probabilistic-javascript

Javascript functions to fit and to simulate probabilistic models

Gaussian Vectors

var means = [0.5, 0.5, 0.5];
var covariance = [[1, 0.1, 0.1], [0.1, 1, 0.1], [0.1, 0.1, 1]];
var glaw = new GaussianLaw(means, covariances);
console.log(glaw.simulate());
console.log(glaw.simulate());

Winner-Take-All Clustering (multi-dimensional)

var observations = (some list of vectors)
var nbclasses = 2;
var lambda = 0.01; // learning rate
var nbepochs = 1000;
var centers = WinnerTakeAll(observations, nbclasses, lambda, nbepochs);
console.log(centers[0]);
console.log(centers[1]);

Gaussian Mixture Model (multi-dimensional)

• Model estimation using EM (expectation-maximization) algorithm

  var nbstates = 2;
  var obsdim = 3;
  var gmm1 = new GaussianMixtureModel(nbstates, obsdim);
  // simulation
  var pathLength = 200;
  var points = gmm1.simulateStates(pathLength, true).observations;
  // estimation with EM algorithm
  var gmm2 = new GaussianMixtureModel(nbstates, obsdim);
  var maxIters = 50;
  gmm2.fitObservations(points, maxIters, false);

• Bayesian sampling of parameters using Gibbs Markov Chain Monte Carlo (MCMC)

  // bayesian estimation with Gibbs sampling
  var observations = (some list of vectors)
  var uncertainty = 1; // variance of bayesian prior of mean
  var maxIters = 50;
  GibbsGMM(nbstates, maxIters, uncertainty, observations);

Hidden Markov Model (multi-dimensional)

Model estimation using Baum-Welch (EM with forward-backward steps) algorithm

var nbstates = 2;
var obsdim = 3;
var hmm1 = new HiddenMarkovModel(nbstates, obsdim);
// simulation
var pathLength = 200;
var points = hmm1.simulateStates(pathLength, true).observations;
// estimation
var hmm2 = new HiddenMarkovModel(nbstates, obsdim);
var maxIters = 50;
hmm2.fitObservations(points, maxIters, false);
//
console.log(hmm2.stateTransitionMatrix);
console.log(hmm2.observationProbabilityCPDs[0].means);
console.log(hmm2.observationProbabilityCPDs[1].means);
console.log(hmm2.observationProbabilityCPDs[2].means);

Dependencies

Rely on package numeric.js for matrix algebra

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/numeric/1.2.6/numeric.js"></script>