webppl
Version:
Probabilistic programming for the web
88 lines • 2.91 kB
JavaScript
;
var ad = require('../ad');
var base = require('./base');
var types = require('../types');
var util = require('../util');
var gaussian = require('./gaussian');
function expGammaSample(shape, scale) {
if (shape < 1) {
var r;
r = expGammaSample(1 + shape, scale) + Math.log(util.random()) / shape;
if (r === -Infinity) {
util.warn('log gamma sample underflow, rounded to nearest representable support value');
return -Number.MAX_VALUE;
}
return r;
}
var x, v, u, log_v;
var d = shape - 1 / 3;
var c = 1 / Math.sqrt(9 * d);
while (true) {
do {
x = gaussian.sample(0, 1);
v = 1 + c * x;
} while (v <= 0);
log_v = 3 * Math.log(v);
v = v * v * v;
u = util.random();
if (u < 1 - 0.331 * x * x * x * x || Math.log(u) < 0.5 * x * x + d * (1 - v + Math.log(v))) {
return Math.log(scale) + Math.log(d) + log_v;
}
}
}
function expGammaScore(shape, scale, val) {
var x = val;
return ad.scalar.sub(ad.scalar.sub(ad.scalar.sub(ad.scalar.mul(ad.scalar.sub(shape, 1), x), ad.scalar.div(ad.scalar.exp(x), scale)), ad.scalar.logGamma(shape)), ad.scalar.mul(shape, ad.scalar.log(scale)));
}
function logBeta(a, b) {
return ad.scalar.sub(ad.scalar.add(ad.scalar.logGamma(a), ad.scalar.logGamma(b)), ad.scalar.logGamma(ad.scalar.add(a, b)));
}
function sample(a, b) {
var log_x = expGammaSample(a, 1);
var log_y = expGammaSample(b, 1);
var v = 1 / (1 + Math.exp(log_y - log_x));
if (v === 0) {
util.warn('beta sample underflow, rounded to nearest representable support value');
v = Number.MIN_VALUE;
} else if (v === 1) {
util.warn('beta sample overflow, rounded to nearest representable support value');
v = 1 - Number.EPSILON / 2;
}
return v;
}
var Beta = base.makeDistributionType({
name: 'Beta',
desc: 'Distribution over ``[0, 1]``',
params: [
{
name: 'a',
desc: 'shape',
type: types.positiveReal
},
{
name: 'b',
desc: 'shape',
type: types.positiveReal
}
],
wikipedia: true,
mixins: [base.continuousSupport],
sample: function () {
return sample(ad.value(this.params.a), ad.value(this.params.b));
},
score: function (x) {
var a = this.params.a;
var b = this.params.b;
return ad.scalar.gt(x, 0) && ad.scalar.lt(x, 1) ? ad.scalar.sub(ad.scalar.add(ad.scalar.mul(ad.scalar.sub(a, 1), ad.scalar.log(x)), ad.scalar.mul(ad.scalar.sub(b, 1), ad.scalar.log(ad.scalar.sub(1, x)))), logBeta(a, b)) : ad.scalar.neg(Infinity);
},
support: function () {
return {
lower: 0,
upper: 1
};
}
});
module.exports = {
Beta: Beta,
sample: sample
};