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Information geometry of Markov Kernels: a survey
Frontiers in Physics, 2023 Information geometry and Markov chains are two powerful tools used in modern fields such as finance, physics, computer science, and epidemiology. In this survey, we explore their intersection, focusing on the theoretical framework.
Geoffrey Wolfer, Shun Watanabe
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Network motif detection using hidden markov models [PDF]
Scientific ReportsGraphical representations model complex networks by encoding entities as vertices and interactions as edges, with recurring subgraphs—or motifs—revealing fundamental organizational principles. We present a novel application of Hidden Markov Models (HMMs)
Costas Bampos, Vasileios Megalooikonomou
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Semipullbacks of labelled Markov processes [PDF]
Logical Methods in Computer Science, 2021 A labelled Markov process (LMP) consists of a measurable space $S$ together with an indexed family of Markov kernels from $S$ to itself. This structure has been used to model probabilistic computations in Computer Science, and one of the main problems in
Jan Pachl, Pedro Sánchez Terraf
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Networks with Complex Weights: Green Function and Power Series
Mathematics, 2022 We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part.
Anna Muranova, Wolfgang Woess
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Non-Stationary Stochastic Global Optimization Algorithms
Algorithms, 2022 Studying the theoretical properties of optimization algorithms such as genetic algorithms and evolutionary strategies allows us to determine when they are suitable for solving a particular type of optimization problem. Such a study consists of three main
Jonatan Gomez, Andres Rivera
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Adversarially Training MCMC with Non-Volume-Preserving Flows
Entropy, 2022 Recently, flow models parameterized by neural networks have been used to design efficient Markov chain Monte Carlo (MCMC) transition kernels. However, inefficient utilization of gradient information of the target distribution or the use of volume ...
Shaofan Liu, Shiliang Sun
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Searching remote homology with spectral clustering with symmetry in neighborhood cluster kernels. [PDF]
PLoS ONE, 2013 Remote homology detection among proteins utilizing only the unlabelled sequences is a central problem in comparative genomics. The existing cluster kernel methods based on neighborhoods and profiles and the Markov clustering algorithms are currently the ...
Ujjwal Maulik, Anasua Sarkar
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Decomposition of Finitely Additive Markov Chains in Discrete Space
Mathematics, 2022 In this study, we consider general Markov chains (MC) defined by a transition probability (kernel) that is finitely additive. These Markov chains were constructed by S. Ramakrishnan within the concepts and symbolism of game theory.
Alexander Zhdanok, Anna Khuruma
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Mathematics, 2023 We consider the computing issues of the steady probabilities for block-structured discrete-time Markov chains that are of upper-Hessenberg or lower-Hessenberg transition kernels with a continuous phase set.
Shuxia Jiang, Nian Liu, Yuanyuan Liu
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Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations
Mathematics, 2020 We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a
Antonio Avilés López +1 more
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