Logistic_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "bf6ac9bd-dc81-49de-9c06-a2bf4904dbac",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scratch.logistic_regression import tuples\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "data = tuples\n",
    "xs = [[1.0] + list(row[:2]) for row in data]\n",
    "ys = [row[2] for row in data]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "4a631198-0bf6-4575-a878-b0188ef48f9a",
   "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": [
    "# salary vs years experience vs paid / unpaid users\n",
    "plt.scatter([row[1]\n",
    "            for row, y in zip(xs, ys)\n",
    "            if y],\n",
    "            [row[2]\n",
    "            for row, y in zip(xs, ys)\n",
    "            if y], label='paid')\n",
    "plt.scatter([row[1]\n",
    "            for row, y in zip(xs, ys)\n",
    "            if not y],\n",
    "            [row[2]\n",
    "            for row, y in zip(xs, ys)\n",
    "            if not y],\n",
    "            marker='+', label='unpaid');\n",
    "plt.title('Paid and unpaid users')\n",
    "plt.xlabel('years experience')\n",
    "plt.ylabel('annual salary')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "dff1945a-dcb2-4d0a-a444-76f1b5786062",
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets model the problem as a linear regression \n",
    "# can we predict who is a paid user in the form paid = B * X ?\n",
    "# we can model it for sure!\n",
    "\n",
    "from scratch.working_with_data import rescale\n",
    "from scratch.multiple_regression import least_squares_fit, predict\n",
    "from scratch.gradient_descent import gradient_step\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "7d9b3b2c-3489-43f8-99d5-c0871b2ef5ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 0.001\n",
    "rescaled_xs = rescale(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "ed59ff8c-b2a3-4c4d-b0ed-e02a12d9f46b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "least squares fit: 100%|██████████| 1000/1000 [00:02<00:00, 473.86it/s]\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": [
    "# issues with negative or over 1 values of predicted\n",
    "# biased values for large experience values, larger error\n",
    "beta = least_squares_fit(rescaled_xs, ys, learning_rate, 1000, 1)\n",
    "predictions = [predict(xi, beta) for xi in rescaled_xs]\n",
    "plt.scatter(predictions, ys)\n",
    "plt.xlabel(\"predicted\")\n",
    "plt.ylabel(\"actual\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "44af53df-4149-4ec8-8927-3bd0d7f54d56",
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets create a link function\n",
    "\n",
    "def logistic(x: float)->float:\n",
    "    return 1.0 / (1 + math.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "33d650c1-caaf-411d-b089-a681f60ce56e",
   "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": [
    "xs2 = [xi / 10 for xi in range(-100, 100)]\n",
    "ys2 = [logistic(xi) for xi in xs2]\n",
    "plt.plot(xs2, ys2)\n",
    "plt.title('Logistic function');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "22de2bc2-3450-4ee1-b1f6-b2c4d8430913",
   "metadata": {},
   "outputs": [],
   "source": [
    "# as the input gets lower --> output approx 0\n",
    "# as the input gets higher --> output approx 1\n",
    "\n",
    "# th elogistic fn also as a convineint derivative\n",
    "def logistic_prime(x: float) ->float:\n",
    "    y = logistic(x)\n",
    "    return y * (1 - y)\n",
    "\n",
    "# we'll use it to fit the model:\n",
    "# y = fn(X * B) + err\n",
    "# where f is the logistic fn\n",
    "\n",
    "# in least squares min the sum squared err and maximizing likelihood of data is the same\n",
    "# in log regression this is not the case so \n",
    "# we'll use the gradient that maximizes the likelihood directly\n",
    "\n",
    "# the pdf for yi can be written\n",
    "# p(y| xi, B) = fn(xi * B)** yi * (1 - fn(xi * B)) ** (1 - yi)\n",
    "# turns out it's easier to maximize the log likelihood\n",
    "# log L(B|xi, yi) = yi * log(fn(xi * B)) + (1 - yi) * log(1 - fn(xi * B))\n",
    "# because log is strictly increasin, any beta that maximizes the log also \n",
    "# maximizes the likelihood\n",
    "\n",
    "from scratch.linear_algebra import Vector, dot\n",
    "\n",
    "# grad descent minimizes, \n",
    "# so we will maximize the negative log likelihood\n",
    "def _negative_log_likelihood(x: Vector, y:float, beta:Vector) -> float:\n",
    "    \"\"\"\n",
    "    The negative log likelihood for one data point\n",
    "    \"\"\"\n",
    "    if y == 1:\n",
    "        return -math.log(logistic(dot(x,beta)))\n",
    "    else:\n",
    "        return -math.log(1 - logistic(dot(x, beta)))\n",
    "\n",
    "# as we assume data points are independent in this model\n",
    "# overall likelihood is the product of individual likelihoods\n",
    "# in log terms that means we can sum the likelihoods\n",
    "\n",
    "def negative_log_likelihood(xs: list[Vector],\n",
