ADEV.jl

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

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.

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.