A central task of Bayesian machine learning is to infer the posterior distribution of hidden
random variables given observations and calculate expectations with respect to this …

Learned neural solvers have successfully been used to solve combinatorial optimization
and decision problems. More general counting variants of these problems, however, are still …

Many lifeline infrastructure systems consist of thousands of components configured in a
complex directed network. Disruption of the infrastructure constitutes a recurrent failure …

It has recently been observed that the permanent of a nonnegative square matrix, ie, of a
square matrix containing only nonnegative real entries, can very well be approximated by …

We prove tight upper bounds on the logarithmic derivative of the independence and
matching polynomials of d‐regular graphs. For independent sets, this theorem is a …

We present a combinatorial characterization of the Bethe entropy function of a factor graph,
such a characterization being in contrast to the original, analytical, definition of this function …

We study the performance of Markov chains for the q-state ferromagnetic Potts model on
random regular graphs. While the cases of the grid and the complete graph are by now well …

In this paper we describe how MAP inference can be used to sample efficiently from Gibbs
distributions. Specifically, we provide means for drawing either approximate or unbiased …

We prove an asymptotically tight lower bound on the average size of independent sets in a
triangle-free graph on $ n $ vertices with maximum degree $ d $, showing that an …

Belief propagation is a remarkably effective tool for inference, even when applied to
networks with cycles. It may be viewed as a way to seek the minimum of the Bethe free …