Understanding the Infer operator

[Isaac Davis]

Hi folks. 

I appreciate all the help I've received, and am very thankful to those who have offered advice. I am a PhD student doing my dissertation on Social Cognition/Theory of Mind, and I am currently working on coding up a panel of simulations in WebPPL. I'm somewhat new to the language and I'm still a little uncertain about the Infer operator and how it works.

Below, I've posted two very simple example programs that (as far as I can tell) should perform the same computations in the same order, but only one of them works. I think the issue has something to do with how Infer is implemented, but I'm not certain.

//------------------------------------------

//simple agent model (version 0): 

//------------------------------------------

//This is an extremely simple model of a rational agent, with preferences [p1, p2, p3] over three "goal" objects [0, 1, 2]. The program "goal_sampler(prefs)" returns a sample from a categorical //distribution over [0,1,2] with weights given by prefs. 

var goal_sampler=function(prefs){

  return categorical({ps: prefs, vs: [0,1,2]})

}

//The program "action_sampler(goal, err)" outputs either a) the correct action for obtaining "goal" with probability 1-err, or a randomly chosen incorrect action with probability err

var action_sampler=function(goal, err){

  var moves=['L', 'M', 'R'];

  if(flip(1-err)){

    return moves[goal]

  }

  else{

    return uniformDraw(remove(moves[goal], moves))

  }

}

//The program "agent_distribution_v0" creates a distribution object over actions for an agent with preferences "prefs" and error rate "err"

var agent_distribution_v0=function(prefs,err){return

Infer(function(){

  var goal=goal_sampler(prefs);

  return action_sampler(goal,err)

})}

goal_sample(prefs) and action_sampler(goal, err) both work correctly, but when I call "sample(agent_distribution_v0)", I get the error message sample() expected a distribution but received "undefined".

Now here is v1:

//------------------------------------------

//simple agent model (version 1): 

//------------------------------------------

//The only difference between v0 and v1 is that the component functions for goals returns a distribution object, rather than a sample from that distribution (and similarly for actions)

var goal_prior=function(prefs){

  return Categorical({ps: prefs, vs: [0,1,2]})

}

var action_distribution=function(goal, err){

  return Infer(function(){

    var moves=['L', 'M', 'R'];

    if(flip(1-err)){

      return moves[goal]

    }

    else{

      return uniformDraw(remove(moves[goal], moves))

    }

  })}

//The "agent_distribution_v1" function then draws a sample from the distribution object returned by goal_prior(prefs), and similarly for action_distribution. Whereas v0 just calls //goal_sampler(prefs), which returns a sampled value

var agent_distribution_v1=function(prefs,err){

  return Infer(function(){

    var goal=sample(goal_prior(prefs));

    return sample(action_distribution(goal, err))

  })

}

When I try "agent_distribution_v1(prefs, err)", I now get an appropriate histogram (or an appropriate sample from sample(agent_distribution_v1(prefs, err))". So this version seems to work. But as far as I can tell, both versions seem to execute the same computations in the same order. e.g. I would assume that "categorical(params)" is the same as "sample(Categorical(params))", so I'm wondering if the discrepancy is due to some property of the Infer operator that I don't understand. 

If anyone could shed some light on this, it would be much appreciated.

Cheers

-Isaac

[null-a]

As written, it looks like you're passing a function rather than a distribution to `sample` in your version zero. i.e. `sample(agent_distribution_v0)`, rather than something like `sample(agent_distribution_v0(prefs, err))`.

[Isaac Davis]

Good catch, thanks for pointing that out. However, I think that was just an error in how I transcribed the code. When I replace "sample(agent_distribution_v0)" with "sample(agent_distribution_v0(prefs, err))", I get the same error message telling me that "Sample expected a distribution but received undefined"

[null-a]

This is an odd one. It looks like you can fix your version zero by removing the newline between `return` and `Infer`. That is, replace:

var agent_distribution_v0=function(prefs,err){return
Infer(function(){

... with say:

var agent_distribution_v0=function(prefs,err){
return Infer(function(){

This is surprising to me, I guess it's a bug.

Cheers,

Paul

[Isaac Davis]

That is very odd, but it does seem to be working. Thanks again!

-Isaac

[null-a]

> it does seem to be working

Great.

> I guess it's a bug.

I take that back. Javascript behaves the same way, the `return` on a line by itself is an early return from the function, with a return value of `undefined` . For example, the following returns `undefined` under Node.js:

var f = function() {
  return
  42;
};

WebPPL aims to follow JS, so I don't think this is a bug.

Cheers,

Paul.

[Isaac Davis]

That is good to know, and may explain some other weird results I'd been getting.

Thanks again!

-Isaac