Day 0 - Numpy Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression in numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook gives an intro to machine learning from scratch using numpy and also covers feature scaling and the gradient descent algorithm.\n",
    "\n",
    "## What is linear regression?\n",
    "\n",
    "Linear = our predictions are a **linear combination** of our inputs\n",
    "\n",
    "Regression = we will learn the relationship that relates features to labels\n",
    "\n",
    "$X$ is a matrix of training data. Each row represents a different training example (of which there are $m$). Each column represents a different feature (of which there are $n$). Hence $X$ has dimensions $m \\times n$, i.e. $X \\in  R^{m \\times n}$.\n",
    "\n",
    "$W$ is our matrix of weights, that controls how much each feature contributes to the hypothesis. If one particular weight equals 5, then changing its associated feature by 1 in the input space, will change the output hypothesis by 5. $W \\in R^{n \\times 1}$\n",
    "\n",
    "$h$ is our hypothesis - our prediction of the mapping from input to output. In this example, our model will predict a single scalar output for each of out $m$ inputs - so $h \\in R^{m\\times n}$.\n",
    "\n",
    "## $ h = X  W = w_1 x_1 + w_2 x_2 + \\dots + w_{n-1} x_{n-1} + w_n x_n$\n",
    "\n",
    "This linear combination is a **weighted sum of the input features**. As we vary the value of one feature, our hypothesis will change proportionately and linearly.\n",
    "\n",
    "Imagine that we are trying to predict house price. Consider:\n",
    "- The weight associated with the feature that is the number of rooms should be large and positive, because the number of rooms contributes lots, and positively to the price of a house. \n",
    "- The weight associated with the age of the house may be negative, as older houses might be found to be worth less from the training data.\n",
    "- The weight associated with a feature that is the age of the person last living there should be zero, because the house price is independent of this feature. It does not contribute at all to the house price.\n",
    "\n",
    "In this case, we will use the mean squared error (MSE) between our predictions and labels as our cost function:\n",
    "\n",
    "## $ MSE\\ Loss,\\ J = \\frac{1}{2m} \\sum_{i=1}^{m} (h^{(i)} - y^{(i)})^2$\n",
    "\n",
    "## Optimization\n",
    "We optimize this model using the gradient descent algorithm where we iteratively calculate the derivative of our cost w.r.t our paramameters and use that to update our weights in a direction which reduces the cost.\n",
    "\n",
    "## The code\n",
    "Firstly we will import some functionality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                      # for mathematical computation\n",
    "import matplotlib.pyplot as plt         # for plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making Data\n",
    "Let's write a function and call it to create some fake data that we know the function of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 100 # specify the number of datapoints that we want\n",
    "\n",
    "def makedata(numdatapoints):            # make some fake data fitted to an arbitrary polynomial\n",
    "    \"\"\"Make some fake data noisily distributed around a polynomial\"\"\"\n",
    "    x = np.linspace(-10, 10, numdatapoints)     # create a vector of numdatapoints(=m) numbers evenly spaced between -10 and 10\n",
