ADEV.jl

Experimental port of the ADEV library to Julia. Not yet documented or stable, and currently has low coverage of Julia language features.

Usage

Defining probabilistic compuations

ADEV exposes primitives, like normal_reparam and flip_mvd, which are functions returning "probabilistic computations." Bigger probabilistic computations can be composed using the syntax @adev begin ... end:

function my_program(theta)
    @adev begin
        let x = @sample(normal_reparam(theta, 1)),
            b = @sample(flip_mvd(sigmoid(theta)))

            if b
                @sample(normal_reparam(x, 1))
            else
                # Recurse
                theta * @sample(my_program(theta - 1))
            end
        end
    end
end

Within an @adev begin ... end block, the following constructs are currently supported:

• @sample(e), where e is a supported expression evaluating to a probabilistic computation;
• let x1 = e1, ..., xn = en; e; end, where e, e1, ..., en are supported expressions;
• if e_cond1; e1; elseif e_cond2; e2; ...; else; en; end, where e_cond1, e1, ..., en are supported expressions;
• e(e1, ..., en), where e, e1, ..., en are supported expressions.
• other Julia expressions (e.g. arr[idx]), so long as they are pure (no mutation, no randomness).

The main limitations, then, are:

• No mutation (e.g. x += 4) or simple imperative assignment (e.g. x = 4). Use let instead.
• No loops (e.g. while or for). Use recursion instead.
• No compound expressions that are not function calls, but not pure (e.g. my_array[@sample(uniform(1:10))]). Use let idx = @sample(uniform(1:10)); my_array[idx]; end instead.
• No function calls with keyword arguments, or splatted arguments.

Estimating derivatives

ADEV currently works with functions of type Real -> ProbabilisticComputation{Real}. For such a function, simulate(f, x) will simulate a value of f(x), and differentiate(f, x) will estimate the derivative of $\mathbb{E}_{v \sim f(x)}[v]$ with respect to $x$. To average more than one sample (e.g. 100), use estimate_derivative(f, x; N=100). A simple version of stochastic gradient descent is implemented by sgd(f; theta=0, step_size=0.01, n_iters=1000, N=100), where N is the number of samples to use for estimating the derivative at each iteration.