uEnf0c6lCqXDUsfelLx58PoNzmXibnrr0FWMdh+o5C8LN/LS0q1Ya7l+\nVB/uGj+I7ik6EaPDqq12zobds8GZJ2jPhsOPD+5q+jNR0U5nn9AFTJSzDH+NM5TiDzyurYGaCmea\n5/piOzm/j50znLmI+pzjXJzlGGc6S2RQx95aOW/CzO85HfoNMyG5O6Xl1fz94008+9lmKqpruerM\n3twzcTC9u3SM+VzkKHwxzpWDug12ToSqr6LUGc4pK4by4sb35SXO+6KinYuPREVDlM9ZZlQ0+GKd\njr9zhjNnfecMiO+sYRU5JgV7fVnPwuwHnA7o+tc4aJL418IN/O2jjeyrqGHq8J7cf+EQBqYne12p\nhIP4VOcmEmQK9jrLXoTZ98Pgi6i44p+8krWbvyz6gt0Hqpg4rDsPTB7CKSfqP6mIhD4FO8D6OTDr\nXvwDJjBj4G94/Ikv2F5awegBXfnbjUM5s28Qj3QQEWkjBXthNvbfN1OaMoTrdnyX3DVrOT2jM7+/\n+nTGDGr6Ar0iIqGsQwe73bOJ6heuorg2mUt33k3XHsn8/aahTDqpu+ZzEZGw1WGD/YuctWTM/CZx\ntVU8mPQQv7h8PFNP6xm8yZhERNpJhwv27K0lPPX+V9y3/X66RO3h0zHP8uzEb+jqOSISMTpMsK/e\nXspjc9azaO3XPJ/wJ4ZHbaH2mheZdPJUr0sTEXFVxAf7xqIDPDZ3Pe+u/JqUeB+z+s3g5B3LYOqf\niFKoi0gEithgLygp44l5eby5rID4GB93TxjEXWYG8Z+9Def9N2Te5nWJIiLtIuKCfdf+Cv68YAOv\nfJGPMYZbx/Tn+xcMpFvBfHjtUTj9ehj/c6/LFBFpN20KdmPM74FLgSpgI3CrtXavG4Udr71lVfz1\no038a/FmamotV2dmcM/EQfRMTXBmxHvr+9BjOEz9k+baEJGI1taOfS7wU2ttjTHmd8BPgR+3vayW\nO1BZwz8/2cw/PtnEgaoaLj/9RO6bNIR+3QLXX6ytdi487a+Fq/91XBfqFREJR20KdmvtnHo/LgGu\nals5LVdRXcuLn2/lL4s2UFJWzUWnnMADFw5laI8jLko8/1dQ8CVc9Rx0HRis8kREPOPmGPttwOvN\nvWiMmQZMA+jTp0+rV1JV4+f1rG08vSCPnfsqGTe4Gz+aPJTTM5q4sPS692HxU841Sk+9stXrFBEJ\nJ8cMdmPMPKBHEy/93Fr7duA9PwdqgJebW461djowHZwLbbSm2Nkrt/O7D9ayrbiczL5deOLakZwz\noGvTb96z9pILAAAGBUlEQVS7Df5zp3Mh4sn/rzWrExEJS8cMdmvtpKO9boy5BZgKTLTtfDmmjbsO\nkhIfw3O3nsoFQ9Kbn8+lwbj68xpXF5EOpa1HxUwBHgTOt9aWuVNS875/wUDunjDo2PO5zP81FHwB\nVz2rcXUR6XDaOsb+NBAHzA10z0ustXe2uapmxEa3YD6XdR/A4ich83bn4r4iIh1MW4+KGeRWIa7Y\nuw3eCoyrX/SI19WIiHgicqY09Pth5jRnfF3j6iLSgUXOlALZz0H+Yrj8zxpXF5EOLTI69n3bYe4v\nof/5MOI7XlcjIuKp8A92a+HdH4K/Bi59XPPAiEiHF/7BvuZtWPcejP8ZpA3wuhoREc+Fd7CXl8B7\n/w09T4dz/svrakREQkJ47zyd8z9QtgdueBN84f1PERFxS/h27JsWwfKXYMw90HO419WIiISM8Az2\nqjKYdZ8zpn5+UKd/FxEJeeE5fvHRb6FkM9w8C2ISvK5GRCSkhF/Hvn0FLH4azrgJ+p/ndTUiIiEn\nvIK9tgbeuRuSusGFv/a6GhGRkBReQzFL/gw7VsI1L0BCF6+rEREJSeHVsSf3gBE3wEmXeV2JiEjI\nCq+O/fRvOzcREWlWeHXsIiJyTAp2EZEIo2AXEYkwCnYRkQijYBcRiTAKdhGRCKNgFxGJMAp2EZEI\nY6y1wV+pMUXA1lZ+vBuw28Vy3KTaWke1tY5qa51wrq2vtTb9WAvxJNjbwhiTZa3N9LqOpqi21lFt\nraPaWqcj1KahGBGRCKNgFxGJMOEY7NO9LuAoVFvrqLbWUW2tE/G1hd0Yu4iIHF04duwiInIUYRXs\nxpgpxph1xpgNxpifeF1PfcaYLcaYVcaYFcaYLI9redYYs8sYk1PvuTRjzFxjTF7g3pNLUDVT2/8Z\nYwoD226FMeYSj2rLMMYsNMasMcasNsbcG3je8213lNo833bGmHhjzBfGmK8Ctf0q8HwobLfmavN8\nuwXq8BljlhtjZgd+dmWbhc1QjDHGB6wHLgQKgC+B66y1azwtLMAYswXItNZ6fnysMeY84ADwgrX2\n1MBzjwLF1trfBv4odrHW/jhEavs/4IC19g/BrueI2noCPa21