webppl/src/dists/kde.js

Probabilistic programming for the web

'use strict';
var ad = require('../ad');
var _ = require('lodash');
var base = require('./base');
var types = require('../types');
var util = require('../util');
var Tensor = require('../tensor');
var stats = require('../math/statistics');
var numeric = require('../math/numeric');
var gaussian = require('./gaussian');
var diagCovGaussian = require('./diagCovGaussian');
var kernels = {
    gaussian: {
        dataType: types.unboundedReal,
        widthType: types.positiveReal,
        sample: gaussian.sample,
        score: gaussian.score,
        defaultWidth: function (data) {
            var sd = stats.sd(data);
            var n = data.length;
            var width = 1.06 * sd * Math.pow(n, -0.2);
            return width;
        }
    },
    mvGaussian: {
        dataType: types.unboundedVector,
        widthType: types.positiveVectorCB,
        sample: diagCovGaussian.sample,
        score: diagCovGaussian.score,
        defaultWidth: function (data) {
            var d = data[0].dims[0];
            var n = data.length;
            var mean = data.reduce(function (acc, x) {
                return acc.add(x);
            }).div(n);
            var sd = data.reduce(function (acc, x) {
                return acc.add(x.sub(mean).pow(2));
            }, new Tensor(data[0].dims)).div(n).sqrt();
            return sd.mul(Math.pow(4 / (d + 2), 1 / (d + 4)) * Math.pow(n, -1 / (d + 4)));
        }
    }
};
var KDE = base.makeDistributionType({
    name: 'KDE',
    desc: 'A distribution based on a kernel density estimate of ``data``. ' + 'A Gaussian kernel is used, and both real and vector valued data are supported. ' + 'When the data are vector valued, ``width`` should be a vector specifying the kernel ' + 'width for each dimension of the data. ' + 'When ``width`` is omitted, Silverman\'s rule of thumb ' + 'is used to select a kernel width. This rule assumes the data are ' + 'approximately Gaussian distributed. When this assumption does not hold, a ``width`` ' + 'should be specified in order to obtain sensible results.',
    params: [
        {
            name: 'data',
            desc: 'data array'
        },
        {
            name: 'width',
            desc: 'kernel width',
            optional: true
        }
    ],
    wikipedia: 'Kernel_density_estimation',
    nohelper: true,
    mixins: [base.continuousSupport],
    constructor: function () {
        if (!_.isArray(this.params.data) || _.isEmpty(this.params.data)) {
            throw new Error('Parameter "data" should be a non-empty array.');
        }
        var data = this.params.data;
        this.kernel = _.find(kernels, function (kernel) {
            return kernel.dataType.check(data[0]);
        });
        if (!this.kernel) {
            throw new Error('Parameter "data" should be an array of reals or vectors.');
        }
        if (this.params.width === undefined) {
            this.params.width = this.kernel.defaultWidth(this.params.data);
        }
        if (!this.kernel.widthType.check(this.params.width)) {
            throw new Error('Parameter "width" should be of type ' + this.kernel.widthType.desc);
        }
    },
    sample: function () {
        var data = this.params.data;
        var width = this.params.width;
        var x = data[Math.floor(util.random() * data.length)];
        return this.kernel.sample(x, width);
    },
    score: function (val) {
        var data = this.params.data;
        var width = this.params.width;
        var n = data.length;
        var kernel = this.kernel;
        return data.reduce(function (acc, x) {
            return numeric.logaddexp(acc, kernel.score(x, width, val));
        }, -Infinity) - Math.log(n);
    }
});
module.exports = { KDE: KDE };