    "    x = x.reshape(-1, 1)    # make it into a column vector (each datapoint is a row)\n",
    "\n",
    "    coeffs = [2, -30, 0.5, 5]   # make some polynomial coefficients for the fake data\n",
    "\n",
    "    y = np.polyval(coeffs, x) + 2 * np.random.rand(numdatapoints, 1)    # evaluate a polynomial with the coefficients we\n",
    "                                                                        # specified to create the labels for our data\n",
    "    y = y.reshape(-1, 1) # reshape into column vector (each datapoint is a row)\n",
    "\n",
    "    return x, y # return column vectors of single inputs and outputs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Features\n",
    "Our made up datapoints are only one-dimensional. Using only these features, we will only be able to form linear combinations of these values - no polynomial characteristic in our hypothesis.\n",
    "So we may choose to give the model a particular set of features based upon how we expect the mapping to look, or just to increase the capacity of our model. For example, house price is probably dependent on floor space, so we might include a power of 2 if our original variable was room length.\n",
    "\n",
    "Let's manually **make some polynomial features** from our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "powers = [2, 3]     # a list of the powers of the inputs which we want to include as features for our model\n",
    "n = len(powers)     # n = number of features of each training datapoint\n",
    "\n",
    "def makefeatures(powers):\n",
    "    features = np.ones((inputs.shape[0], len(powers)))  # initialise a design matrix with the right shape (mxn)\n",
    "    for i in range(len(powers)):    # for each power in the list powers\n",
    "        features[:, i] = (inputs**powers[i])[:, 0] # set a column of the design matrix = inputs raised to that power\n",
    "    print(features)\n",
    "\n",
    "    return features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature Scaling - normalisation/standardisation\n",
    "\n",
    "If the scale of variables is different, it is likely that one of the variables will start further from an acceptably sufficient position than another. When the first one of them reaches a sufficient value, it needs to stop jumping around and settle, however, any other variables need to keep moving and being optimised. \n",
    "If variables vary over the same domain, but have ranges of different scales\n",
    "The learning rate needs to be small enough to ensure that the parameters converge, but large enough to ensure that this happens at a suitable rate.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale_features(features):   # center all features around their mean and divide by their range\n",
    "\n",
    "    avg = np.mean(features, axis=0) # calculate the mean of each of our features over the whole dataset\n",
    "    print(avg)\n",
    "    ranges = np.ptp(features, axis=0)   #  calculate the peak-to-peak values for each feature (ptp of the rows)\n",
    "\n",
    "    scaled = features - avg     # center all features about their mean\n",
    "    scaled = np.divide(scaled, ranges)  # divide features by their range so that they are all between 0 and 1\n",
    "    print(scaled)\n",
    "\n",
    "    return scaled, avg, ranges  # return our scaled features and the averages and ranges of each feature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's build our model class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "epochs = 100    # number of times we want to pass through the whole dataset when training\n",
