Implement EnIF

[Blunde1]

Basic implementation (no streaming) for medium sized problems.

Given

• $G_u$ or $\Lambda_u$
• $\Lambda_\epsilon$
• H optionally

One runs

• fit(U_prior_sample, Y=None) : Fit precision of X and (sparse) mapping H:x->y if needed (Y required then).
• transport(U_prior_sample) -> U_posterior_sample : Transport X from a sample from the prior to the posterior

fit() consists of

self.fit_precision(U) # fit precision of u to data w.r.t. G_u
if self.H is None: # if H is not provided
    self.H = self.fit_H(X, Y) # learn (sparse) H

transport() consists of

canonical = self.pushforward_to_canonical(prior) # nu = Prec_u_prior u
updated = self.update_canonical(canonical, d) # nu = nu + H.T Prec_epsilon y
return self.pullback_from_canonical(updated) # u = Prec_u_posterior^{-1} nu

Note that

• $H$ is either entirely learned or entirely passed
• No streaming
• No implementation on base classes with KR-triangular map datastructures