logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use([\"seaborn-paper\", \"seaborn-white\"])\n",
    "plt.rcParams[\"image.cmap\"] = \"viridis\"\n",
    "\n",
    "np.random.seed(321)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data generation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function can be used to generate a 2D dataset, with observations belonging to either the \"0\" or \"1\" class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(n, alpha=0.1, beta=1, initial_point=(0, 0), add_bias=True):\n",
    "    \"\"\"\n",
    "    Iteratively generate a 2-class, 2D dataset with a \"nudge-and-flip\" method.\n",
    "    \n",
    "    Keyword arguments:\n",
    "    alpha -- larger value increases spread (default 0.1)\n",
    "    beta -- larger value increases jitter (default 1.0)\n",
    "    initial_point -- coordinate of first observation\n",
    "    add_bias -- Add a bias feature (i.e. prepend a column of 1s)\n",
    "    \"\"\"\n",
    "    \n",
    "    data = np.empty((n, 2))\n",
    "    # Define an initial point\n",
    "    data[0, :] = initial_point\n",
    "    \n",
    "    # Randomly \"scale\" the upcoming reflection\n",
    "    a = np.random.uniform(low=(-1-alpha), high=(-1+alpha), size=n)\n",
    "    \n",
    "    # \"Flip\" previous point and add some noise\n",
    "    for k in range(1, n):\n",
    "        data[k, ] = a[k]*data[k-1, :] + beta*np.random.normal(0, 1, size=2)\n",
    "    \n",
    "    # Add a bias variable\n",
    "    if add_bias:\n",
    "        data = np.hstack((np.ones((n, 1)), data))\n",
    "    \n",
    "    # Labels are two classes (0, 1), strictly alternating, because of \"flipping\" above\n",
    "    labs = np.array([0, 1]*(n//2 + 1))[:n]\n",
    "    \n",
    "    return data, labs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An example dataset is generated and visualised below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x147d32e66a0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "demo_data, demo_labs = generate_data(1000, initial_point=[10, 10])\n",
    "\n",
    "plt.scatter(demo_data[:, 1], demo_data[:, 2], c=demo_labs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auxiliary functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For validation and testing, we need some way of splitting up our dataset into separate sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_sets(data, labels, props, shuffle=True):\n",
    "    \"\"\"\n",
    "    Divide data/labels into proportional sets.\n",
    "    \n",
    "    Keyword arguments:\n",
    "    data -- dataset of features\n",
    "    labels -- matching set of labels\n",
    "    props -- list of proportions, which must sum to 1, e.g. [0.6, 0.2, 0.2] for a 60%/20%/20% split\n",
    "    \"\"\"\n",
    "    \n",
    "    if sum(props) != 1:\n",
    "        raise ValueError(\"proportions must sum to 1\")\n",
    "    \n",
    "    m = data.shape[0]\n",
    "    idx = np.random.permutation(m) if shuffle else range(m)\n",
    "    \n",
    "    sets = []\n",
    "    cursor = 0\n",
    "    \n",
    "    for p in props:\n",
    "        dset = data[idx, :][cursor:(cursor+int(p*m)), :]\n",
    "        sets.append(dset)\n",
    "        lset = labels[idx][cursor:(cursor+int(p*m))]\n",
    "        sets.append(lset)\n",
    "        \n",
    "        cursor = int(p*m)\n",
    "    \n",
    "    return sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we split our demo data into three distinct `*_train`, `*_val` and `*_test` sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, y_train, X_val, y_val, X_test, y_test = make_sets(demo_data, demo_labs, [0.6, 0.2, 0.2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we had 1000 observations to begin with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((600, 3), (200,))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will require an activation function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'sigmoid(z)')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-10, 10)\n",
    "plt.plot(x, sigmoid(x))\n",
    "\n",
    "plt.axhline(y=0, color=\"red\", linestyle=\"--\", alpha=0.7)\n",
    "plt.axhline(y=1, color=\"red\", linestyle=\"--\", alpha=0.7)\n",
    "plt.axhline(y=0.5, color=\"grey\", linestyle=\":\", alpha=0.5)\n",
    "plt.axvline(x=0, color=\"grey\", linestyle=\":\", alpha=0.5)\n",
    "\n",
    "plt.xlabel(\"z\")\n",
    "plt.ylabel(\"sigmoid(z)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model gives predictions by calculating a weighted sum, and activating the result. We use matrix operations to efficiently do this for multiple observations at a time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(features, weights):\n",
    "    Z = np.dot(features, weights)\n",
    "    return sigmoid(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We initialise our weights with 0 (but anything would be fine). There are 3 weights: one for the bias unit, and one for each of the two features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_weights = np.zeros(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = predict(X_val, init_weights)\n",
    "preds[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our predictions are currently values in the range between 0 and 1. To give a class to each prediction we need to set some threshold (generally 0.5) which defines the boundary between classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def classify(predictions, threshold=0.5):\n",
    "    return (predictions >= threshold).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds_classes = classify(preds)\n",
    "preds_classes[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To assess the performance of the model, we'll need some sort of metric - accuracy is simplest, and fine for us since our classes are balanced. Pre-training we'd expect ~50% accuracy, equivalent to randomly guessing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(predicted, actual):\n",
    "    return np.mean(predicted == actual)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(preds_classes, y_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although it won't be pretty to look at for now, we'll also want to look at the \"decision boundary\" later, so we'll define a function that plots predictions behind the data as a contoured surface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_boundary(data, labels, weights, subdivs=200, alpha=0.2):\n",
    "    \n",
    "    # Get plot limits\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.scatter(data[:, 1], data[:, 2], c=labels)\n",
    "\n",
    "    xmin, xmax = ax.get_xlim()\n",
    "    xstep = (xmax-xmin)/subdivs\n",
    "    ymin, ymax = ax.get_ylim()\n",