    "lr = 0.5    # proportion of the gradient by which we want to move our parameters each optimisation step\n",
    "batch_size=32   # number of data points to train on each optimisation step\n",
    "\n",
    "class LinearModel():    # create a class as a framework for our linear model\n",
    "\n",
    "    def __init__(self): # class initialiser\n",
    "        self.weights = np.random.rand(n, 1)     # randomly initialise a nx1 (in x out) matrix of weights\n",
    "        print(self.weights)\n",
    "        self.bias = np.random.rand(1) # initialise a random initial bias (offset)\n",
    "        print(self.bias)\n",
    "\n",
    "    def forward(self, x):   # define what happens when data is passed forward through our model\n",
    "        out = np.matmul(x, self.weights) + self.bias # output is the biased, linear combination of our inputs\n",
    "        return out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now define our criterion - the mean squared error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MSE(h, y):  # mean squared error loss as our model criterion\n",
    "    diff = h - y    # vector of raw differences between prediction hypothesis and labels\n",
    "    J = 0.5 * np.matmul(diff.T, diff) # cost = 0.5 diff^2\n",
    "    return float(J) # return the cost as a float rather than a 1x1 matrix\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And define our optimiser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def SGD(datain, batch_size):    # stochastic gradient descent\n",
    "    sample = np.random.randint(m, size=batch_size)  # create a list of batch_size=32 random indices to include in the\n",
    "                                                    # training batch\n",
    "\n",
    "    batchfeatures, batchlabels = datain[sample], labels[sample] # index the randomly selected batch from the training data\n",
    "\n",
    "    prediction = mymodel.forward(batchfeatures) # make a prediction for the training batch using the current parameters\n",
    "    cost = MSE(prediction, batchlabels) # determine how bad the model performs on this batch by calculating the mena square error\n",
    "\n",
    "    dJdw = np.matmul(batchfeatures.T, (prediction - batchlabels))/m # rate of change of cost wrt weights\n",
    "    mymodel.weights -= lr * dJdw    # move the weights a small step in the right direction\n",
    "\n",
    "    dJdb = np.sum(prediction - batchlabels)/m # rate of change of cost wrt bias\n",
    "    mymodel.bias -= lr * dJdb# move the bias a small step in the right direction\n",
    "\n",
    "    return cost # return how bad the model is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's write a function to train our model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(datain):\n",
    "    costs=[]    # initialise an empty list of costs for visualisation\n",
    "    for e in range(epochs): # for however many epochs specialises\n",
    "\n",
    "        print('b', mymodel.bias[0]) # print bias\n",
    "        print('w', mymodel.weights) # print weights\n",
    "\n",
    "        cost = SGD(datain, batch_size)  # calculate cost for a specified batch size\n",
    "        costs.append(cost) # add cost to list of history\n",
    "        print('Epoch', e, 'Cost', cost)\n",
    "        \n",
