Kalman filtering in pairwise Markov trees

Desbouvries, François; Lecomte, Jean; Pieczynski, Wojciech

doi:10.1016/j.sigpro.2005.07.026

Cited by 8 publications

(2 citation statements)

References 18 publications

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“…This setting arises as a special case of our framework. Extensions of filtering on Triplet Markov Trees and pairwise Markov trees are dealt with in Bardel and Desbouvries (2012) and Desbouvries et al (2006) respectively.…”

Section: Related Workmentioning

confidence: 99%

Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

Meulen¹,

Schauer²

2020

Preprint

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We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models. Observations are represented by leaf vertices. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et. al, 2020) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules.The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems,state space models, branching diffusions and Gamma processes.

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Section: Related Workmentioning

confidence: 99%

Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

Meulen¹,

Schauer²

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…are obtained through the Kalman-like recursions given by Algorithm 1, that we will refer to as the PMM-KF in the sequel. Although a demonstration is provided in [19] and [20] for particular pairwise Markov chains and trees, respectively, for the sake of completeness we provide a derivation for the considered general case in Appendix A.…”

Section: Pairwise Markov Model (Pmm)mentioning

confidence: 99%