Parameters

[zenna]

In current plan, parameters (or free variables) share much of the structure of random variable.

• They are functions from some space
• There are primitive exogenous parameters from which more complex ones can be constructed
• They can be conditioned

But there are some differences

• There's no sampling from them, as they have no associated probability space
• They can be used for optimization

Interfaces

solve(X; alg = SolverAlg) should try to find a value/model/solution projected to X which satisfies anything its conditioned on.

argmax(X, l; alg = OptimAlg) should produce a value for X that maximises l where both X and l are free-variables

What if l = f(X, Y)? Then we should optimize over both X Y and project to X

If there are condiitons these should be solved too, i.e. constrained optimization

Interaction of Free and Random Vaariables

The kinds of thing we want to do that rely on both interacting are:

• Distributional inference -- construct parametric space of distributions and optimize, e.g. variational inference
• Opposite, dists over parameteized models, or solvers in the loop

Q: Should we allow mixed models? e.g.:

function testvar()
  n = 1 ~ Choice(1:10)
  μ = [(2, i) ~ Normal(0, 1) for i = 1:n]
  s = sum(μ)
end

Q: Different types, Omega and Phi or just Omega?

Q: Should we be able to treat randvars as parameters?

Q: Should we be able to treat params as randvars?