Reviews: Robust Conditional Probabilities

This paper studies the problem of computing probability bounds, more specifically bounds over probability of atoms of the joint space and conditional probabilities of the class, under the assumption that only some pairwise marginal as well as some univariate marginal values are known. The idea is that such marginals may be easier to obtain than fully specified probabilities, and that cautious inferences can then be used to produce predictions. It is shown that when the marginals follow a tree structure (results are extended to a few other structures), then the problem can actually be solved in closed, analytical form, relating it to cover set and maximum flow problems. Some experiments performed on neural networks show that this simple method is actually competitive with other more complex approaches (Ladder, VAE), while outperforming methods of comparable complexity. The paper is elegantly written, with quite understandable and significant results.