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 …

Belief propagation is a well-studied message-passing algorithm that runs over graphical
models and can be used for approximate inference and approximation of local marginals …

One of the most common types of functions in mathematics, physics, and engineering is a
sum of products, sometimes called a partition function. After “normalization,” a sum of …

A factor-graph representation of quantum-mechanical probabilities (involving any number of
measurements) is proposed. Unlike standard statistical models, the proposed representation …

This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its
applications to Ising-type models of statistical physics, using graphical models of linear and …

A conceptual framework involving partition functions of normal factor graphs is introduced,
paralleling a similar recent development by Al-Bashabsheh and Mao. The partition functions …

This thesis is about several extensions of a general framework and about the application of
these extensions to various problems arising in signal processing. The general framework is …

For more than a decade, the model-based approach to signal processing based on state
space models (SSMs) and factor graphs is being pursued at the Signal and Information …

Holant problems are a general framework to study the algorithmic complexity of counting
problems. Both counting constraint satisfaction problems and graph homomorphisms are …

The partition function of a factor graph and the partition function of the dual factor graph are
related to each other by the normal factor graph duality theorem. We apply this result to the …