{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Piecewise linear kernel density estimation\n", "\n", "We will approximate the density of our distribution by a piecewise linear distribution on the interval $[a,b]$, with node points $z_i, i=0\\ldots N$.\n", "\n", "The height at each node point is given by: \n", "$$h_i=e^{q_i} / M(\\vec{q}), i=1\\ldots N$$\n", "$$h_0=1/M(\\vec{q})$$\n", "\n", "We use this parameterization because scipy's optimization methods work better unconstrained, and any value $\\vec{q} \\in \\mathbb{R}^{N+1}$ is valid.\n", "\n", "$$M(\\vec{q}) = \\int_a^b p(x) dx = \\sum_{i=1}^N \\frac{1}{2} (e^{q_i}+e^{q_{i-1}})(z_i-z_{i-1})$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Holding the node points $z_i$ fixed, let us calculate $\\nabla_q h_i$. This will be necessary to do gradient ascent and find a max likelihood/max aposteriori parametric curve given data.\n", "\n", "Preliminary calculations:\n", "\n", "$$\\frac{\\partial M(\\vec{q})}{\\partial_{q_j}} = e^{q_j}(z_j-z_{j-1}) + e^{q_j}(z_{j+1}-z_j) = e^{q_j} (z_{j+1}-z_{j-1}), j=1\\ldots N-1$$\n", "\n", "$$\\frac{\\partial M(\\vec{q})}{\\partial_{q_N}} = \\frac{1}{2} e^{q_N}(z_N-z_{N-1})$$\n", "\n", "We can then use this to calculate $\\frac{\\partial h_i(\\vec{q})}{\\partial_{q_j}}$.\n", "\n", "$$\\frac{\\partial h_i(\\vec{q})}{\\partial_{q_j}} = \\frac{e^{q_i} \\delta_{ij}}{M(\\vec{q})} - \\frac{e^{q_i} e^{q_j}(z_{j+1}-z_{j-1})}{M(\\vec{q})^2} , j > 1$$\n", "$$= e^{q_i} \\left(\\frac{\\delta_{ij} M(\\vec{q}) - e^{q_j} (z_{j+1}-z_{j-1}) }{M(\\vec{q})^2} \\right)$$\n", "and\n", "$$\\frac{\\partial h_0(\\vec{q})}{\\partial_{q_j}} = \\frac{-1}{2 M(\\vec{q})^2} \\frac{\\partial M(\\vec{q})}{\\partial_{q_j}}$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.10906815 -0.07311056 -0.09868894 -0.17982297 -0.04067764]\n", " [ 0.7683937 -0.12053894 -0.16271055 -0.29647796 -0.13413217]\n", " [-0.12053894 0.55480897 -0.10906815 -0.19873512 -0.08991149]\n", " [-0.16271055 -0.10906815 0.71075533 -0.26826435 -0.12136781]\n", " [-0.29647796 -0.19873512 -0.26826435 1.07453548 -0.22114657]\n", " [-0.26826435 -0.17982297 -0.24273562 -0.44229314 1.21447136]]\n" ] }, { "data": { "image/png": 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\n", 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