ANN: Probabilistic programming in OCaml

[oleg@okmij.org]

Chung-chieh Shan and I would like to announce the OCaml library
HANSEI, to express probabilistic models and perform probabilistic
inference. OCaml thus becomes a probabilistic programming
language.

The canonical example of Bayesian net, the grass model, looks as
follows

open ProbM;;
let grass_model () =   (* unit -> bool *)
  let rain = flip 0.3 and sprinkler = flip 0.5 in
  let grass_is_wet =
       (flip 0.9 && rain) || (flip 0.8 && sprinkler) || flip 0.1 in
  if not grass_is_wet then fail (); 
  rain;;

The model first defines the prior distributions of two events: of
raining and of the sprinkler being on. We then specify the Bayesian:
grass may be wet because it rained or because the sprinkler was on, or
-- with the probability 10% -- for some other reason. We also consider
that there is 10% chance rain did not wet the grass. We observe that
the grass is wet. What are the chances it rained? To find out, we
execute 
	exact_reify grass_model;; 
	- : bool pV = [(0.322, V false); (0.2838, V true)]
which after normalization tells the posterior probability of raining,
about 7/15.

The probabilistic model is the regular OCaml function; the independent
random variables rain and sprinkler and the dependent random variable
grass_is_wet are regular OCaml boolean variables. We can pass the
values of these random variables (which are just booleans) to regular
OCaml functions such as 'not' and use the result in the regular if
statement.

HANSEI can handle models that are far more complex than the grass
model, supporting variable (or bucket) elimination, on-demand
evaluation of probabilistic expressions, memoization of stochastic
functions, and importance sampling.

Here is an example of on-demand evaluation:
      let lazy_pair () =
	let x = letlazy (fun () -> flip 0.5) in 
	(x (), x ());;
      exact_reify lazy_pair;;
      - : (bool * bool) pV =
        [(0.5, V (true, true)); (0.5, V (false, false))]

We do not observe the pair (true, false).  Evaluating the expression
x () several times gives the same result -- in the same possible
world. That result may be different in another possible world. For
that reason, we cannot use OCaml's own 'lazy' evaluation: OCaml's lazy
is not thread-safe.

A particular feature of HANSEI is that it permits calls to inference
procedures (e.g., exact_reify) appear in models.  After all, both are
OCaml expressions. Distributions thus can be parameterized over
distributions and inference procedures can reason about their own
accuracy.

	The HANSEI code is available at
	http://okmij.org/ftp/kakuritu/
The web page also presents HANSEI code for sample probabilistic models
and standard benchmarks (HMM, noisy-or, population estimation, belief
networks).

The current documentation includes two complementary papers
	http://okmij.org/ftp/kakuritu/dsl-paper.pdf
to be presented at the IFIP working conference on domain-specific
languages and
	http://okmij.org/ftp/kakuritu/embedpp.pdf
to be presented at `Uncertainty in AI'. The papers are written for
different audiences. The first paper explains the implementation of
probabilistic primitives whereas the second describes 
the applications of the library.