Markov processes and exponential families

Vector-Space Markov Random Fields via Exponential Families

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet di...

Vector-Space Markov Random Fields via Exponential Families Appendix

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Exponential families

Bisimulation for Markov Decision Processes through Families of Functional Expressions

We transfer a notion of quantitative bisimilarity for labelled Markov processes [1] to Markov decision processes with continuous state spaces. This notion takes the form of a pseudometric on the system states, cast in terms of the equivalence of a family of functional expressions evaluated on those states and interpreted as a real-valued modal logic. Our proof amounts to a slight modification o...

ON THE INFINITE ORDER MARKOV PROCESSES

The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.