KDE_1D.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "18ac6ecf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.integrate import quad\n",
    "from scipy.optimize import minimize, Bounds\n",
    "from scipy.stats import describe, iqr, norm\n",
    "from sklearn.model_selection import LeaveOneOut\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b00c1872",
   "metadata": {},
   "source": [
    "# Gaussian Kernel Density Estimation\n",
    "\n",
    "Kernel density estimator (KDE) function:\n",
    "\n",
    "$$\n",
    "\\hat{f}(x \\, | \\, h) = \\frac{1}{nh} \\sum^{n}_{i=1} K \\left( \\frac{x - x_i}{h} \\right)\n",
    "$$\n",
    "\n",
    "Gaussian kernel:\n",
    "\n",
    "$$\n",
    "K(u) = \\frac{1}{\\sqrt{2\\pi}} \\exp \\left(-\\frac{1}{2} u^2 \\right)\n",
    "$$\n",
    "\n",
    "KDE function now becomes:\n",
    "\n",
    "$$\n",
    "\\hat{f}(x \\, | \\, h) = \\frac{1}{n} \\sum^{n}_{i=1} \\frac{1}{h \\sqrt{2\\pi}} \\exp \\left(-\\frac{1}{2} \\left(\\frac{x - x_i}{h} \\right)^2 \\right)\n",
    "$$\n",
    "\n",
    "where the inside of the sum is identical to $\\mathcal{N}(\\mu = x_i, \\, \\sigma = h)$.\n",
    "\n",
    "Bandwidth $h$ is computed using leave-one-out cross validation:\n",
    "\n",
    "$$\n",
    "\\min_{\\hat{h}} \\left[ \\int{{\\hat{f}(x \\, | \\, h)}^2 \\, dx} - \\frac{2}{n} \\sum^{n}_{i=1} \\hat{f}_{-i} (x_i \\, | \\, h) \\right]\n",
    "$$\n",
    "\n",
    "References: \n",
    "\n",
    "David W. Scott, Stephan R. Sain,\n",
    "9 - Multidimensional Density Estimation,\n",
    "Editor(s): C.R. Rao, E.J. Wegman, J.L. Solka,\n",
    "Handbook of Statistics,\n",
    "Elsevier,\n",
    "Volume 24,\n",
    "2005,\n",
    "Pages 229-261,\n",
    "ISSN 0169-7161,\n",
    "ISBN 9780444511416,\n",
    "https://doi.org/10.1016/S0169-7161(04)24009-3.\n",
    "(https://www.sciencedirect.com/science/article/pii/S0169716104240093)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f4f8541",
   "metadata": {},
   "source": [
    "## Derivation of the CDF\n",
    "\n",
    "Let $\\phi_{i}(x | h) = \\phi(x | \\mu = x_{i}, \\sigma = h) $ be the PDF of the normal distribution, and let $\\Phi_{i}(x | h) = \\Phi(x | \\mu = x_{i}, \\sigma = h) = \\int_{-\\infty}^{x} \\phi_{i}(u | h) du$ be the CDF of the normal distribution.\n",
    "\n",
    "The CDF $\\hat{F}(x | h)$ of the kernel density estimate is derived as follows:\n",
    "\n",
    "$$ \\hat{F}(x | h) = \\int_{-\\infty}^{x} \\hat{f}(u | h) \\,du $$\n",
    "\n",
    "$$ \\hat{F}(x | h) = \\int_{-\\infty}^{x} \\left[ \\frac{1}{n} \\sum_{i=1}^{n} \\phi_{i}(u | h) \\right] \\,du $$\n",
    "\n",
    "$$ \\hat{F}(x | h) = \\frac{1}{n} \\sum_{i=1}^{n} \\int_{-\\infty}^{x} \\phi_{i}(u | h) \\,du $$\n",
    "\n",
    "$$ \\hat{F}(x | h) = \\frac{1}{n} \\sum_{i=1}^{n} \\Phi_{i}(x | h) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "914cdc14",
   "metadata": {},
   "outputs": [],
   "source": [
    "class KDE_1D:\n",
    "    def __init__(self, data):\n",
    "        self.data = data\n",
    "    \n",
    "    def pdf(self, x, h):\n",
    "        # probability density function of kernel density estimate\n",
    "        return np.sum([norm.pdf(x, loc=x_i, scale=h) for x_i in self.data]) / len(self.data)\n",
    "    \n",
    "    def cdf(self, x, h):\n",
    "        # cumulative distribution function of kernel density estimate\n",
    "        # returns nonexceedance probability P(X <= x)\n",
    "        return np.sum([norm.cdf(x, loc=x_i, scale=h) for x_i in self.data]) / len(self.data)\n",
    "    \n",
    "    def ucv(self, h):\n",
    "        # unbiased cross-validation, see Scott & Sain, 2005 (pg. 236)\n",
    "        loo = LeaveOneOut()\n",
    "        er_sq = quad(lambda x: self.pdf(x, h) ** 2, -np.inf, np.inf)[0]\n",
    "        er_lo = (2 / len(self.data)) * np.sum([\n",
    "            np.sum([norm.pdf(self.data[test], loc=x_i, scale=h) for x_i in self.data[train]]) / len(train)\n",
    "            for train, test in tqdm(\n",
    "                loo.split(self.data),\n",
    "                desc='Computing LOO component',\n",
    "                total=len(self.data)\n",
    "            )\n",
    "        ])\n",
    "        return er_sq - er_lo\n",
    "    \n",
    "    def find_bandwidth(self):\n",
    "        # find optimal bandwidth by minimizing error\n",
    "        # start with suboptimal bandwidth\n",
    "        h0 = [0.9 * np.minimum(np.sqrt(describe(self.data).variance), iqr(self.data) / 1.34) * np.power(len(self.data), -1 / 5)]\n",
    "        # bandwidth constrained to be positive\n",
    "        bounds = Bounds([1e-8], [np.inf])\n",
    "        return minimize(self.ucv, h0, method='trust-constr', bounds=bounds).x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "86a6f4d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 157.40it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 162.85it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 169.76it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 146.85it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 118.42it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 134.16it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 137.69it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 161.63it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 146.17it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 157.66it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 141.25it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 155.90it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 159.02it/s]\n",
      "Computing LOO component: 100%|██████████| 100/100 [00:00<00:00, 151.24it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8353284227588791"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.random.normal(5, 1.5, 100)\n",
    "k = KDE_1D(data)\n",
    "h_best = k.find_bandwidth()\n",
    "h_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a36318e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 10, 200)\n",
    "y = [k.pdf(xn, h_best) for xn in x]\n",
    "y0 = norm.pdf(x, loc=5, scale=1.5)\n",
    "plt.hist(data, density=True)\n",
    "plt.plot(x, y, c='black', label='KDE')\n",
    "plt.plot(x, y0, 'r--', label='Actual')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b4e4b57f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}