    "    return costs # return a list of the history of costs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's use the functions that we made above to create the data, create features from it, and scale those."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      " [ -3.10612245e-01   2.53169384e-03]\n",
      " [ -3.03265306e-01   3.53447752e-03]\n",
      " [ -2.95102041e-01   4.77224031e-03]\n",
      " [ -2.86122449e-01   6.26971686e-03]\n",
      " [ -2.76326531e-01   8.05164181e-03]\n",
      " [ -2.65714286e-01   1.01427498e-02]\n",
      " [ -2.54285714e-01   1.25677755e-02]\n",
      " [ -2.42040816e-01   1.53514535e-02]\n",
      " [ -2.28979592e-01   1.85185185e-02]\n",
      " [ -2.15102041e-01   2.20937051e-02]\n",
      " [ -2.00408163e-01   2.61017480e-02]\n",
      " [ -1.84897959e-01   3.05673818e-02]\n",
      " [ -1.68571429e-01   3.55153411e-02]\n",
      " [ -1.51428571e-01   4.09703607e-02]\n",
      " [ -1.33469388e-01   4.69571751e-02]\n",
      " [ -1.14693878e-01   5.35005189e-02]\n",
      " [ -9.51020408e-02   6.06251269e-02]\n",
      " [ -7.46938776e-02   6.83557336e-02]\n",
      " [ -5.34693878e-02   7.67170738e-02]\n",
      " [ -3.14285714e-02   8.57338820e-02]\n",
      " [ -8.57142857e-03   9.54308930e-02]\n",
      " [  1.51020408e-02   1.05832841e-01]\n",
      " [  3.95918367e-02   1.16964461e-01]\n",
      " [  6.48979592e-02   1.28850488e-01]\n",
      " [  9.10204082e-02   1.41515657e-01]\n",
      " [  1.17959184e-01   1.54984701e-01]\n",
      " [  1.45714286e-01   1.69282355e-01]\n",
      " [  1.74285714e-01   1.84433355e-01]\n",
      " [  2.03673469e-01   2.00462435e-01]\n",
      " [  2.33877551e-01   2.17394329e-01]\n",
      " [  2.64897959e-01   2.35253772e-01]\n",
      " [  2.96734694e-01   2.54065499e-01]\n",
      " [  3.29387755e-01   2.73854245e-01]\n",
      " [  3.62857143e-01   2.94644744e-01]\n",
      " [  3.97142857e-01   3.16461730e-01]\n",
      " [  4.32244898e-01   3.39329939e-01]\n",
      " [  4.68163265e-01   3.63274104e-01]\n",
      " [  5.04897959e-01   3.88318961e-01]\n",
      " [  5.42448980e-01   4.14489245e-01]\n",
      " [  5.80816327e-01   4.41809690e-01]\n",
      " [  6.20000000e-01   4.70305030e-01]\n",
      " [  6.60000000e-01   5.00000000e-01]]\n",
      "[  3.40067340e+01   2.16004992e-14] [   99.98979696  2000.        ]\n"
     ]
    }
   ],
   "source": [
    "inputs, labels = makedata(m) # call the above function to make the data\n",
    "features = makefeatures(powers) # make our features with the powers we specified\n",
    "scaled, avgs, ranges = scale_features(features)     # scale our features (try and see what happens when you don't scale)\n",
    "print(avgs, ranges) # show us mean and ranges for each feature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make our model and and train it on the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.22766182]\n",
      " [ 0.26402366]]\n",
      "[ 0.77729049]\n",
      "b 0.777290491039\n",
      "w [[ 0.22766182]\n",
      " [ 0.26402366]]\n",
      "Epoch 0 Cost 30300113.44326989\n",
      "b -133.588759579\n",
      "w [[-32.64166191]\n",
      " [ 17.21959744]]\n",
      "Epoch 1 Cost 57486546.67178522\n",
      "b -330.059833789\n",
      "w [[-99.69560594]\n",
      " [ 68.00073134]]\n",
      "Epoch 2 Cost 37719638.98053326\n",
      "b -464.902219203\n",
      "w [[-152.93152997]\n",
      " [ 101.088429  ]]\n",
      "Epoch 3 Cost 23677586.850044593\n",
      "b -546.257505931\n",
      "w [[-188.925881  ]\n",
      " [ 123.97233249]]\n",
      "Epoch 4 Cost 37213027.44055974\n",
      "b -636.514848551\n",