    "    ystep = (ymax-ymin)/subdivs\n",
    "    \n",
    "    # Clear axes\n",
    "    plt.cla()\n",
    "    \n",
    "    # Plot again!\n",
    "    grid = np.mgrid[xmin:xmax:xstep, ymin:ymax:ystep].reshape(2, -1).T\n",
    "    n = grid.shape[0]\n",
    "    grid_with_bias = np.hstack((np.ones((n, 1)), grid))\n",
    "    \n",
    "    preds = predict(grid_with_bias, weights)\n",
    "    \n",
    "    plt.contourf(np.arange(xmin, xmax, xstep), np.arange(ymin, ymax, ystep),\n",
    "                 preds.reshape(-1, subdivs).T,\n",
    "                 alpha=alpha)\n",
    "\n",
    "    plt.scatter(data[:, 1], data[:, 2], c=labels)\n",
    "    \n",
    "    plt.contour(np.arange(xmin, xmax, xstep), np.arange(ymin, ymax, ystep),\n",
    "                preds.reshape(-1, subdivs).T,\n",
    "                levels=[0.5],\n",
    "                colors=\"black\", linestyles=\"dashed\")\n",
    "    \n",
    "    plt.show()\n",
    "    \n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\matplotlib\\contour.py:1243: UserWarning: No contour levels were found within the data range.\n",
      "  warnings.warn(\"No contour levels were found\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary(X_val, y_val, init_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we define the binary cross-entropy cost function..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_cost(features, labels, weights):\n",
    "    \n",
    "    m = features.shape[0]\n",
    "    preds = predict(features, weights)\n",
    "    \n",
    "    cost = -(labels*np.log(preds) + (1-labels)*np.log(1-preds)).sum()\n",
    "    \n",
    "    # Average cost per observation\n",
    "    return cost/m\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_cost(X_train, y_train, init_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then the first-order gradient of the cost function, with respect to the model's weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_grad(features, labels, weights):\n",
    "    \n",
    "    m = features.shape[0]\n",
    "    preds = predict(features, weights)\n",
    "    \n",
    "    # Average gradient over all observations\n",
    "    grad = np.dot(features.T, (preds - labels)) / m\n",
    "    \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01333333, 13.11543754, -0.77495361])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_grad(X_train, y_train, init_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define a basic training routine, which runs either for the number of iterations specified in `iters` or terminates earlier if an improvement of less than `tolerance` is made to the cost. It returns the optimised weights and the values of the cost function at all iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(features, labels, init_weights, iters=1000, rate=0.1, tolerance=1e-6, verbose=True, report_level=100):\n",
    "\n",
    "    cost = get_cost(features, labels, init_weights)\n",
    "    \n",
    "    if verbose:\n",
    "        print(\"Training in progress...\")\n",
    "        print(\"\")\n",
    "        print(\"Iter | Cost\")\n",
    "        print(\"---- | ----\")\n",
    "        print(\"0000 |\", cost)\n",
    "\n",
    "    cost_history = np.empty(iters+1)\n",
    "    cost_history[0] = cost\n",
    "    weights = init_weights[:]\n",
    "    \n",
    "    for k in range(1, iters+1):\n",
    "        \n",
    "        # Update weights based on gradient of cost function\n",
    "        grad = get_grad(features, labels, weights)\n",
    "        weights = weights - rate*grad\n",
    "        \n",
    "        new_cost = get_cost(features, labels, weights)\n",
    "        \n",
    "        # Stopping criterion\n",
    "        if abs(cost - new_cost) < tolerance:\n",
    "            if verbose:\n",
    "                print(\"Tolerance reached - terminating early!\")\n",
    "            \n",
    "            cost_history = cost_history[:k]\n",
    "            break\n",
    "            \n",
    "        else:        \n",
    "            cost = new_cost\n",
    "            cost_history[k] = cost\n",
    "        \n",
    "            if verbose and k % report_level == 0:\n",
    "                print(str(k).zfill(4), \"|\", cost)\n",
    "    \n",
    "    if verbose:\n",
    "        print(\"\")\n",
    "        print(\"Training complete!\")\n",
    "        print(\"Iterations completed:\", k)\n",
    "        print(\"Final cost:\", cost_history[-1])\n",
    "    \n",
    "    return weights, cost_history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try running this with a smallish learning rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training in progress...\n",
      "\n",
      "Iter | Cost\n",
      "---- | ----\n",
      "0000 | 0.6931471805599453\n",
      "0010 | 0.1678468407907179\n",
      "0020 | 0.15540493583957077\n",
      "0030 | 0.1502942358492958\n",
      "0040 | 0.14777605914446323\n",
      "0050 | 0.14641236507851643\n",
      "0060 | 0.1456291885227473\n",
      "0070 | 0.14516092121184054\n",
      "0080 | 0.1448725560446095\n",
      "0090 | 0.14469086809145348\n",
      "0100 | 0.14457421946061733\n",
      "0110 | 0.14449807572248818\n",
      "0120 | 0.14444757848656517\n",
      "0130 | 0.14441353401468582\n",
      "0140 | 0.14439015600507227\n",
      "0150 | 0.14437375283617332\n",
      "0160 | 0.1443619433473207\n",
      "Tolerance reached - terminating early!\n",
      "\n",
      "Training complete!\n",
      "Iterations completed: 161\n",
      "Final cost: 0.1443619433473207\n"
     ]
    }
   ],
   "source": [
    "optw, ch = train(X_train, y_train, init_weights, iters=2000, rate=0.01, report_level=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's inspect the cost history (we expect a smooth decrease) and the optimum weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x147d34baa90>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.00832463, -0.25347881, -0.12698687])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can assess the accuracy of our trained model..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = predict(X_val, optw)\n",
    "preds_classes = classify(preds)\n",
    "\n",
    "accuracy(preds_classes, y_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... and plot the new decision boundary!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary(X_val, y_val, optw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularisation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Large weights increase sensitivity of output to small changes in input. It would be better if we coukd \"spread\" this sensitivity over the weights, to reduce reliance on any individual weights, thus improving robustness (and hopefully improving generalisation).\n",