    "                            ys: list[float],\n",
    "                            beta: Vector) -> float:\n",
    "    return sum(_negative_log_likelihood(xi, yi, beta)\n",
    "               for xi, yi in zip(xs, ys))\n",
    "\n",
    "# now for the gradient\n",
    "\n",
    "from scratch.linear_algebra import vector_sum\n",
    "\n",
    "def _negative_log_partial(x: Vector, y: float,\n",
    "                          beta: Vector, j:int) -> float:\n",
    "    \"\"\"\n",
    "    The jth partial derivative for one data point\n",
    "    ith is the index of the data point\n",
    "    \"\"\"\n",
    "    return -(y - logistic(dot(x, beta))) * x[j]\n",
    "\n",
    "def _negative_log_gradient(x: Vector, y: float,\n",
    "                           beta: Vector)-> Vector:\n",
    "    \"\"\"\n",
    "    The Gradient for one data point\n",
    "    \"\"\"\n",
    "    return [_negative_log_partial(x, y, beta, j)\n",
    "            for j in range(len(beta))]\n",
    "\n",
    "def negative_log_gradient(xs: list[Vector],\n",
    "                          ys: list[float],\n",
    "                          beta: Vector)-> Vector:\n",
    "    return vector_sum([_negative_log_gradient(xi, yi, beta)\n",
    "                       for xi, yi in zip(xs, ys)])\n",
    "\n",
    "# applying the model\n",
    "\n",
    "from scratch.machine_learning import train_test_split\n",
    "import random\n",
    "import tqdm\n",
    "\n",
    "random.seed(0)\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(rescaled_xs, ys, 0.33)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "43c93024-0a53-406b-8e24-0128e0b23255",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "loss: 39.963 beta: [-2.0239032476251424, 4.693047853942649, -4.469811321910748]: 100%|██████████| 5000/5000 [00:20<00:00, 248.66it/s]  \n"
     ]
    }
   ],
   "source": [
    "learning_rate = 0.01\n",
    "\n",
    "# random starting point for beta\n",
    "beta = [random.random() for _ in rescaled_xs[0]]\n",
    "with tqdm.trange(5_000) as t:\n",
    "    for epoch in t:\n",
    "        gradient = negative_log_gradient(x_train, y_train, beta)\n",
    "        beta = gradient_step(beta, gradient, -learning_rate)\n",
    "        loss = negative_log_likelihood(x_train, y_train, beta)\n",
    "        t.set_description(f\"loss: {loss:.3f} beta: {beta}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "318b7b06-9846-4926-ac0d-7504b94e1a88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8.927236932527311, 1.6482026277676038, -0.00028768900920142336]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# these are the coef for the rescaled data\n",
    "# lets convert them back to original scale\n",
    "\n",
    "from scratch.working_with_data import scale\n",
    "\n",
    "means, std = scale(xs)\n",
    "beta_0 = (beta[0] - beta[1] * means[1] / std[1]) - (beta[2] * means[2] / std[2])\n",
    "beta_unscaled = [beta_0,\n",
    "                 beta[1] / std[1],\n",
    "                 beta[2] / std[2]]\n",
    "beta_unscaled\n",
    "\n",
    "# not as easy to interpret as liner regression\n",
    "# all else being equal an extra year of experience\n",
    "# adds 1.6 to the input of logistic fn\n",
    "\n",
    "#the impact on the output also depends on the other inputs as well\n",
    "# if dot(beta, x_i) is already large/ small increasing bi a lot or little will\n",
    "# not affectc the outcome of the probability\n",
    "\n",
    "# all else being equal - people with more experience\n",
    "# are more likly to pay for accounts\n",
    "# and people of larger salary less likely \n",
    "# to pay for accounts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "e9908b46-bd1a-4094-be3f-50db97fba5bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.75, 0.8)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Goodness of Fit\n",
    "# ie how good is this model\n",
    "\n",
    "tp = fp = tn = fn = 0\n",
    "\n",
    "# nice implicit control flow\n",
    "for xi, yi in zip(x_test, y_test):\n",
    "    prediction = logistic(dot(beta, xi))\n",
    "    if yi == 1 and prediction >= .5:\n",
    "        tp += 1\n",
    "    elif yi == 1:\n",
    "        fn += 1\n",
    "    elif prediction >= .5:\n",
    "        fp += 1\n",
    "    else:\n",
    "        tn += 1\n",
    "        \n",
    "precision = tp / (tp + fp)\n",
    "recall = tp / (tp + fn)\n",
    "precision, recall"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "b2552bcf-2edd-4731-8a10-af4833046bf0",
   "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": [
    "predictions = [logistic(dot(beta, xi)) \n",
    "                        for xi in x_test]\n",
    "plt.scatter(predictions, y_test, marker='+')\n",
    "plt.title('Logistic Regression Predicted vs. Actual')\n",
    "plt.xlabel('predicted probability')\n",
    "plt.ylabel('actual outcome');"
   ]
  }
 ],
 "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": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}