      "w [[-250.78189245]\n",
      " [ 164.1083518 ]]\n",
      "Epoch 5 Cost 32668674.520104457\n",
      "b -721.256145381\n",
      "w [[-308.18982585]\n",
      " [ 199.66745346]]\n",
      "Epoch 6 Cost 15529444.587085538\n",
      "b -755.660712899\n",
      "w [[-338.08903965]\n",
      " [ 216.62922109]]\n",
      "Epoch 7 Cost 7450389.214398697\n",
      "b -735.593283958\n",
      "w [[-359.95417205]\n",
      " [ 222.27930496]]\n",
      "Epoch 8 Cost 21759928.341232207\n",
      "b -778.145168829\n",
      "w [[-401.64695593]\n",
      " [ 247.50984571]]\n",
      "Epoch 9 Cost 8884360.984087048\n",
      "b -790.088088965\n",
      "w [[-421.16724469]\n",
      " [ 256.87351138]]\n",
      "Epoch 10 Cost 29244012.388661742\n",
      "b -858.221508717\n",
      "w [[-476.30372113]\n",
      " [ 292.79709694]]\n",
      "Epoch 11 Cost 20537089.9468486\n",
      "b -869.10754632\n",
      "w [[-521.28423278]\n",
      " [ 317.02110184]]\n",
      "Epoch 12 Cost 25500102.591395542\n",
      "b -934.011026972\n",
      "w [[-569.79189479]\n",
      " [ 350.93240614]]\n",
      "Epoch 13 Cost 22046915.21308721\n",
      "b -960.710057398\n",
      "w [[-617.47058931]\n",
      " [ 378.90463261]]\n",
      "Epoch 14 Cost 16302454.773753539\n",
      "b -953.150827239\n",
      "w [[-656.10884421]\n",
      " [ 398.53624857]]\n",
      "Epoch 15 Cost 5629807.034685814\n",
      "b -926.703487441\n",
      "w [[-669.79361277]\n",
      " [ 405.65718096]]\n",
      "Epoch 16 Cost 18212725.404481314\n",
      "b -951.837775577\n",
      "w [[-707.50319941]\n",
      " [ 431.16999474]]\n",
      "Epoch 17 Cost 7976639.690897208\n",
      "b -942.62804521\n",
      "w [[-726.31614284]\n",
      " [ 441.54591145]]\n",
      "Epoch 18 Cost 15994350.048768668\n",
      "b -954.801435768\n",
      "w [[-762.96048167]\n",
      " [ 462.74448229]]\n",
      "Epoch 19 Cost 24463839.015696183\n",
      "b -1011.33076046\n",
      "w [[-813.58783685]\n",
      " [ 498.78838806]]\n",
      "Epoch 20 Cost 11182701.939243183\n",
      "b -1008.33090364\n",
      "w [[-836.79214694]\n",
      " [ 516.15994281]]\n",
      "Epoch 21 Cost 11812702.544831565\n",
      "b -1016.00910942\n",
      "w [[-859.61876148]\n",
      " [ 535.79986044]]\n",
      "Epoch 22 Cost 13170156.370350493\n",
      "b -1017.63201637\n",
      "w [[-886.01649804]\n",
      " [ 557.4127612 ]]\n",
      "Epoch 23 Cost 13901728.01903652\n",
      "b -1006.97326115\n",
      "w [[-917.67211237]\n",
      " [ 578.26161055]]\n",
      "Epoch 24 Cost 14970655.376284705\n",
      "b -1012.97266005\n",
      "w [[-948.77761198]\n",
      " [ 602.9712457 ]]\n",
      "Epoch 25 Cost 8507173.141712403\n",
      "b -990.338443778\n",
      "w [[-969.56562025]\n",
      " [ 615.40973456]]\n",
      "Epoch 26 Cost 14940404.169989238\n",
      "b -1006.29617693\n",
      "w [[-1001.96924585]\n",
      " [  639.89026684]]\n",
      "Epoch 27 Cost 16072466.51320408\n",
      "b -1019.43710321\n",
      "w [[-1037.84714187]\n",
      " [  666.250003  ]]\n",
      "Epoch 28 Cost 10210411.30565596\n",
      "b -1006.96560184\n",
      "w [[-1065.46733716]\n",
      " [  680.53507683]]\n",
      "Epoch 29 Cost 5877236.377575517\n",
      "b -981.881442509\n",
      "w [[-1079.65536133]\n",
      " [  689.97601119]]\n",
      "Epoch 30 Cost 16044705.26919061\n",
      "b -1023.47671619\n",
      "w [[-1115.04442382]\n",
      " [  717.3932848 ]]\n",
      "Epoch 31 Cost 8961060.000111435\n",
      "b -1012.94342201\n",