    "\n",
    "We'll discourage large weights by adding a penalty term to the cost function: (squared) L2-norm of all weights. This means we need to redefine our cost/grad functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_cost(features, labels, weights, gamma):\n",
    "    \n",
    "    m = features.shape[0]\n",
    "    preds = predict(features, weights)\n",
    "    \n",
    "    # Log-loss cost function\n",
    "    cost = -(labels*np.log(preds) + (1-labels)*np.log(1-preds)).sum()\n",
    "    \n",
    "    # Add regularisation term\n",
    "    cost = cost + (gamma/2)*(weights[1:]**2).sum()\n",
    "    \n",
    "    # Average cost per observation\n",
    "    return cost/m\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_cost(X_train, y_train, init_weights, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_grad(features, labels, weights, gamma):\n",
    "    \n",
    "    m = features.shape[0]\n",
    "    preds = predict(features, weights)\n",
    "    \n",
    "    # Gradient of cost function\n",
    "    grad = np.dot(features.T, (preds - labels))\n",
    "    \n",
    "    # Add gradient of regularisation term\n",
    "    regs = gamma*weights\n",
    "    regs[0] = 0\n",
    "    grad = grad + regs\n",
    "    \n",
    "    # Average grad per observation\n",
    "    return grad/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01333333, 13.11543754, -0.77495361])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_grad(X_train, y_train, init_weights, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Likely there will be virtually no difference here, but we would see the effect more clearly if we had more dimensions..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variable step size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multiple possible approaches - but we'll implement a simple \"grow/slash\" method, which successively increases the learning rate at each iteration, and then reduces it dramatically when it is too large.\n",
    "\n",
    "We redefine our training method to include a `gamma` parameter (to control regularisation) and using the new adaptive learning rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(features, labels, init_weights, iters=1000, rate=0.1, gamma=0, tolerance=1e-6, verbose=True, report_level=100):\n",
    "\n",
    "    cost = get_cost(features, labels, init_weights, gamma)\n",
    "    \n",
    "    if verbose:\n",
    "        print(\"Training in progress...\")\n",
    "        print(\"\")\n",
    "        print(\"Iter | Cost\")\n",
    "        print(\"---- | ----\")\n",
    "        print(\"0000 |\", cost)\n",
    "\n",
    "    cost_history = np.empty(iters+1)\n",
    "    cost_history[0] = cost\n",
    "    weights = init_weights[:]\n",
    "    \n",
    "    for k in range(1, iters+1):\n",
    "        \n",
    "        # Update weights based on gradient of cost function\n",
    "        grad = get_grad(features, labels, weights, gamma)\n",
    "        \n",
    "        new_weights = weights - rate*grad\n",
    "        new_cost = get_cost(features, labels, new_weights, gamma)\n",
    "        \n",
    "        while np.isnan(new_cost) or new_cost > cost:\n",
    "            if verbose:\n",
    "                print(\"  Rate change!\", rate, \"->\", rate/2)\n",
    "            rate = rate/2\n",
    "            new_weights = weights - rate*grad\n",
    "            new_cost = get_cost(features, labels, new_weights, gamma)\n",
    "        \n",
    "        # Grow rate\n",
    "        rate = rate*1.1\n",
    "        \n",
    "        weights = new_weights\n",
    "        \n",
    "        # Stopping criterion\n",
    "        if abs(cost - new_cost) < tolerance:\n",
    "            if verbose:\n",
    "                print(\"Tolerance reached - terminating early!\")\n",
    "            \n",
    "            cost_history = cost_history[:k]\n",
    "            break\n",
    "            \n",
    "        else:        \n",
    "            cost = new_cost\n",
    "            cost_history[k] = cost\n",
    "        \n",
    "            if verbose and k % report_level == 0:\n",
    "                print(str(k).zfill(4), \"|\", cost)\n",
    "    \n",
    "    if verbose:\n",
    "        print(\"\")\n",
    "        print(\"Training complete!\")\n",
    "        print(\"Iterations completed:\", k)\n",
    "        print(\"Final cost:\", cost_history[-1])\n",
    "    \n",
    "    return weights, cost_history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's retrain..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training in progress...\n",
      "\n",
      "Iter | Cost\n",
      "---- | ----\n",
      "0000 | 0.6931471805599453\n",
      "  Rate change! 1 -> 0.5\n",
      "  Rate change! 0.5 -> 0.25\n",
      "  Rate change! 0.25 -> 0.125\n",
      "  Rate change! 0.125 -> 0.0625\n",
      "  Rate change! 0.0625 -> 0.03125\n",
      "  Rate change! 0.03125 -> 0.015625\n",
      "0002 | 0.17558679495910615\n",
      "0004 | 0.16914013383163512\n",
      "0006 | 0.16376693074874116\n",
      "0008 | 0.15950186240550793\n",
      "0010 | 0.15629650797145545\n",
      "0012 | 0.15403143070168135\n",
      "0014 | 0.15254001330694555\n",
      "0016 | 0.15163648836825025\n",
      "0018 | 0.15114151837871323\n",
      "0020 | 0.15090157501473225\n",
      "0022 | 0.15080050055796923\n",
      "0024 | 0.1507624510500704\n",
      "0026 | 0.1507464412502737\n",
      "0028 | 0.150735182847062\n",
      "0030 | 0.15072336482050624\n",
      "0032 | 0.15070983619777578\n",
      "0034 | 0.15069436101736655\n",
      "0036 | 0.15067686073428302\n",
      "0038 | 0.150657351738181\n",
      "0040 | 0.15063597837373352\n",
      "0042 | 0.15061305187315166\n",
      "0044 | 0.15058908278872046\n",
      "0046 | 0.1505647945520386\n",
      "0048 | 0.15054110214549063\n",
      "0050 | 0.15051903980747267\n",
      "0052 | 0.15049962938639536\n",
      "0054 | 0.15048370001947808\n",
      "0056 | 0.15047171350129987\n",
      "  Rate change! 3.5743994123476157 -> 1.7871997061738079\n",
      "  Rate change! 1.7871997061738079 -> 0.8935998530869039\n",
      "  Rate change! 0.8935998530869039 -> 0.44679992654345196\n",
      "0058 | 0.15046703080131008\n",
      "Tolerance reached - terminating early!\n",
      "\n",
      "Training complete!\n",
      "Iterations completed: 59\n",
      "Final cost: 0.15046703080131008\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: divide by zero encountered in log\n",
      "  import sys\n",
