Bayesian model evidence gives a clear criteria for such model selection. However, computing model evidence requires integration over the likelihood, which is challenging, particularly when the likelihood is non-closed-form and/or expensive.

Let defined denote conditional (x)= P(y =1|x).

Wethenseparate theoptimization process into two steps, corresponding to weight update and structure parameter update. For the former step, we use the conventional chain rule, which can be sparse via exploiting the sparse structure.

Apart from linguistic transformations, synthesizing among statements usually requires specific synthesis rulesofstatements.

However, statements different from the original statement could also be logically consistent with respecttoagivencontext.