      "w [[-1135.01952255]\n",
      " [  733.12185245]]\n",
      "Epoch 32 Cost 12536794.123567805\n",
      "b -1028.20634327\n",
      "w [[-1164.62063081]\n",
      " [  754.50233367]]\n",
      "Epoch 33 Cost 5592515.348855114\n",
      "b -999.745800744\n",
      "w [[-1182.73490349]\n",
      " [  761.32529326]]\n",
      "Epoch 34 Cost 6863772.524319159\n",
      "b -1002.97334058\n",
      "w [[-1200.90332901]\n",
      " [  772.24285912]]\n",
      "Epoch 35 Cost 14320998.186980017\n",
      "b -1018.12437421\n",
      "w [[-1231.16530976]\n",
      " [  799.57756926]]\n",
      "Epoch 36 Cost 12569847.65935932\n",
      "b -1023.96673753\n",
      "w [[-1261.35026645]\n",
      " [  822.09230608]]\n",
      "Epoch 37 Cost 7288622.814139995\n",
      "b -993.083795615\n",
      "w [[-1276.23019914]\n",
      " [  836.73798754]]\n",
      "Epoch 38 Cost 10342521.884943958\n",
      "b -993.767714025\n",
      "w [[-1302.76413545]\n",
      " [  854.88338342]]\n",
      "Epoch 39 Cost 6524866.580725482\n",
      "b -980.387074825\n",
      "w [[-1319.07290393]\n",
      " [  866.85634759]]\n",
      "Epoch 40 Cost 16894896.15457803\n",
      "b -1015.24705434\n",
      "w [[-1360.05312456]\n",
      " [  898.28810981]]\n",
      "Epoch 41 Cost 8896228.055273827\n",
      "b -1021.07226748\n",
      "w [[-1381.36733157]\n",
      " [  915.6192241 ]]\n",
      "Epoch 42 Cost 17813184.871845692\n",
      "b -1048.10877289\n",
      "w [[-1429.11001504]\n",
      " [  948.24072717]]\n",
      "Epoch 43 Cost 8344339.80590781\n",
      "b -1028.73545504\n",
      "w [[-1452.63840503]\n",
      " [  963.18550946]]\n",
      "Epoch 44 Cost 11980280.03801247\n",
      "b -1043.95113255\n",
      "w [[-1485.43893645]\n",
      " [  985.88924088]]\n",
      "Epoch 45 Cost 11353276.582746215\n",
      "b -1042.21910114\n",
      "w [[-1510.84822989]\n",
      " [ 1010.66816782]]\n",
      "Epoch 46 Cost 10530208.331642691\n",
      "b -1041.07617215\n",
      "w [[-1533.28866412]\n",
      " [ 1034.59305867]]\n",
      "Epoch 47 Cost 3603164.035994166\n",
      "b -1000.83204089\n",
      "w [[-1538.02892442]\n",
      " [ 1043.98531738]]\n",
      "Epoch 48 Cost 9478164.592153123\n",
      "b -997.773838266\n",
      "w [[-1561.52790572]\n",
      " [ 1064.35207318]]\n",
      "Epoch 49 Cost 7458660.963438235\n",
      "b -1011.77372488\n",
      "w [[-1573.61637233]\n",
      " [ 1083.66956924]]\n",
      "Epoch 50 Cost 6146514.195991004\n",
      "b -1009.02604568\n",
      "w [[-1585.85716161]\n",
      " [ 1098.68044271]]\n",
      "Epoch 51 Cost 5821126.413814244\n",
      "b -983.143603759\n",
      "w [[-1595.4329102 ]\n",
      " [ 1114.05257894]]\n",
      "Epoch 52 Cost 10627827.777709512\n",
      "b -993.094620532\n",
      "w [[-1622.96602446]\n",
      " [ 1137.26749117]]\n",
      "Epoch 53 Cost 7665798.421054243\n",
      "b -1002.10590958\n",
      "w [[-1643.7612288 ]\n",
      " [ 1153.89605289]]\n",
      "Epoch 54 Cost 3198609.969907284\n",
      "b -965.166756409\n",
      "w [[-1652.08724532]\n",
      " [ 1161.28058942]]\n",
      "Epoch 55 Cost 9461496.829414003\n",
      "b -989.337830601\n",
      "w [[-1677.60466606]\n",
      " [ 1181.97458027]]\n",
      "Epoch 56 Cost 5725821.590700543\n",
      "b -1006.49206669\n",
      "w [[-1693.93462172]\n",
      " [ 1194.40413134]]\n",
      "Epoch 57 Cost 7376792.621821905\n",
      "b -998.028436219\n",
      "w [[-1712.67103917]\n",
      " [ 1211.9107097 ]]\n",
      "Epoch 58 Cost 4762483.921132952\n",