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in multiply\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "optw, ch = train(X_train, y_train, init_weights, rate=1, gamma=100, iters=2000, report_level=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we converged and terminated in many fewer iterations!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x147d3590588>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In particular note the sharper elbow in plot (as a result of adaptive rate).\n",
    "\n",
    "For now, we don't see much adaptation _during_ training... though it means we don't have to be quite so careful with our initial rate (we can just set it \"too high\" and let the backtracking work its way back down)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We wouldn't expect our weights to be too different to before, though due to regularisation they might now be slightly smaller in magnitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.1002087 , -0.24030256, -0.12069693])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Certainly we would hope that our accuracy and decision boundary are similar!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds = predict(X_val, optw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds_classes = classify(preds)\n",
    "accuracy(preds_classes, y_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary(X_val, y_val, optw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might now want to tune our hyperparameters - e.g. gamma - either by trial and error or some more methodical method such as grid search..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma: 0.1\n",
      "gamma: 0.3\n",
      "gamma: 1\n",
      "gamma: 3\n",
      "gamma: 10\n",
      "gamma: 30\n",
      "gamma: 100\n",
      "gamma: 300\n",
      "gamma: 1000\n",
      "gamma: 3000\n",
      "gamma: 10000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: divide by zero encountered in log\n",
      "  import sys\n",
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in multiply\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "gammas = [0.1, 0.3, 1, 3, 10, 30, 100, 300, 1000, 3000, 10000]\n",
    "costs = []\n",
    "accs = []\n",
    "\n",
    "for gamma in gammas:\n",
    "    print(\"gamma:\", gamma)\n",
    "    optw, ch = train(X_train, y_train, init_weights, rate=1, gamma=gamma, iters=2000, verbose=False)\n",
    "    preds = predict(X_val, optw)\n",
    "    preds_classes = classify(preds)\n",
    "    accs.append(accuracy(preds_classes, y_val))\n",
    "    costs.append(ch[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gammas, costs)\n",
    "plt.xscale(\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gammas, accs)\n",
    "plt.xscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Really it looks like our regularisation is having virtually no effect at all, until our scale parameter `gamma` is ridiculously large! And then, the effect is certainly not beneficial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p6Ck391yn+phPPviAI+VlXH7ddexZup3li7cRbAiSP/0Uzr1zHrLS/EPrxU8s4f2/v48e1AFY/dYa7njydpJdyc0e05L1H26MBO+j6qrq2PDhJs69cU6HzikIR3Vo+oXH48kFbgHqPR5PEjDb6/V+B/gncGsC+9fnyPqOmDYpTpvQcamNDzG3Lt7Mkp++webFm/F+5uW9h9/hzV+83uxxddV1LH9+eSR4AxRuKGT58582e0xrnCmx5frC7eIvLqHzOhTAvV5vqdfrfQCoAzKBssZNxcDABPWtT7KIU4dS6nu1KXtSqtuFr7aW9a+tRfeHorZt+mATelCLe9zB7QepLY8tiFxxoOMl16ZcNJkho6NTNAz2DGTqRad3+JyCcFQixsDLgKzGnwcDsevGhQjTMRvZX4REOAOihQPDMadnO9UFcpIGURbooaIO7jTqfD60QChmmxYIYRhm3A/+sAnDyBiYQdWhqqj23JH9O9wXm13ltj/ezEfPfcLhonL6Dc1m3k1zsTk6Pq4uCEd1OoB7vV7d4/Es83g8jwEZwB2d71bfZTgvxpLTUELrAAXDcSamXdyNJZJnbAGz553LqAmj2fbhV1HbRk4bhSM5/rCGI9nBebfPZ+Gf36GhugEkGHvWWM76xlmd6k/WoEyu/cmVnTqHIMTTqQDu9XrPb/z3L4npzsnBdMzCdMzq2MGWiRxaiWTsx1KGYtrP6PKVpL3N7HnzmHvuNAzLjq+slnVvrsMK6Iycls+VD17V4rEzvzaTgtkFbFm2lewhWRTMKhDztoUTlphG2JtYFra6R1C0FeGXgKGtQ0/5HoggA4DdLCQr9GdqyjaT0z+Db/3kPAq+eTcj3Fltrn+ZOTCTs26Yzb7N+3jm3n9x5EA5uSNymXf7PAaOCj/iGTIql6JdpeQNzuzKtyMILRIBvBeRQ+uQtaZUpxKghD7HsM/G6i0ZDC0Dh74WU0pFU8a2/sVj6aQbb5Nk7UEjmyrlCky5mfnTlsUAHuHLDSuZc0Uxmz8ZSoHnP+Qlp6HYrm9XN+uq6/jXD/4deYB54KtiDnoPcd/rP4qaF759pZdNy7aiKDKTLzqd4acObdd1BKEzRADvRSSzOCoNLoCEhWwcwODED+A2fQdpgb9iNwuxkAkqp1HlfABLdjd7zEDt17jNZZHXqeYq9tsewZJj52WrVhnJbCbNHR5Sqqk1kYAs2xZiyxy3bPUbq2NmnxzaeYj176xn+oLpAGxc/CXLnvqQUCA8q2XNog3c/ND1jD1zTDuvJggdIwJ4Ilk6iv8dJGMPyGnojvNATdwdmal6sFAiM1gALGyY6okdMBRjH67gyzj0VSiEc21LmCQZG3D5/4Ulp6CaRRhyLvX2KzCU8DBFkrGNVDO6PJrT2km6sZAq+Wsx1zGlFAwrhXR3OANhTW04gZVO+xfhmEacROGArjX9t9/0wZeR4A1QX9PAp6+sFAFc6DYigCeQWv8Yaqhp0YesfUko9cfI2jYkqxbTNh7L1vFfbstWgOG4ACW4BIkQFg50x/kndhk2K0SG/3fYzfgV4J3GUhSjsaiFAQ5jM0eS/8gIVz98tZ8ho8cco1IV0wZgSqn4rLmkud8AoLrWRCOdA/6zSbNpyKqMorZtHHzKJZP55Nll1BwzLzx7aDaTL2maMVRfHVvdyVfZ3nt9Qeg4EcATxTiEEloV1SSbZdhrf4lMuHCDFXgLPekajOQrOnwZPeVmDMdZSPouLNWDpeZ1qttdzal90mzwBpCPqUgEYDOLSNYWU+9YQCUT0HGj0hRELWQa5NOaPV+J9H0yUnORpB9RUjuGTYe+y4s/3sjhDQtxpCRx2kUTueSBS5HllmfupOemc/1DN7D0maWUHygnd3gu8++YR9IxKyhz8wfgO27hT16BKFQtdB8RwBNEMiqQiF04cjR4A0hoKMFFGEnzQU7p8LUsdTiWOrzDx3enY4d74m+P02Y1oBp7GcufUKjFatxPI40a5RLqlTOi9t9bf0xOcEmhSv06y7ddSKrbzXO3PkPhx9sBqK+qZ+kTH5GW42bOLfGLEhdt3c8XL39BfXU9wyYM466n74x71x6oDw/TqDYFXTOQJBgzYzQX33lei+9XEBJJTCBOEMtWgClHj3fHG0WVrSok82D3dOoE4LfNRZPanl3BxEnAdgauwDO42YNEU5D3MZsjtlui9s/PyIo5B0B6ZiZG0GDPit0x27wrvHGOgOLtxTx111OseGUFm5Zs4u2H3+aln78cd9/XH3qDXSu9kTFxy4IRE/JISe/4F7MgtJcI4IkiKWgpt2Aoo7CQMKVMTCW2ULIp52Apw7q/fz3EkpKodv4IvzIFXcrBJPZu1iAZEzuaPJQax63o8nDsxs6Y/RzS/jZf9+GfPcjLz/4LR4o99jzO+CsxV76+kurD0XVKN36wkZojsflRvKtivwR2rNrV5v4JQiKIIZQEsmwFaO6HwKpsTFAlge+PyPoGJCwsKQ3deTVIsUGlQ4xSZL0Q0zYe5BM3IZamFlCl/pKU4BukBZ+M2mYBNY5bCdlmYEqpIClgWRhyBspxBZ51qe2LZrZu3MiRgWVMv+gcPnvqk0i7I8XBlAVT4x7jr42tn+mv81NX4SMtO3qqY7xcJqpd/DoJ3Ut84hJNkkBq+rNecz2ApG1CMsswbVNASUASf8tCbXgWJbgUiQZMKQPdeTVm0vzOnzuBbMYB0oMvYjMLMaQcDCm2bJkESJKMKR+zTZJosF2IEnwSpXEWikYG1cplbb620+HkwPYivn1FEoMyNXat9pOUojJ9wRCGnj02Zv+8oVlsLRgAC4ka+8obn8fAU2KHgCbMm8CSPUui3wgWH7+wnFlXzaCypIrinQcpmDGaZFc31l4VTioigHc1ScKynxZ3PLyj5NA6lOB7kUU9slWFreElgon6gkgESycr9B/sVjg5pWodwSApZh67ThYB9YyYwxscl1IcTGagtBObVQKynVRjBbqUgSa3PPNmzUur2L96P75gDU/c/D6T5/r52dP7SEq2sKxdlBhjqbUujjlu7AUTsSoaWPPWGuoq6xg2YRhXPHB53FwoF99zEcGARum2AxwuKqf6cA07Vu1ix6pdfPjvZfjrA2h+jfQcNxffeQEzroh/1y8InSECeC8kG944KzJrkbUvMZX4syu6mxxaGwneRykECMinopqHUKlEkwbic3y92ZWY1dIEBsiHSDXWIZnh9+sKLafY/htCcvwC0FpA48NHPoCghI6GZUmsXermrX9m87W7y5EkSJY2xg3gkiRx2Q8v5YK7zsfv8+Pu5242kZUsy0y/agZqIMjDX/9r1LbaI01zwavLaln42PtMOHssKWniAaeQWCKA90JmnLFgCxuWcuLk4bAkR2T637FC6gSq7D9HNYvRlBEtPg+QrQBpxgdRX1Z2DpOuL6TMfm/cYw5tO0jFviP0YyCpNA3L7N/VNH/bxNVi3+1OO3Zny88pgg1BlvzjA/at30MoTt7xY9WW1/LVF16mXjipxf0Eob1EAO+FzKRzMLQVKMeUYjPsM7Bs+T3Yq2iW7TRMdXRUH3WyabCdiyWnosmjWz2HDR9KnFWXKtVx9g7LGdUfd24alEa35w4NB1nNyqHavKSN76J5Lz34Ml++t75N+9qddgZ7BnT6moJwPBHAeyPJgZb6U8zgEiTzCFgSklmKreZ+LGUkuvNaUOJXYO++PspoKffSUPcsdqsSU+5Hnf1yTKXtgSxINn5pDMnWtqh2v9R8OoKakhos0yJo+amhin4MYNipTqZdP5xKYzrV5uWEiD/80uZ+1QfZ9um2uNvsDhv2ZAd1VU2FjKdeNImBI0UAFxJPBPDeSnZiOC9D0nZh9/0Kica8HEYhklmO5v5/Pds/ACWbKsfXOl5WTZIoU++kv/5XnNYuDJyEGEiasZg0Ywn1ylTK1W9HHfLRXxbjK6uliiNsZTVncSnOnAK2aVfi0fu3uoT+eCW7S1jy+BJK9pSSPSSbc759DgPz4wdjxaaQPSSL6ZdNxdRNqsurySsYwhQxdCJ0ERHAezkl9FlT8G4k61uQ9D1Y6sge6lXiBJRxFMlPkGTuwGV8TJbZVFU+ydiDhcxumsqVHd5ZAoBKeJ62jsbuL3ZROP8PZA/KYtZNs5lx/cw2XVsLafzrB//mkDf8MLZ4WzH7t+7nvld/xOgzR7P+uCEUQzM4tLuUhX97j2/+5kbmf3Nup967ILRGrMTs9cz4bVb8yuu9kiQTUApItrbEbEoxoxOIZQ0Nz8E/NoDrIZ2QL8ihHYd485dvUriusE2X3fDehkjwPqryYCWr317D1/7vWmZ+bSaZg2IfKOshg01LN7fpGoLQGSKA93KGfRoW0UvDTXU0Vg9Ug+968T6u0W1z7jyHjMGZUQH8WKGGIFs/iv0iiMfQ4yfiMnUDp8vJ1/7vWq7/3Y3ISuxUw/YO1QhCRyTkU+bxeIZ6PJ6NHo/n3x6P5zeJOKfQNpZtHFrKrRiKB1POwbCdgZZyV5+pkXkkeCDyc508I2b78W3DJo/gnvd/xIXfvwR3cjpWnCVUrU0RPGryxZPpN6xfVJsr28WoaaOwrPB5tZCOacZeY8Rpw9p0DUHojESNgZ8FHG78eUWCzim0kemYg+mY09PdSLgRrn4U+sojryvUr2Mh4TJXABZ18hlUqDfCcVMN3f3cXP7A1Vz246t4/NpH2fVpU+KpzCFZTLtmepuub3faufG3X+eDfyymdE8pWOD3+fnTdX9m2Lg8rnjgCj5+4sO4aSfLispjGwUhwRIVwNcAHxEO4h95PJ4PvF5vHxqEFU4Ikkyl7UYqubFtu0sS33jiW3z0l8UUbtzHwKE5nPXNOWQMaHu6gRETR3DXk3ey+s3VPP+TFyLBeu/Gfbz6y9eQmhkqqa9taPM1BKGjEhXAJwIrvV6v6fF46hBj672TZSFpm5CNIkx1FJatoNu7oBj7cQefw2bsxpCyqLHOAlqucpOfkcXuqmOKOjS65tx5XHzVAr7x8zvYW1rRbO7wtti1elfMnfaBrw4w5crp7N9SFNUuKzIXicIOQjdIVADfBTzs8XjKgUVerzfY2gHCCcayUOsfbZyWaGKhYDjOQ0/5VpdeVjEOYaFgKv3BMsnw/xG7GR7yUK1SRrGHA8ZYgkpsBsHW1NXWUn74cOs7toHTHZtR0JHiYNLFpxOqqmPz8q+wTAubQ+X8W84ls/8JklRM6NMSEsC9Xu964JpEnEvoGXJoLUro00jeEQkDJfghhn1WlxRNlo0jpAcewWFsxEIiqE6mQTkHmxldKEElgNtYTnkHAniq201dbWKKDM+4egYbl2yiqqRpvH3MzDFsWbyJzAEZXP2jy3C6nZw6a4xIWiV0G7GQRwBAMoviZDjUwsWTExHALYvk0Hs49HUg2VD0YuzsbbwOOPWVKPrBxlfHPxVsWyX547ncbupqY6vpdMSAUQO4/fHb+Py/X1BXWUfGoAw2f7SZigMV4R7aFC797gUieAvdSgRwAQBLzsNCigriFjYsNTF336nB/+AKvRA5f7z86Hb2o5OFSkWkLYSLWvWcjl3T5cJ3TAAP1AdY+Z8vqC2vZeS0UZx6TnTJu7yhWRTur2BETvzKP4NHD+Zr/3ctAC89+FIkeEN4FeZnr61k7vWzUG3i10roHuKTJgBg2qdgaLMax8CtxjHwcxM2fOLUP4n6cmhulrpEgHr1HGxmEYaUyR5jNqrcsSyLt//g+5H52v7qBv7+vX+yf3O4ruayp5dy7h3ncPX9w9DIQadthZcDdQGKtxdTeSg2S2L14Rr8Pj+uzJbT1QpCoogALoRJEnrK3ZjySJTQYiSzDknfixxciemIrZjTLpaFZPnbtKtMPSBTkfwwluyk2ldOdpzz2c3dmFIyujyo2XMVTJgQ+Xnzy2siwRtg/Bm1XHX1Y+TZ/BhWMrXmXA6b97XYt0+eX877f3+f+qr6uNuHjB5EasaJW5tU6HtEABeOoaOGPkI2G/N/GLXI9QcIKQOx1DwkbQ9K8H0ksxJTHY6RtADk5NZPK0mElFNR9U9a3xVI0T9ECgSoTv5pzHa7uZ/+2h9ItrZgYaNOPoMS9YG459q0dh1frl3DzXfdhexrmhglyxa3/e8hhp0SLmKsSA1kKO8RJJ+L17LvAAAgAElEQVQi4iegKtldwjt/fodgffwJVrkj+nPZ3Rc2W8FHELqCmK8tRMihNcjmgag2iXrk0AowSrHVPYwa+gRF34wt8Da2ukdaPWdO0iB03UtN0u341TMxSEUngwZlBmYLH78kfS2ycSSmvZ/+OCnWZiQsZEK4zeVkG/+Oe45N69fx2O8fBmDg2KY79aGnBMgfF1uBPon4Ob7XLFzDY7f+o9ngfcblU/npyz/klCknTkEN4eQgArgQYTUmgIqlogSXIVvRAVXWNyFpO9t2bjmDquT/pTzlSYLqVGzGbqS4mRTDJHRorEjfdBIDp7k9Zt8kc0dMG0Cqy03A70cLhTjjxplkDAsPxrgyNPQ464QNYuduF24o5OWfv0JVnDHvo4aNHYpi69hMGUHoDDGEIkRY9tMxAqegGE1B2ZSyMBxnoQbei9lfwgCrpl3XcIWeJUVf3Op+QeU0TCUXODaniIxOOupxuU8MKX71oVR3+GFinc9HRlYWAyYOpWrfEW64twz1uO8qK/J8NfpLZeOHG5u984bw9MHcCcPjbqstr+XNv77H3s1FpKQlM+PyqZx5ZdvysAhCW4g7cKGJpKClfh/dfjaGko9hm46W+n1QcjDsk2Lu0E15KJatHdVmLBOHvqH5zYBBMg3qWVQnfS9O/yRqlAsxj7nv0EmjSrk07vlc7nC1+zpfeDHPoNPzSEoxyB8f+0BVkiBLeYVRmc9FtStqy3fWhmaw5Zjc36ZhUrzzEPW1Dbzwi1dY/c46yorK2bu5iJd/9yablm1t8XyC0B7iDlyIpvRDT70rptmyTUB33ogSXBx5iKk7rwepPUMHEi3dM4Qf/9mpSboDS46/FL3KdjWa1J9UcxUmdmqU+QSVAjhm7vhRuQMHMue88yK5uT0XTcA6WENNxS5cafHvqvunrORQ0Iz0c+qlU1n+/KeE/M1Xnj+0vRiAHat28saf36HYe4jktGT8vugvCj2os3HpFibMPTXeaQSh3UQAF9rMcF6IkXQeEAIpNjeIpB/CkhygNJM0SpIIqNNI1RY2ew2FauyGl6Dc/FBDnTqbOma32t/ho0bx1+eePebyEpc8cCVK6BCW9XLclOmKHOLYZUYDRg3g/O+cz8I/NN9np9uJoRu8+oe3KdldCkBDTfxshJIsZqkIiSMCuNA+kgIcF7yNEmz1TyDr2wEV03Z6uKiEnBRzeG3SbZhSMs7Qp6iUxCzf13GjGIdQ5AOYkotxtqXUBo5g2ubjV8a1q6uWZeGrqcFmt+NMbpruWGP/LsnmYVzyJxwfTyv94zh+6f78W+ehB3U+fPJDtGD000+bw8b48ydSuHFvJHg3x+G0c/r8CS3uIwjtIcbAhU6zNTyPom9FwkAiiKKtwFb7MyRtN5JejGQdM1whqdQl3YwpZ8UEbwtQqCM99CQ59XeQU/ct0kL/YgjvMET7Eena67SHFgox0zOaxW+/HbOtxPwlRfpj1BsT0KwMNCubamM+24/cEvdcF373Am5/4jaS06K/vLSgxsZFG8gcmIkj2RFz3GDPQAZ7BuGZOorr/vcq7A4ba9//klBApMsXOk/cgQudY5lIeuxUQsUsRPb9DxImA3DTYFxOXdL1Tdut+HerR6cWShgoNA1DyATJMN6kWr0MpLZ9bO0OB3aHA18zGQmDjOOA+SiYFuHZJwq6GTuWftSSJz6koSb2AejWj7dw8bfP5vT5E1jx1ppIe+bADEaMzyMU0MjN78/aRRvYttKLZVj0G5zFNT+5grFnjmnTexGEeEQAFzpJAskFVnWcLeFgrFKLK/QiIWUUIdsUADR5GKpRfvyZWmTjMAq1GMQmm2quqIPL7cZX29pUR4nWMh5WllSyZ+2euNu0QIhNy7ZSV1NPakYqsgxDRg+m7EA5n766Mu4x5cUVvPPYYgpmjBarN4UOE0MoQudIEoZjLlYrHyUJg6RjphDWOW5Ak5oq7Ri0nkMkKI3AIP6c7+YkKie4oRvISvz3qKgKa95dz+ZlX1FXVUdtRR3bV+2kfH/zd/MAB3ceovZIYvKVCycnEcCFTjOcl6Kl3IvZSnA1JHfkZ00dTXnq36my340mDUShLu4xR0fJgwzgiPJNkNr3kXW5XJ3OCb71k6389ca/xTzAPMrQDUr3lkW1mUbzq0yPysxNJyW9DblkBKEZYghF6DzThxJajYSGRfyhEE0eSoP9gqYGy8Jm7CBZX4zNOtTsqSWgklMpdzyMJTmRrCDp+hvYOUiIIVSrl4enLjbjb88/T1Jy7JTH5hyfE9yyLN7/+/tRlXjidjJegvMWqHaV2deeKXKHC50iPj1Cp6kNz6JoXzS7PUQ/Kp2/xJLTkcwq0gJP4NA3IOOLmYkSj406LMkJlsEg7aekmusi21KsdRTbftfsnXlWTr/2v6Fj+H1+Sne3XFczb/wwzJDGge0H23zecbMLOOfrZ3Wqb4KQkCEUj8czyOPxvOTxeB7zeDzfScQ5hd4jPP+7eQFlTLhoMZAeeJRk/RMUatsUvAF0wmXKXMbyqOANkGKuJdX4rNlj33jxPzz8swfbdJ14klKSyBocv0IPEpx23mlceM/FfPOhGyiYOTrunx/p/d0xbQd3lXS4T4JwVKLGwG8H/ur1eu8CLvJ4PM2ltRP6pOaHMEw5lzrbTAAkqx67vqldZzZJ4nDjqkubFXsnLAG2ZqYkAhTu9LJ8yZLI691VLT9YPJ6syMy6flbcbcnuZL7+0A24c9LIHd6f7z56KxfeNi8mM2FdVbxVme0ccxGEOBIVwHOBo4mkq4C0BJ1X6AUM+5lYx9x6Wijoyli0pAWEXA+SmTwJXfcCClYLo3YGTjQGEZRGEZAn0aCeQ5XzJxyRZgBQr0zBICnmmDplarPndKWlRaYRDs9tZol/K/SQHrd96KlDSUqN7s8Ft8wjrV/0xz/e8QUzRneoL4JwrESNge8HBhMO4plA7KRgoc8ynFdiSako+gZAwbDPwHTMjNnPkpIIqtNR9Q9itpnYOZL8CIaaF3uBQHi+eFDOp0K5iQzjVWxUopFJpXItmhw/nSuEc4L7an1YltWh+damaeJrZqqfK9vF43c8weHCwwwdPYgLbp2HOyuV2vLYWS/ufi7S+6Wh6wZjpp3CZd+7sN19EYTjJSqAPw38yePx3Ay84fV649+yCH2TJGE6z8PkvFZ3rXF+B7tvCzaiH/hJ6LiDzyEF69HkfOocN2DJsbNHKm3XUa1cSJK1jYA0FlOOHV8+Vqrbha5pBAMBkpxtn43y2X8/47P/fk7lwUpUR/xfk41LNqL5w1MLy4vKObyvjPufvwd3P1dM0WM9pPOjZ+8Ws06EhErIp8nr9ZYC17e6oyBINhrsZ5MWev74DTiN8EyWJGMjSfoqGuwX41dncPyTQVNOo4G2FVoeM248d/zoh5Hq9G2xb81u3n7odYyQEW6IP0U9EryPKvYeYuPSLeQOz4kJ4A01fvZs3IdHlF0TEkgs5BG6Xb3jahrUM7Eal68buMLVfY5hs4pJCz5Ov/q76Wd9Hi6ZY7X/D7tTCsZw1333RWUjbM2eL3Y0Be/mNDMaY5omQ8cMiWl3up30z+vclEZBOJ74e07odjajEJtRdEzQbn5sWqGGYfwXgotQ8OGXCyhT70CTh7bpWv6GBjatW8+YcaeSlhG/SETMNdswzNF/ZH8aqhuixscH5ucyad4E6qrr2bz8Kw4dM1XwjEumkJ4jnu0LiSUCuNDtUoMvYrOKI68VaptdwQlgpxaJ8INBl7kCWfNzwPHnNl2roqyc266+msdffokZc+a06ZixF5zGxtdXY+rxl8PLiswFd15AcpqTpc8uo+JABekDMrnqnotQbSrp/dL43uO389lrK/FV+Bg5cTiTz5/Ypmt3hmmabFn+FfXVfibOH48zJTYfu9C3iAAudBuHthKHsRG7sS1mW0vzQ47flmxtwmYeQJNjhyqOd7Swsa+m7cWX+43M5bTzJrDhvS/jblcdKkMKBtN/RH8KZhUAcGBXKUOOWfDjznJx0e3z23zNzvJV+nj6vufYtb4QgEVPLeG6/1nA2JkiXW1fJgK40C3SA6/gMr9oNWXs8eLdmZs4MI+vCtSM1MbCxs3lBD/qq6VfsWnRl5iWxcDTR6Daml+LFmoI8fQ9/+T0CyZx5rVn4spytakvR2khndojtaTnpLVaNLmtFv9rWSR4A1QequK9J5ZQcKZIV9uXiQAudD29GJe5ot3BG47mibIh0TTjo06egSFnR16XbC9h65KtBFJkjEvHkZ8+ILJNVVWcycnU+ZrPSLjuzbW8/JP/RgoXKwvXM3j0oBb7VbKzhHd3vse699ZzxxO3t/n9fPLfz/n4xU+pKK5gwMj+XHj7fE6ff1qbj29O6Z7Y1aglu0vx+wIku9s+fVLoXUQAFzrOspCDnyMHP0CyGjDVMRjOBTFFjZXAkrh5TyzkSNGHlhi4qCKfZEnDLxdQoX4jsu2Txz/hnZ+/E1ntuPWlDXznxbtJyUiJ7DNwyOAWz7/qlZVRVeeNkI6/1o+iKhh6y7NRSneX8ukLnzJlwYxW30fRVwd466/vRa5Vsucwr/3+LTxT8knNaD0feksyB8Y+oM0anEVSSvNpDoTeTwRwocMU/8uogdcid9ZK6ABKaAuhtF+D0rTARmqmBJpBOiqVrV7HklPwWneT7Yge8w7UBXjn/96JWqpeuqGY5U8u5cIfXxJpe/PTT1s8f0N1fUybJMEVD1zB6rdWU1Najb8ugNZMHcv1izZwcGcJuYOzyB6SzawF07E77TH7bfl0W9QXBUDNER8fPbecy++5qMU+tubsG89i9/rCSF5yR4qDudfParYIhdA3iAAudIwVRAl+GDMsIlOCEvwQI3lBpM2wT0UOLkKmKdAaOKl0/j8yAn9oMR84EF7MEyd2fv7Pz9GDsXPDC1fubtdbyZs4jIPboleGDjttOHNuPIs5N4ZTvtbX1LPu3XV88NjimKX1NYdrqDlcg7fx9bL/fsadf/kWg/IHRO2XkhZ/LvqWT7/qdADPzcvhh//+LiveWkOwIcSEs09liKflYSCh9xNfz0LHWHVIVvxxZcmKnvFhqR6q1MsJMRQDOyFGUJn8C3RbAT7bVXHz8mn0JyiPo8b+TeocN8W9jq7FX9ijJkU/gPzlfffz4Pd/0Oxbufi+Sxk3fzy2JBuqXWXsOady2s2zo/ZJSUth9vWzcbpaH0+uPFjJ7254hGX/iU5zO+OKqXEr11eWVOGvC7R63takpKUw76a5XHzneSJ4nyTEHbjQMVImpjISxYi+27UAUy2IvJZDK1H8C0k3DqLLw6h23E/QNhPJ9JPe8CuS9DUcTyeDypRfYSgtTxMcc84YFj+8GFM7ZhxdhvN/FJ0oyldTQ3lZ80UZUjJSuOWp26gqrcIyLDIHZVIUp55lWWEZZfvK4pwhlh7UWfLMUqZeNImUtPB4vMPpoGCGhy8/2hy1b1q/NOxJIgOz0H7iDlzoGElCT74JU25aHm6hotsvwbRPCzcYh7HVPYVi7EKhAYe5jbTA40hmLanBF0jWP0cmFBmGMUiKFC1OC/wD+zFFkOPJm5jHBfdfgDM9fFfscDk444dnM2zyiKj9XGlpbSpsnJGbQeagZoo3EA70ztS2z+ioOVKLd230F9z8m+eS0b9pRaaiypx55bSETScUTi7iDlzoMMs2hlDao0jaVjBqsOzjQWkqbKwEV0ZWUB6lWkdwap9gN3fGnC8czMNDCapRhdpQxJGUv2EqzQfV+T+cz7SvT2Pv6r2MnDGSw0ooZp9UtwtfY2Hj4blZ7C6tID+j/bnBUzNTmXj+aax4dWWb9ldUhRHjhkW15Z06lO/+43ZWvb2GQEOQsTPHMP6sse3uiyCACOBCZ0kKln1C3E3NFRu2pGRMKTYvyPFTClUqcOpLqVeuarELaf3TOO3S8Fzqw3Eq7mSk1tHgKyfH/AfVnA+0nIK2OcXbipFkmYGnDMSyLPLG51FzuIbtn8cvKefKSiW9f+z7HDCiP1d8/5I4RwhC+4gALnQZ0zEHM7gY2WzKexKSR+G3zcGQs7Drm1Ea79CbnxPeuVG+dHMh37xoBWcVZNCP/5DOYsrUHwLxy6Q159DOQzx+1xNUlzTVKskZ1g8tqCGrMqZhxlRJmzD31E71XRBaIwK40HVkJyHXfaj+hUhmKQ1WOvVJt6KYpTi0LwkoE5AJYcoZBJSJuEMvYjP3Rw7XpVwabOd2qguZvMWgfCjIDy+UsVHBMOcifO0M4CteWREVvAE2fbg57r6SIuGZks+F3ZgLRTg5iQAudC1lEHrqnQBUBQ6SZPnI9P8C1QqXSbNQqVW/SdB+FlXKUFKDL6GaxRjyAOrsV2G1UnGnRZaJyhH2F2u8+k4d377eTXqaQpJcSeuPNKM11PrbtN+o00dy8XfOJ3/icJGDROhyYhaK0K1StIWR4A3hUmrJoUVgGejKcKqTf8KR1L9Tlfz/0NROFv6VZAKcQlGxzv2/OEJxSXjeeI0+opUDY42a2rZKOrkj+jNq0oguDd7V5TWUFx/psvMLvYe4Axe6lWJWxbZZlUgEsEiJc0TnlHEbSWn7gWKqasHHNHY2XMOw2JXuLZq+YDqlew6zZuEafBU+JEnCMqMHvRVVYcblUxPX+eOEAhrPP/gSWz7dhqHpjJqcz3U/XUC/IdmtHyz0SeIOXOhWISX2TlaT87GkxAdvgIB8CjXuPwCw03c7++U/oFvtH5aRJIkrfnw5Dy7+Gb9Y+n+MPtMTs8/Ys08lb2zrOco76t1/fMD6xRsJ+UMYusmOVTt548/vdNn1hBNfp+/APR7Pg8A4wqVfX/V6ve91uldCn1VvvxabWUSSvhYJnZA8gtqkb7Z63AhXPwp9B2ISWrWFKz2cqa/S1/x88rZKSk0iKTWJKx+4kpeDr7Bn/R6SkpOYMG88M78xt9Pnb8m+LUVx2vZjWZYYbz9JJWIIZQawG3AA6xNwPqEPs2QnVckPohq7UcxqgupEkKJXIUpmLcmhd1GsI+jKKBps82P2aY/klBSmzZpFWkZ66zu30YD8Adzz3PeoOFBBUmoSqZmpHNgVm5M7kZLjJMNKSUsWwfsk1u4A7vF4bgOuP6bpLeAvwFjgF8Btiema0BvIwc9RAouQzAosdTh60rVYtuFR+0jaTiR9NzYzHUsNDz3oSj56nJgsmQ1kNfy/ppWaGtj0bdQk/7DNfdpbX8bwlJymPsoyT732avvfXCskSSJ7aPeNP8+8cjq71u3B7wuvVpUVmemXTunUOStLKjE0k37d+D6ExGl3APd6vU8CTwJ4PB4JuN/r9Voej6cCaOejIaE3k7Rd2OqfRKIh3KBVgFGBlvbbyB2zWv80SvBjJDT6o1JvFuJz3tHsOZO192KW2Tv15dQbl9OWFZT5GVnsqSoDywon9W6khULouo4zOX5K197g1FkF3PHnb7Fm0Xr0kM7YWQVMPq9j1XwafA08/+DLbPvCi2kYnDIlnxsevJbM3MT9lSJ0vU4NoTQGbtXj8fwDSAF+lZhuCb2Boq1qCt5H28y96NoGLPsUJG1LY87wcFUbGZ1U7V0Ctlloajj/h2yUo1hVaEo+SDKyFVvgQSaEahQRftTSPLu5mxz9SYY7dmBa/aiyLqFKDuclv+6885kwZTL/+/vfJ+Cd95xRk0cyavLITp/nnUc/YNPSrZHX21fu5K1H3uX8W87lg6c/oqTwMNmDMjnnG3PInzi8hTMJPanTY+Ber/fXieiI0PtYxI6BWEgc/UNM1ndHgvdREjp2YweaMpp0/yMk6Z8hEcAgk3r7JWDGFjLWySSoToVgC4tpLJMB2h9xWtsb51bV4uDvaOYg6uTppLrdbcpIeLLYt3V/TFvh5n0885MXOLSrBICDOw+xf3sx979wD2nZnVhQJXQZMY1Q6DDDMQdLiq7FaKpjsGzjwz8rQxsDehMLGdk4SL+6W0nWP0QmgASoVOIOPUuK/n5MlZ+gOgFLbrlmpNPcQpIVnVRKRsPFFwCkulwtFjY+Xt7QLArLWi/31lulpMdO25SQIsH7qKrSala/s667uiW0kwjgQscpAwml3othm4ah5KPbz0VLuScy9mzZJmHYZ0aCuAVo8lBc+qK4ZdQkQCZOZZpmamoey5BSsYgtimASzojobmNO8JPFjCum4Tim4LFqVxg5aVjcfU0zXs0k4UQgVmIKnWLZxqLZmslnLUnoKd/DtJ2BZBZRpbvI0Ba1+xqG1Hru7pA8knp5Ci5zRaRNI7MxfWw4J3htTU1zh590Jp07nhS3k3WLN2LoBuPnnMrYGR6Kvirm8N6mqkPubBdTL5zUgz0VWiICuNC1JAnTMRWYSsB/AEl/Kybt6rHCmySkxp9C8nAabBe36VKH1J+SrT+LFdqKqg6gkisIyuGVn7f/4Afceu+9QOeKOvQlnqmj8EwdFdV28y+vY9FTH1K65zBZg7M49xtnkTkgo5kzCD1NBHCh2+Q4hxAM5qFa0YmYjj60tLDRoJ5DQD0du7kVkwwa7BdgybFFEeKx5BTK7Xexu76C4facqG1Z/fo1c9TJp7qshj1f7mXU6SNwH/dwMu/Uodz5l2/3UM+E9hIBXOhaRi1KcAmSVYOpjqbcdgWSkYpd3wySjYB6Bg22c7Eb29GUfLTGgsjBdubrbs2G1at55d/P8utH/4ainLz1Jxc9uYRlL35GfU0DqRkpnHvjWcz/1jk93S2hg0QAF7qOUY3N9ysUcx8AVvAD0tQ5VCf/BCwNkCMLfnR1VPPnSYCykhIWvfEG//Obh3Cnt2+xyorXVrD+vQ3oQQ3PDA/n33k+shL/+X9RcSV5gzufc6Ur7Nu6n8X/XIoW1ACoq6pn0dMfMXZ2AYPyB/Rw74SOEAFc6DJKcHEkeANIWKToq2gwKjCV7h1/TnWHhwp8tbXtCuArX1/Fyw++gqGH57PvWV+I3xdgwU+ujNl3yKjcLs+H0hneNbsiwfuoUEOI7Su9IoD3UmIaodBlJDN2HrWCH9WMzarXIitEkvYJadZmsCwcxnYytedw6+813sm3zuUKB/A6X/umEn75/oZI8D5qy8dbsKzeN7Uua2Ccvwwk6DdY5EHprcQduNBlTHUEhD6OatPIJqS2vdivTd9Cuv+v2KwDZACh4IvYKEcmHLjTjfcptv0Ws5WFPqluFwC+dk4l1DUjps3Q9F6ZwnXSvAmsXLiW7Su8kbZxswsYP6eZaaDCCU8EcKHLmI5z0fXdKKEvkAhhSv2otl0IUttznrkCz2OzDgDhmSoOohcAJVtbyTBep0K+qcXz9Ovfn5vuupPs/v3b9R7GzBzNzlXRybWS01OQ5d73x6usyNzxyLf47NUVlO0/Qu7wHGYumN7rvoiEJiKAC11HUtBTv4OhX4JkFGPaT8cfPNL2D50VwmbubXU3GyWt7uNOT+eHDz7Y1itHZA2KHasvKyqjdE8puSNz232+nmRZFvu2FJGek8bsa2ag2sSvf28n/g8KXc5Sh2KpQztwpA1D7oditjxuHSSvTWfb+uWXZOfkkDtoUJt7cNAbu+Rf82vsXrcnbgC3LIvNy79i94ZC0rJdnLlgOknJSW2+Xlfx1/l55scvsG2VF8uwyB2Rw9f+5ypOSUBmQ6Hn9L6/A4WThyRRb78Mk6YAGCIVvbH4sYVEnTyNajV6Rkh+RhZ768s43l3X38DCl19pVxdyhufEtNmSbOSNi/+FtPzZZTzx/X/x0bOf8Pof3+GRWx+nvrq+XdfsCu8//TFffbEDywg/fC0tLOOdv7/fKx/GCk3EHbhwQvPbz0NT8nBqK7GwsyM0mQx7f1zmCjQpl3r5jKjCDS1JdbnwtSMjIcDki09n45KNbPl4CwCSLHHGgukMKYitzVl9uJrNizdGVavf/9UBPn3lCy64bX67rptoh+L8JVHsPUSgLoDT5eyBHgmJIAK4cMLTldH4lNEAhLRyDDmXajl2HnZrXB3ISKioCrf+7RY2vL+Bsn3lDJuQx5iZY2L2K9lVwqJH38fvi81ZXnm455NopfWPTUeQ0T8NR7Ijzt5CbyECuHDSSHW58NW2L5gWllUyIieTyRdPbnaf7Z9v57n7n8dXEf/LYYhnYLuu2RXmXj+LnWt3U3EwPDff5rAx+5ozm11RKvQOIoALJ42MrMx2jfnmDc2iaH9Fq/t98vzyuMFbtStMPHcCZ145vV397AqDTxnI95++ixVvrSHoDzFu9hhOmZzf090SOkkEcOGk8YennuqS81aXVse0pWakcNdfv82wcW2bIdMdMgdkcPGd5/V0N4QE6lAA93g8NwFTvF7vdz0eTyrwOFAB1Hi93p8lsoOCcKIbPHowB3ccjGobdfrIEyp4C31TuwfAPB7PNUAuTcH/GmCR1+u9Bxjq8XjaPslWELrRa8+/wM2XXQ40FnWoan14pC0uuPt8RkwaEXmdVzCYi+4Qd7pC12v1Dtzj8dwGXH9M073AGuCBxte5wGeNPx8EBjT+KwgAyMGVKKF1WJJCf/uZHNZBVT3d3o+G+jq2bdqU8PNmD87m3hfvYccXOzi8/whzL5sqHg4K3aLVAO71ep8Enjy2zePxDDvm5X5gcOPPg4DYCafCSUv2v4/N/ywSOgBKaAVJ9uvQuyuAWxYSGhY2XG43Ab8fLRTCZm97Ppa2kGWZglkFuHaViuAtdJtEfNJeBy70eDyPAru93jgrBoSTlhJcFgneABIBXPqqbrl2qrmCYdZdnGJdwXDrDrJTi4H2p5RtjyGjcikqjk2jKwhdoUMPMb1e7z7gjsaf/cCNCeyT0IdI1MW0yVYXLy23DOwcYSAPYyNcf1NlG8PcO4BwUYeMrJO7oLHQN4hphEKXspRTwIzOSxKUh3XRxSyy9adxGcsYmVSJjUDU5kkFIR79+w0ieCdQ2f4jFG7cS/7kkWTHKxghdCkRwIUupSXfCA31yNpWQMa0TaJGuYiuKCucbrxBlvEiEoSThx8nJ1vlslKgCNcAABFoSURBVCtnUiW7YzcKzdKCGm8+8i471+7G5rAxcd4E5t00h4V/W8Tyl78gUB8k2e1k7g2zuej2ns35crIRAVzoWkoWmuunYJQDKigZWIGOT1Ia4epHoe8A2Y7YZFIp5vp4cTuiOpjHEy8dYcqs3QzP7/urEFe9s5bNn3yFrMhMmjeBSfMmdOg8r/zuLb54o+m5RdG2A9QeqWX5y19gNFYsaqj18+G/l3Ha3FMZdEpT6oDyA0dY8sxSSvYeJj0njQEjchkxIY/R008RhSQSQARwoXso/br8EiaxiZkMHPgZTYghlLCAXz0wk1888uc+H8A/fv4T3njk3Uj62M3