For feasibility classification using a GP, exact inference is intractable. Thus, Atlas approximates the classification posterior using variational inference. Assume a dataset of n binary constraint function c(x) measurements, D c = {(x i , ỹi )} n i=1 , where ỹ ∈ {0, 1} (0 for feasible measurements and 1 for infeasible measurements). For brevity, we denote the n feasibility measurements as ỹ = {ỹ i } n i=1 and the design matrix as X = {x i } n i=1 . GP classification squashes the latent GP output f through a sigmoidal inverse-link function, ϕ(x) = x -∞ N (a|0, 1)da and a Bernoulli likelihood function conditions the function values. The joint distribution of the feasibility measurements and the latent values is