      "b -981.156610027\n",
      "w [[-1722.49598683]\n",
      " [ 1224.49157875]]\n",
      "Epoch 59 Cost 4903310.215365194\n",
      "b -975.875711729\n",
      "w [[-1734.97723748]\n",
      " [ 1236.40910492]]\n",
      "Epoch 60 Cost 7880344.085064164\n",
      "b -982.162723325\n",
      "w [[-1758.90783611]\n",
      " [ 1253.80611277]]\n",
      "Epoch 61 Cost 12343958.477033187\n",
      "b -1014.21236946\n",
      "w [[-1792.83460441]\n",
      " [ 1282.9192204 ]]\n",
      "Epoch 62 Cost 5672478.760117558\n",
      "b -1005.80175696\n",
      "w [[-1807.40916035]\n",
      " [ 1297.24914265]]\n",
      "Epoch 63 Cost 8361674.431178629\n",
      "b -1028.20729854\n",
      "w [[-1829.46842605]\n",
      " [ 1318.26420949]]\n",
      "Epoch 64 Cost 6237024.173153043\n",
      "b -1010.53055572\n",
      "w [[-1845.85728767]\n",
      " [ 1334.19101681]]\n",
      "Epoch 65 Cost 6199855.942276864\n",
      "b -1008.83820192\n",
      "w [[-1862.09631322]\n",
      " [ 1350.33759492]]\n",
      "Epoch 66 Cost 7536837.906094953\n",
      "b -1030.69252157\n",
      "w [[-1881.47239714]\n",
      " [ 1370.31376239]]\n",
      "Epoch 67 Cost 5964588.136113059\n",
      "b -1026.77678244\n",
      "w [[-1900.24787011]\n",
      " [ 1384.90689353]]\n",
      "Epoch 68 Cost 3526539.7559949434\n",
      "b -1020.89846576\n",
      "w [[-1911.06473588]\n",
      " [ 1393.75314552]]\n",
      "Epoch 69 Cost 4616142.390080197\n",
      "b -1009.2825488\n",
      "w [[-1925.79965805]\n",
      " [ 1405.20543981]]\n",
      "Epoch 70 Cost 5424882.054613277\n",
      "b -1009.8669374\n",
      "w [[-1937.78476421]\n",
      " [ 1421.05880739]]\n",
      "Epoch 71 Cost 6000116.141436612\n",
      "b -1018.94413771\n",
      "w [[-1952.23312343]\n",
      " [ 1438.26338729]]\n",
      "Epoch 72 Cost 2071434.6054837417\n",
      "b -998.273372744\n",
      "w [[-1956.60011734]\n",
      " [ 1444.48028483]]\n",
      "Epoch 73 Cost 3392582.103333357\n",
      "b -983.64883532\n",
      "w [[-1967.20355482]\n",
      " [ 1453.46615497]]\n",
      "Epoch 74 Cost 8149126.851682353\n",
      "b -1000.72738602\n",
      "w [[-1991.71873741]\n",
      " [ 1475.20798679]]\n",
      "Epoch 75 Cost 5096177.801060444\n",
      "b -995.216319418\n",
      "w [[-2002.36358412]\n",
      " [ 1491.09060985]]\n",
      "Epoch 76 Cost 4602391.910206824\n",
      "b -983.035900347\n",
      "w [[-2014.26533248]\n",
      " [ 1504.72163354]]\n",
      "Epoch 77 Cost 3621562.0441374327\n",
      "b -975.209511218\n",
      "w [[-2024.2287883 ]\n",
      " [ 1515.33223361]]\n",
      "Epoch 78 Cost 3131103.758680079\n",
      "b -959.706198543\n",
      "w [[-2028.94340393]\n",
      " [ 1526.26031497]]\n",
      "Epoch 79 Cost 4229490.600561915\n",
      "b -961.898154423\n",
      "w [[-2036.85599224]\n",
      " [ 1540.11440864]]\n",
      "Epoch 80 Cost 4848796.34985958\n",
      "b -968.340746764\n",
      "w [[-2048.32854897]\n",
      " [ 1555.10642874]]\n",
      "Epoch 81 Cost 4192418.818454051\n",
      "b -970.657593356\n",
      "w [[-2058.59053688]\n",
      " [ 1568.13592572]]\n",
      "Epoch 82 Cost 6638749.657843948\n",
      "b -982.462407619\n",
      "w [[-2080.04681859]\n",
      " [ 1586.82687954]]\n",
      "Epoch 83 Cost 5392886.211799573\n",
      "b -996.368458361\n",
      "w [[-2095.86018151]\n",
      " [ 1602.86641495]]\n",
      "Epoch 84 Cost 6942524.768112774\n",
      "b -997.823703701\n",
      "w [[-2113.43032234]\n",
      " [ 1625.07144237]]\n",