LvyIUCDH9kintOo9pmmxbsSO60YItn26LBO+jQv4QO9bsjgRwXdN5+v7nOLD92C/s8DTOsTNHc8vvvyGSaXWSmO8k9Bm18jwMolOjVnMRRfKjlMg/Bmc+docDX037Usr2RmsWfRkJ3gB6UGf1u+s7dK54d8r2JFvsfrJE/2H/v717j4+qPBM4/ptbEjKZSSBAYiDcw8tVGjCChABW65VdpHJZWcX1gtrVCm3F6tba1tqLYl3drV1La92q/XzqnVK1LLCCFURBXEQovECRSwghISH360zO/jHJJONEkgmTmZyZ5/tXzptzzjwzOfPM5D3v+7ztH9Qfr9/9heTdbt/WA2x6YUuP4hHtJIGLmFFrn0mR/SGqrAXUWKZxsGkBjQzD3fK/YPiGMrrc7pBrgptRQ21DcFtNcFtXrFYrE2eNC2izWC0ULLyEybMnBLTnXjaZifnt+zY1NJ3z3EWHi0OORwSSLhQRU2rt+dSST4pnK9n2J+mHb0x2rTGJE8ajpLjdIdcEN6MxuSMpPX4moG107sgenWvhqutISErg4M5DOBITmHrFFGYvzid/wQy2r9vJ6aMlZI3JZPq8iwK+rV90VS4bn3+XsqKznZ53QGZaj+IR7SSBi9hjGKR7X6SftX1CjZO9DOQP5OblkZF1QRSDi4yvf+sfaKhr4sCHGqvNhsobTfb4oVSUVpI2KHhxh3NxJNi5/jv/GNRuc9iYdf2Xl8pNdvXjnx9ezPrnNnFs3wka65ugtVcnK+cC5i4tCCkOEUwSuDAlR8txUrzb8VgGUm2bC5b2gYlWakgwjgcdk8hxHnn6qZAeZ/iwdI4cL2PUYHONcXamOVm+ehn1NQ1sfuk9trz8AZ9s3IMzLZmvLi2I2BJv42aMZdyMsRiGwd93H2Xftv04XcnM/Pp0kmUpt/MmCVyYTqaxkRFNr2GjDoBa71sUOn6CYU0GoIVkmsnCxt8DjmsiC8Mw8Hg8OBzBN+FiUXlRORte2EJTna8/uraijvXPvcuE/PEMnxg8FLO3WCwWxuSOZEwPu3FE5+QmpjAVi9HAUN72J28Ap/F/DPC+3mEnG2X2JTQZTn9TPaMoYwk/XnU/N117bSRDjqr9Hx70J+82zY3NHPjoYJQiEuEk38CFqdi9R0giuI63wygM2K62X4GuyWBC0l5acFJhuQbD0o9kZ3LAMMLDZ8sY0z92p9YPyu78uQ0c0re6hMpPleP1tDAoe2C0QzEVSeAi4gYnDaGkQfeoJrjHNooGBpBEYMW/ZkvwOiJ1xlDKrFMD2lypqdS0DiMcmZnO58XhWdShr7pw7iQmFYxn7/v7/W3jZypyezgrM9zqqut46QevsG/bAVq8XtTFOSx9eLGMUOkmSeDCVAxLEie5lhG83t4HbplCue36bh3vcruprqrGMIyYncrdVN/EJxs/JTktmUmzxnPHk//C1tc+pPhoCYOHDaRg0Uys1r7Re/rnX65n97uf+bf/9oFm7dNvcevPboxiVOYhCVyYzinLFeC4DJd3O82WQVTbLg0YhXIuKW43nuZmGhsaSOoXe6MgDnx4kN89+CI1Z30fbsmuftz2+E3MvWFWlCPr3NG9waOFPt9zLAqRmJMkcGFKzdYRlPegLO3cK65g7ft/DfuKPB1l52Ry7FAxw4dGtp/ZMAxefWKdP3kD1FXX8/y//YGfb/phn1spyNPswTCMoPaUNGcne5+bYRhse/MjDnx4EEeig+nzpjFu+thwhNmnSQIXccWdloY7LTb7Vxvrmzh97HRQe83ZWvZu3c+FcyZGIarO7du2n9dWr+P00cBa8fYEG5fMvzjk87397AbeWbPBP1Foz+a93PrYjUzMHx+OcPusvvWRLEQvKyku5kffuY9jR45EO5SwS0hykJzSebdQv5SkCEfz5Vq8Lbz51NtByXvEpGxufWwZsxfPDPl8O9/Z5U/eAPU1DXywdkc4wu3TJIGLuNLU2MjrL73EyePBfa9mZ7VauXTp7KD2jJGDGTN1VBQi6lzhwVMUHToV1D54+GC+cumkkM/n9bZQ30mhrvrq0It3mU2PErhS6ubWRYxRSiUqpfYqpf5bKfWb8IYnRLBRrkGcaTzh2zA82I3TYDR361iX27caT3VlZW+FF1VXL7+cRavmY09s7x0tPXGGt5/dEMWoAg24ILXTfm73QFePzudIsDNqyoig9tFfCW6LNSEncKXUYiCT9v7zi4EqwAtEZrlxIQCXZyMjG29jdOMSRjbeQqpnXZfHOF2+JFEdwxUJG2ob8DR6/Nstnhb++so2qsr6xnNOSUthxvy8gGXvMkYMomBRaF0nHS28bz4TZo7DkeAgJc3JzAXTueq2y895TIu3hcKDRdRW1Z1zv76sy5uYSqk7gKUdmlYCO4AHWrePAsu01oeVUi8rpTZorU+EPVIhOkgwyhjseQYHFQAkUshgz6+ps15I8zlGp9jtdpKdTv9knlhUdiq4fGvN2VoKdRETZoY+eao3LFg5j+xxQzi86wjOtGRmLZx5XpN3Bg5N555fLae6vBp7gqPLPv+28eaFuoiUNCcz5uexYOU8080N6DKBa63XAGs6timlRnTYHAf+aXFnu3NOIc5XOh/7k3cbG7W4vFv9wwvH9E/n8NkSRjoHB+z3T7fcwtgJgYsRxJKsMcHlcvtnpjE6d0Tkg/kSFouFvKunknf11K53DsGuDZ/ywdod1JytYcTkYSxYMS9oer632csrj79JydFSAGoqatn0+y0MybmA6fMuCjpni7eFipJKXANScCT2rSJo4Ui2h4AnlFKFwCmt9edhOKcQ59RE5zWtvZaua12v/P5D4Q6nT5mzOJ/Dn3zOni17afG2kNI/hWvu/BqJ/WJ7/cndm/fy+i/W+dfq3H36M+qq6lm55htUl9ew/U878Xo8pGWk+ZN3Rx/9eWdQAv90817e+q//4eTBItKHDGDOknwuXzY3Ek+nW3qUwLXWR4G7Ovy8MHwhCdG1Mi6m1vI+TmOPv63eMo4q25VdHlt47Bher5fho/rOyIxwsjlsLH9iGYc+PkzJ8TImzR4f8iIOZvTZe/uCFlo+vOsIO9d/wss/fYO6qnoAEpM7n8RVURp4j6C+pp5XHnuTs8W+//TKTpaz7pm/MHxiNjnTRvfCMwiddHcIc7JYOen4MQO8r5BgnKCZLMrsizAsXc+w/OmDD2Kz2fnPF1/o1kOZcVEHi8XC2LwcxublRDuUiLHbg8sp2Ow23vz3t/zJG6CxrvO1Oj1NzQE1cna/u9efvP37NHrYt033mQQu48CFabVYUznjWE5RwiOUJtxFi7V7ZWFTXO6YvokZr/KumUqyO3Ai09i80VSWBv+tLdbgm5VnCssDJv/0z0jtdL8vPkY0SQIXccfldgfUBBexYczUUdz86FImz5nIyCnDuXRpAVffcTlGS3C9lWRX56NUDu1qX8VJXZwTNGona3QG+QtCn+rfW6QLRcSdFLcroCb44eLYXtQhnkyePYHJs9tHGBmGwRCVxUldFLDfRVdPY8fbu6ivrg9o77hOp8Vi4fbHl7Hx91soOlxM/8w0vrq0AGdq6MW2eoskcBEV57Oow/lyuVNpburezE1hbhaLhZt+uITXVq/lyKfHSExOZNb1M7huxbV4mprZ9sZH/n37Z6SSv2B6wPGJyYnM+0bXN8ajRRK4iDu33ftNbl9xb7TDEBEybPxQvv27e6guryHJmegfy33D9xaSOSqDI7uP4kxzUrDwEoaMzYpytKGRBC7ijtlm24nwcA1ICdi22qxcduMcLrtxTpQiOn9yE1PEnT27PuGGK6+k9HRw7exwyc7J5Fhhedc7CnEeJIGLuOPxNLNv96dUlEuCFeYmCVzEnRSXr6RsTXXfqM4nRE9JAhdxx53amsCrZCy4MDdJ4MKUAhZ1CFFK66IOVTKZR5icJHARd5KdTr6/+nEmT82NdihCnBcZRihiWmc1wa1WK4uWLYtiVEKEhyRwEZfefecvpA8axJS84AL+QoRTQ10DG5/f7J+Of+nSgqBFJnpKEriIS79avZopeRdJAhe9yjAMfrvqRf627YC/7cBHh/j283eTEoaaKtIHLuJSittNTQwvbCz6Br3jEPu364C24iOn+aBDDZbzIQlcxCWX2011VWW39x8+LJ0jJTLxR4Sm4nRlp+Vs66obwnJ+SeAiLrnkG7iIgCmXTSY9q39AmyPRweSCcWE5vyRwEZdG5uQwdPjwaIchYlw/ZxKLvruA7HFDsNgsDMxOZ/691zA6NzzrsYZ8E1Mp9QNgKJAOPAYUAr8AyoF9WutnwhKZEL1o+coV/p9lUQfRmy6cM5FJBeOpKq3G2d+JIyF8Y0dC+gaulLIAWmu9HPgJcB1wJ/AfWut/Ba5VSjnCFp2IaYOThuDx6K537CWGEdw3KURvsFqtpGWkhjV5QzcSuFLqDqXUFqXUFmAzcEAplQHcD/wSyATa5jSfBVLDGqEQveBPf/wj04Zm4/V6ox2KED3W5ceB1noNsKZtWymVD/wcuFtrfUYpdRxfl8oJYABQ0UuxChE2iUlJeDweaqurcael9drjHCssZ/jQAb12fhHfQu1CSQXeABKBp5RStwG/Bb6plPo18IbW2hP+MIUIL1eq7x/FqsruDyUMVXZOZq+dWwgI8Sam1roSyOjkV0vDE44QkSE1wUUsiNRUehvA6eKyCD2cMIszjWXY7T1b2uxMTRktCV3fMy+vPIszObCv29PchN1up/DoUQakp1NeWkFJY9M5z1N2pgKn0RhSjGXlpSQlnPu8QnyZM2WlbT/aOvu9JRJ34pVSs4D3e/2BhBAiNhVorbd+sTFS38B3AgXAKUBu+wshRPfYgAvw5dAgEfkGLoQQIvxkKr0QQpiUJHAhhDApSeBCCGFSpl+RRyl1M5Cntb5HKZUCPAuUAZVa64eVUjcBs4Fk4Eda64NRDLfXtRYbmwzUAK8Cu4nTYmNKqSHE6XNvo5QaBqzDdx2cwndTLBFfyYs7tdahjYs0KaXUGOBVrXWuUmoVMALfa/AtIAGTXiem/gaulFqMrxZL2wfRYuAdrfUKYFjrG/jm1uJbDwH3RSfSiJoJnAY8wC7iu9hYPD/3NnPwXQ8AxUBq6/vjPeD6qEUVQUqpTOB2oFYplQTM1lrfDTwHLMfE14mpvoErpe4gcNbnSmAH8EDrdibt481P4ht+09y6XQhkRSDMiOrkNVkLPA1MBB5pbftisbEzEQswujortBYvz73NDmATviS+CV9BOvC9H6ZEK6hI0loXAw8opdbjq9dU0vqrtpyQgEmvE1Ml8C8W1gJQSo3osNlWWAtgCFAEtLRuD23djikdX5PWcr/3a60NpVQZvgvzMPFbbEwKrUEusF1r3dJ6fbStJBCT74duKMG3lgG0vwZWTHqdmH4ceGsCf0BrfZdSqh++ZFYJFGutH1VKLQG+BriBVVrrY9GLtvcppb6H72J0Ao8CVcCTQDXwsdb6N1EML6Ja/3WOy+feRik1DfguUAp8BgzDd22kAsu11s3nODymKKXWa62vUkqtABTQH7gL6IdJrxPTJ3AhhIhXpr6JKYQQ8UwSuBBCmJQkcCGEMClJ4EIIYVKSwIUQwqQkgQshhElJAhdCCJP6f+yc/PVbC4LQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary(X_val, y_val, optw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll choose `gamma=1` and retrain one last time. The performance on the test set then indicates how well we are likely to perform on unseen data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "optw, ch = train(X_train, y_train, init_weights, rate=0.01, gamma=1, iters=2000, verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.945"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = predict(X_test, optw)\n",
    "preds_classes = classify(preds)\n",
    "accuracy(preds_classes, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary(X_test, y_test, optw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimental: Generating higher-dimensional problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Choose negative/positive range - all positive leads to potentially all observations on one side of boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 10000\n",
    "d = 3000\n",
    "\n",
