Supplementary information for: Natural image synthesis for the retina with variational information bottleneck representation

To obtain a bound on the Information Bottleneck Gaussian Process (IB-GP) objective, we use the Markov chain constraint Y X Z and the factorized joint distribution [2]: p(X,Y,Z) = p(Y|X,Z)p(Z|X)p(X) = p(Y|X)p(Z|X)p(X) (1) to expand the mutual information terms in LIB = max I(Z,Y) βI(Z,X) . Henceforth, we use the stochastic encoder pϕ(Z|X)parameterized by ϕas an approximation for p(Z|X). In practice computation of H(Z) might be intractable (even though P(Z)is well defined). Therefore, a variational approximation ρ(Z) is used in place of p(Z) such that KL(p(Z),ρ(Z)) is minimal. In practice computation of p(Y,Z)and p(Y|Z)might be intractable (even though they are well defined).