      "Epoch 85 Cost 2980730.487341512\n",
      "b -985.28316327\n",
      "w [[-2119.0398905 ]\n",
      " [ 1635.54345362]]\n",
      "Epoch 86 Cost 2522181.897102868\n",
      "b -975.138524461\n",
      "w [[-2122.84026252]\n",
      " [ 1644.86108285]]\n",
      "Epoch 87 Cost 6974678.304628543\n",
      "b -1008.02546015\n",
      "w [[-2147.90821268]\n",
      " [ 1664.48261136]]\n",
      "Epoch 88 Cost 4089256.8422275633\n",
      "b -1002.80533614\n",
      "w [[-2156.87882173]\n",
      " [ 1678.64607612]]\n",
      "Epoch 89 Cost 4360340.6394259175\n",
      "b -1007.56641779\n",
      "w [[-2170.21480828]\n",
      " [ 1692.47594592]]\n",
      "Epoch 90 Cost 2788180.4009631546\n",
      "b -995.676121648\n",
      "w [[-2176.76217287]\n",
      " [ 1702.17434199]]\n",
      "Epoch 91 Cost 4362539.543448731\n",
      "b -1003.24961591\n",
      "w [[-2196.4191881 ]\n",
      " [ 1713.98052416]]\n",
      "Epoch 92 Cost 4917421.462356707\n",
      "b -1011.62412577\n",
      "w [[-2217.67702117]\n",
      " [ 1727.89141202]]\n",
      "Epoch 93 Cost 2499361.8822004437\n",
      "b -993.073166872\n",
      "w [[-2218.06653918]\n",
      " [ 1738.71308195]]\n",
      "Epoch 94 Cost 5943055.893101356\n",
      "b -1012.30014459\n",
      "w [[-2236.68075565]\n",
      " [ 1758.25920777]]\n",
      "Epoch 95 Cost 2786406.3065181337\n",
      "b -1003.23817246\n",
      "w [[-2244.6463513 ]\n",
      " [ 1767.92289361]]\n",
      "Epoch 96 Cost 3678370.062391949\n",
      "b -991.766159408\n",
      "w [[-2250.599748  ]\n",
      " [ 1782.36201299]]\n",
      "Epoch 97 Cost 5906140.689420827\n",
      "b -1015.61081025\n",
      "w [[-2268.9598852 ]\n",
      " [ 1802.43479618]]\n",
      "Epoch 98 Cost 5371538.6008671345\n",
      "b -1032.99060941\n",
      "w [[-2287.82871727]\n",
      " [ 1820.49882653]]\n",
      "Epoch 99 Cost 6376046.388169734\n"
     ]
    }
   ],
   "source": [
    "mymodel = LinearModel() # create an instance of a linear model\n",
    "\n",
    "datain = scaled # set the data going in to our model as our scaled data (not necessary really)\n",
    "\n",
    "costs = train(datain)     # finally, call the function to train our model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets create some plots to visualise how the model trained"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efd57ee7da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 20))  # create a figure\n",
    "\n",
    "ax1 = fig.add_subplot(121)  # add an axis called ax1 to our figure (height=1, width=2, axis number=1)\n",
    "ax1.set_xlabel('Input')\n",
    "ax1.set_ylabel('Output')\n",
    "ax1.scatter(inputs, labels, s=5, label='raw inputs')    # scatter plot our labels against our inputs with size=5 markers\n",
    "ax1.plot(inputs, mymodel.forward(datain), c='g',label='hypothesis')  # plot hypothesis against inputs\n",
    "ax1.grid()  # add a grid to our axis\n",
    "ax1.legend()\n",
    "\n",
    "ax2 = fig.add_subplot(122)     # add another axis called ax2 to our figure (height=1, width=2, axis number=2)\n",
    "ax2.set_title('Error vs epoch')\n",
    "ax2.grid()\n",
    "\n",
    "\n",
    "ax2.plot(costs)\n",
    "\n",
    "plt.show()  # show the plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Play around with the no. epochs, the learning rate, the batch size etc. When does it fail to converge? What is the necessary capacity of the model required to form a decent looking hypothesis?"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}