Bayesian Multi-Object Filtering for Pairwise Markov Chains

Pairwise Markov Chains and Bayesian Unsupervised Fusion

Particle Filtering in Pairwise and Triplet Markov Chains

The estimation of an unobservable process x from an observed process y is often performed in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is given by the Kalman filter. On the other hand, particle filters provide approximate solutions in more complex situations. In this paper, we propose two successive generalizations of the classica...

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 ...

Visual place recognition using Bayesian filtering with Markov chains

We present a novel idea to use Bayesian filtering in the case of place recognition. More precisely, our system combines global image characterization, Learned Vector Quantization, Markov chains and Bayesian filtering. The goal is to integrate several images seen by a robot during exploration of the environment and the dependency between them. We present our system and the new Bayesian filtering...