y4wxnYBs4JvALXi87Y5S2zV4vO2M\nMQZIstYeMMbEAJ8C9wJX4v12a662KYTG79wDQCaQYq2d6tb/03Dq2EcBG6y1m6y1VcBrwOUe1xSS\nrLUfA8VHPH058Hzg8fM4oRB0zdQWEqy1X1trlwUe7wdygV6EwLY7Sm2es44DgR9jAjdLaGy35mrz\nnDGmN/AN4B/1nnZlm4VTsPcCttX7uYAQ+cUOsMA8Y0y2MWaa18U04QRr7deBxzuAE7wspgl3G2NW\nBoZqPL9SuTGmHzASWEqIbbsjaoMQ2HaBIYUVwC5grrU2ZLZbM7WB99vtceBBwF/vOVe2WTgFe6gb\na60dAVwM3BUYcghJ1hl/C4muJeAZYAAwAvga+KOXxRhjkoE3gfustfvqv+b1tmuitpDYdtba2sDv\nf29glDHm1CNe92y7NVObp9vNGDMV2GWtzW7uPW3ZZuEU7IVARr2feweeCwnW2sLA/S7gPzhDR6Fk\nZ2Cctm68dpfH9Rxird0Z+M/nB/6Oh9suMA77JvCytXZm4OmQ2HZN1RZK2y5Qz15gIc4Ydkhst6Zq\nC4HtNga4LLBv7jVggjHmJVzaZuEU7F8Cg40x/Y0xscC1wDse1wSAMSYpsEMLY0wSMBnIOfqngu4d\n4ObA45uBtz2spYG6X+SAK/Bo2wV2tP0TyLXWPlbvJc+3XXO1hcK2M8akG2M6Bx4n4BzgsJbQ2G5N\n1ub1drPW/tRa29ta2w8nyxZYa2/ArW1mrQ2bG3AJzpExG4Gfe11PvboGAF8Fbqu9rg14FefrZTXO\nvojbga7AfCAPmAekhVBtLwKrgJWBX+yeHtU2Fuer70pgReB2SShsu6PU5vm2A4YDywM15AD/G3g+\nFLZbc7V5vt3q1XgBMNvNbRY2hzuKiEjLhNNQjIiItICCXUQkwijYRUQijIJdRCTCKNhFRCKMgl1E\nJMIo2EVEIoyCXUQkwvx/rFbgsx70bl4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a806780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sknn.mlp import Regressor\n",
    "from sknn.mlp import Layer\n",
    "\n",
    "# Design Network\n",
    "hiddenLayer = Layer(\"Rectifier\", units=6)\n",
    "outputLayer = Layer(\"Linear\", units=1)\n",
    "nn = Regressor([hiddenLayer, outputLayer], learning_rule='sgd',\n",
    "               learning_rate=.001,batch_size=5,loss_type=\"mse\")\n",
    "\n",
    "# Train Model\n",
    "X,y = get_cubic_data(-2,2,.1)\n",
    "nn.fit(X,y)\n",
    "\n",
    "# Predict\n",
    "predictions = nn.predict(X)\n",
    "\n",
    "# Visualize\n",
    "plt.plot(predictions)\n",
    "plt.plot(y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1423,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Parameters(weights=array([[ 0.53861075,  0.07695764, -1.19058596,  2.45308343,  0.59022941,\n",
       "         0.5929086 ]]), biases=array([-0.17245001, -0.14660981, -1.33888264, -2.35898558, -0.20223226,\n",
       "        0.56735499]), layer='hidden0'),\n",
       " Parameters(weights=array([[ 0.48303523],\n",
       "       [-0.24537579],\n",
       "       [-1.82607692],\n",
       "       [ 3.41004184],\n",
       "       [ 0.4742989 ],\n",
       "       [-0.94205058]]), biases=array([-0.19954963]), layer='output')]"
      ]
     },
