kernel_density_estimator.js

/**
 * Kernel density estimator
 */
export default class KernelDensityEstimator {
	// https://ja.wikipedia.org/wiki/%E3%82%AB%E3%83%BC%E3%83%8D%E3%83%AB%E5%AF%86%E5%BA%A6%E6%8E%A8%E5%AE%9A
	// http://ibis.t.u-tokyo.ac.jp/suzuki/lecture/2015/dataanalysis/L9.pdf
	/**
	 * @param {number} [h] Smoothing parameter for the kernel
	 * @param {'gaussian' | 'rectangular' | 'triangular' | 'epanechnikov' | 'biweight' | 'triweight' | { name: 'gaussian' } | { name: 'rectangular' } | { name: 'triangular' } | { name: 'epanechnikov' } | { name: 'biweight' } | { name: 'triweight' } | function (number): number} [kernel] Kernel name
	 */
	constructor(h = 0, kernel = 'gaussian') {
		this._h = h
		if (typeof kernel === 'function') {
			this._kernel = kernel
		} else {
			if (typeof kernel === 'string') {
				kernel = { name: kernel }
			}
			switch (kernel.name) {
				case 'gaussian':
					this._kernel = x => Math.exp((-x * x) / 2) / Math.sqrt(2 * Math.PI)
					break
				case 'rectangular':
					this._kernel = x => (Math.abs(x) <= 1 ? 0.5 : 0)
					break
				case 'triangular':
					this._kernel = x => (Math.abs(x) <= 1 ? 1 - Math.abs(x) : 0)
					break
				case 'epanechnikov':
					this._kernel = x => (Math.abs(x) <= 1 ? (3 * (1 - x ** 2)) / 4 : 0)
					break
				case 'biweight':
					this._kernel = x => (Math.abs(x) <= 1 ? (15 / 16) * (1 - x ** 2) ** 2 : 0)
					break
				case 'triweight':
					this._kernel = x => (Math.abs(x) <= 1 ? (35 / 32) * (1 - x ** 2) ** 3 : 0)
					break
			}
		}
	}

	/**
	 * Fit model.
	 *
	 * @param {Array<Array<number>>} x Training data
	 */
	fit(x) {
		this._x = x

		if (this._h > 0) {
			return
		}

		// Silverman's method
		const n = x.length
		const k = x.map(d => Math.sqrt(d.reduce((s, v) => s + v ** 2, 0)))
		const mean = k.reduce((s, v) => s + v, 0) / n
		const std = Math.sqrt(k.reduce((s, v) => s + (v - mean) ** 2, 0) / n)
		k.sort((a, b) => a - b)
		const q = p => {
			const np = (n - 1) * p
			const np_l = Math.floor(np)
			const np_h = Math.ceil(np)
			return k[np_l] + (np - np_l) * (k[np_h] - k[np_l])
		}
		const sgm = Math.min(std, (q(0.75) - q(0.25)) / 1.34)

		this._h = (1.06 * sgm) / Math.pow(n, 0.2)
	}

	/**
	 * Returns probabilities of the datas.
	 *
	 * @param {Array<Array<number>>} x Sample data
	 * @returns {number[]} Predicted values
	 */
	probability(x) {
		const n = this._x.length
		return x.map(d => {
			let s = 0
			for (let i = 0; i < n; i++) {
				s += this._kernel(Math.sqrt(d.reduce((a, v, j) => a + (v - this._x[i][j]) ** 2, 0)) / this._h)
			}
			return s / (n * this._h)
		})
	}

	/**
	 * Returns probabilities of the datas.
	 *
	 * @param {Array<Array<number>>} x Sample data
	 * @returns {number[]} Predicted values
	 */
	predict(x) {
		return this.probability(x)
	}
}