    "X = np.random.uniform(-1, 1, size=(m, d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 3000)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`gamma` will control the spread of results shortly, and will correspond to regularisation later..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = 0.3\n",
    "w = np.random.normal(0, gamma**2, size=d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3000,)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = sigmoid(np.dot(X, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000,)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect our linear outputs to be approximately normal here, since `w` is normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  20.,  137.,  755., 2008., 2885., 2547., 1226.,  365.,   50.,\n",
       "           7.]), array([-10.36255555,  -8.17410153,  -5.98564751,  -3.79719348,\n",
       "         -1.60873946,   0.57971456,   2.76816858,   4.95662261,\n",
       "          7.14507663,   9.33353065,  11.52198467]), <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.dot(X, w))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we want our activated outputs to fall in general close to 0 or 1, but with some intermediate values for the sake of interest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2229.,  947.,  735.,  574.,  520.,  562.,  581.,  722.,  944.,\n",
       "        2186.]),\n",
       " array([3.15926158e-05, 1.00027442e-01, 2.00023292e-01, 3.00019142e-01,\n",
       "        4.00014992e-01, 5.00010841e-01, 6.00006691e-01, 7.00002541e-01,\n",
       "        7.99998391e-01, 8.99994241e-01, 9.99990090e-01]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now generate labels which are 1 with a probability of `mu` (activated output), and 0 otherwise, for each observation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.random.binomial(1, mu, size=m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With symmetry of sigmoid, we expect approx hald of our observations to have a label of 1, and half of 0..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4926"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we proceed to train as before on this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, y_train, X_val, y_val, X_test, y_test = make_sets(X, y, [0.6, 0.2, 0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_w = np.random.uniform(-0.1, 0.1, d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training in progress...\n",
      "\n",
      "Iter | Cost\n",
      "---- | ----\n",
      "0000 | 1.011704686695222\n",
      "0005 | 0.28233903497141793\n",
      "0010 | 0.19265892890934527\n",
      "0015 | 0.14438333626161776\n",
      "0020 | 0.11066062834924285\n",
      "0025 | 0.08596094550219581\n",
      "0030 | 0.06876567797410332\n",
      "0035 | 0.058217204070738805\n",
      "  Rate change! 123.650722131483 -> 61.8253610657415\n",
      "  Rate change! 61.8253610657415 -> 30.91268053287075\n",
      "0040 | 0.05603689094547328\n",
      "  Rate change! 45.25925556817607 -> 22.629627784088036\n",
      "0045 | 0.05439981363583461\n",
      "0050 | 0.05324755917052514\n",
      "  Rate change! 71.02146599221592 -> 35.51073299610796\n",
      "0055 | 0.05243126444700643\n",
      "  Rate change! 57.19039059756185 -> 28.595195298780926\n",
      "0060 | 0.0519298019520018\n",
      "0065 | 0.05152549139434756\n",
      "  Rate change! 74.16857220130005 -> 37.084286100650026\n",
      "0070 | 0.051229069866970595\n",
      "  Rate change! 49.3591847999652 -> 24.6795923999826\n",
      "  Rate change! 27.14755163998086 -> 13.57377581999043\n",
      "  Rate change! 13.57377581999043 -> 6.786887909995215\n",
      "  Rate change! 6.786887909995215 -> 3.3934439549976076\n",
      "  Rate change! 3.7327883504973687 -> 1.8663941752486843\n",
      "  Rate change! 1.8663941752486843 -> 0.9331970876243422\n",
      "  Rate change! 0.9331970876243422 -> 0.4665985438121711\n",
      "  Rate change! 0.4665985438121711 -> 0.23329927190608554\n",
      "  Rate change! 0.23329927190608554 -> 0.11664963595304277\n",
      "Tolerance reached - terminating early!\n",
      "\n",
      "Training complete!\n",
      "Iterations completed: 73\n",
      "Final cost: 0.051184333648648606\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: divide by zero encountered in log\n",
      "  import sys\n",
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in multiply\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "optw, ch = train(X_train, y_train, init_w, rate=4, gamma=1, iters=5000, report_level=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x147e2d669b0>]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = predict(X_train, optw)\n",
    "preds_classes = classify(preds)\n",
    "accuracy(preds_classes, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds = predict(X_val, optw)\n",
    "preds_classes = classify(preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.707"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(preds_classes, y_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we try a few different values for `gamma`, we _should_ observe that our highest accuracy comes at the `gamma` value we used during our data generation process..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training with gamma=0.01\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: divide by zero encountered in log\n",
      "  import sys\n",
      "C:\\Users\\ojones\\AppData\\Local\\Continuum\\miniconda3\\lib\\site-packages\\ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in multiply\n",
      "  import sys\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training with gamma=0.03\n",
      "Training with gamma=0.1\n",
      "Training with gamma=0.3\n",
      "Training with gamma=1\n",
      "Training with gamma=3\n",
      "Training with gamma=10\n",
      "Training with gamma=30\n",
      "Training with gamma=100\n",
      "Training with gamma=300\n"
     ]
    }
   ],
   "source": [
    "gammas = [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100, 300]\n",
    "accs = []\n",
    "final_costs = []\n",
    "\n",
    "for gamma in gammas:\n",
    "    print(\"Training with gamma=\" + str(gamma))\n",
    "    optw, ch = train(X_train, y_train, init_w, rate=4, gamma=gamma, iters=5000, verbose=False)\n",
    "    preds = predict(X_val, optw)\n",
    "    preds_classes = classify(preds)\n",
    "    accs.append(accuracy(preds_classes, y_val))\n",
    "    final_costs.append(ch[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gammas, final_costs)\n",
    "plt.xscale(\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gammas, accs)\n",
    "plt.xscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results seem inconclusive, but for now we'll move on."
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}