Introduction

WebPPL is a probabilistic programming language based on Javascript. WebPPL can be used most easily through webppl.org. It can also be installed locally and run from the command line.

The deterministic part of WebPPL is a subset of Javascript. Assignment is generally not allowed (except by using the globalstore). This also means looping constructs (such as for) are not available; we use functional programming instead to operate on arrays. (Note that tensors are not arrays.)

The probabilistic aspects of WebPPL come from: distributions and sampling, marginal inference, and factors.

Resources
- Language intro from DIPPL.
- Language intro from AgentModels.
- Generative and cognitive modeling ideas (with Church).
- WebPPL packages (e.g. csv, json, fs).
- If you would rather use WebPPL from R: RWebPPL.

Two simple models

Here is an example using distributions and sample.

// We build a function that returns 'H' and 'T' with equal probability:

var coin = function(){
  var aDist = Bernoulli({p: .5});
  return sample(aDist) ? 'H' : 'T';
};

var flips = [coin(), coin(), coin()];
print("Some coin flips: " + flips);

Here is an example using factor and Infer, and illustrating stochastic recursion.

// Defining the geometric distribution as a stochastic recursion:

var geometric = function(p) {
  return bernoulli(p) ? 1 + geometric(p) : 1
};

// Favoring values around 10 via factor:
var skewedGeometric = function(){
  var g = geometric(0.5);
  factor(-Math.pow(10-g,2))
  return g
}

// Finding the marginal distribution via Infer:
var m = Infer({method: 'enumerate', maxExecutions: 100},
              skewedGeometric)

print('Histogram of skewed Geometric distribution');
viz.auto(m);

Some things to note:

The short form bernoulli(p) which is the same as sample(Bernoulli({p: p})).
We can access deterministic functions from Math (and other js standard libraries) transparently. From the command line additional libraries can be required as packages.
The viz package provides easy visualization methods. (It is pre-loaded in the browser version.)

Regression

Here is a simple logistic regression model.

//some data:
var data = [{feature: -10, label: false},
            {feature: -5, label: false},
            {feature: 2, label: true},
            {feature: 6, label: true},
            {feature: 10, label: true}]

//a helper fn:
var sigmoid = function(x) {
  return 1 / (1 + Math.exp(-x))
}

var model = function() {
  //slope, intercept, and noise for the regression:
  var m = gaussian(0, 1)
  var b = gaussian(0, 1)
  var sigmaSquared = gamma(1, 1)

  //the regression model itself
  var labelDist = function(x) {
    var y = gaussian(m * x + b, sigmaSquared);
    return Bernoulli({p: sigmoid(y)});
  }

  //include observed data
  map(function(d){factor(labelDist(d.feature).score(d.label))},
      data)

  return sample(labelDist(0))
//   return labelDist(0).score(true) //alternate return to explore confidence
}

viz.auto(Infer({method: 'MCMC',
                samples: 10000,
                callbacks: [editor.MCMCProgress()]},
               model))

HMM

var transition = function(s) {
  return s ? flip(0.7) : flip(0.3)
}

var observe = function(s) {
  return s ? flip(0.9) : flip(0.1)
}

var hmm = function(n) {
  var prev = (n == 1) ? {states: [true], observations: []} : hmm(n - 1);
  var newState = transition(prev.states[prev.states.length - 1]);
  var newObs = observe(newState);
  return {
    states: prev.states.concat([newState]),
    observations: prev.observations.concat([newObs])
  };
}

var trueObservations = [false, false, false];

var stateDist = Infer({method: 'enumerate'},
  function() {
    var r = hmm(3);
    map2(function(o,d){condition(o===d)}, r.observations, trueObservations)
    return r.states;
  }
)

viz.hist(stateDist)

LDA

var nTopics = 2;
var vocabulary = ['zebra', 'wolf', 'html', 'css'];
var docs = {
  'doc1': 'zebra wolf zebra wolf zebra wolf html wolf zebra wolf'.split(' '),
  'doc2': 'html css html css html css html css html css'.split(' '),
  'doc3': 'zebra wolf zebra wolf zebra wolf zebra wolf zebra wolf'.split(' '),
  'doc4': 'html css html css html css html css html css'.split(' '),
  'doc5': 'zebra wolf zebra html zebra wolf zebra wolf zebra wolf'.split(' ')
};

var makeWordDist = function() { dirichlet(ones([vocabulary.length,1])) };
var makeTopicDist = function() { dirichlet(ones([nTopics,1])) };

var model = function() {
  var wordDistForTopic = repeat(nTopics, makeWordDist);

  mapObject(function(docname, words) {
    var topicDist = makeTopicDist();
    map(function(word) {
      var topic = discrete(topicDist);
      var wordDist = wordDistForTopic[topic];
      var wordID = vocabulary.indexOf(word);
      factor(Discrete({ps: wordDist}).score(wordID));
    }, words);
  }, docs);

  return map(function(v) { return _.toArray(v.data); }, wordDistForTopic);
};

var post = Infer({
  method: 'MCMC',
  burn: 10000,
  samples: 1,
  callbacks: [editor.MCMCProgress()]
}, model);

var samp = sample(post);

print("Topic 1:"); viz.bar(vocabulary, samp[0]);
print("Topic 2:"); viz.bar(vocabulary, samp[1]);