     "execution_count": 1423,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn.get_parameters()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Universal Function Approximation Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1393,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weights\n",
      "(1, 6)\n",
      "(6, 1)\n",
      "[[-5.  -1.2  1.2  1.2  2.   5. ]]\n",
      "[[-1.]\n",
      " [-1.]\n",
      " [-1.]\n",
      " [ 1.]\n",
      " [ 1.]\n",
      " [ 1.]]\n",
      "Biases\n",
      "(1, 6)\n",
      "(1, 1)\n",
      "[[-7.7 -1.3  1.  -0.2 -1.1 -5. ]]\n",
      "[[-0.]]\n",
      "(40, 1)\n",
      "(40, 1)\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "Update the predict function in the NN class above to be:\n",
    "\n",
    "def predict(self, X, y_min, y_max):\n",
    "    return self.feed_forward(X)\n",
    "'''\n",
    "\n",
    "np.random.seed(3)\n",
    "\n",
    "nn = NeuralNetwork(1,6,1)\n",
    "\n",
    "print (\"Weights\")\n",
    "print (nn.Wh.shape)\n",
    "print (nn.Wo.shape)\n",
    "\n",
    "hiddenWeights = np.array([\n",
    "    [-5.0, -1.2, 1.2, 1.2, 2.0, 5.0],\n",
    "])\n",
    "\n",
    "outputWeights = np.array([\n",
    "    [-1.0],\n",
    "    [-1.0],\n",
    "    [-1.0],\n",
    "    [1.0],\n",
    "    [1.0],\n",
    "    [1.0]\n",
    "])\n",
    "\n",
    "\n",
    "nn.Wh = hiddenWeights\n",
    "nn.Wo = outputWeights\n",
    "\n",
    "print (nn.Wh)\n",
    "print (nn.Wo)\n",
    "\n",
    "print (\"Biases\")\n",
    "print (nn.Bh.shape)\n",
    "print (nn.Bo.shape)\n",
    "\n",
    "hiddenBias = np.array([\n",
    "    [-7.7, -1.3, 1.0, -0.2, -1.1, -5.0]\n",
    "])\n",
    "\n",
    "outputBias = np.array([\n",
    "    [-0.0]\n",
    "])\n",
    "\n",
    "nn.Bh = hiddenBias\n",
    "nn.Bo = outputBias\n",
    "\n",
    "print (nn.Bh)\n",
    "print (nn.Bo)\n",
    "\n",
    "#x**3 + x**2 - x - 1\n",
    "\n",
    "X,y = get_cubic_data(-2,2,.1)\n",
    "print (X.shape)\n",
    "print (y.shape)\n",
    "predictions = nn.predict(X,y_min=cubic(-2), y_max=cubic(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictions w My Weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1394,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jKvd8b6LTkcQHwsMMvdun0rv9JGASJeUu1m/dxPGNX5CQvYRuR+eScOxTeljD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bccd9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(X, y)\n",
    "ax.plot(X, predictions)\n",
    "ax.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}