The Pairwise-Markov Bernoulli Filter

Pairwise Markov Chains

We propose a new model called a Pairwise Markov Chain (PMC), which generalizes the classical Hidden Markov Chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like Maximum A Posteriori (MAP), or ...

Pairwise Choice Markov Chains

As datasets capturing human choices grow in richness and scale—particularly in online domains—there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce’s choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not ...

Pairwise Markov Logic

For many tasks in fields like computer vision, computational biology and information extraction, popular probabilistic inference methods have been devised mainly for propositional models that contain only unary and pairwise clique potentials. In contrast, statistical relational approaches typically do not restrict a model’s representational power and use high-order potentials to capture the ric...

Resolving Markov chains onto Bernoulli

Multi-Bernoulli filter and hybrid multi-Bernoulli CPHD filter for superpositional sensors

Superpositional sensor model can characterize the observations in many different applications such as radio frequency tomography, acoustic sensor network based tracking and wireless communications. In this paper we present two filters based on the random finite set (RFS) theory the multi-Bernoulli filter and its variant the hybrid multi-Bernoulli CPHD filter for superpositional sensors. We prov...