An Elementary Derivation of the Large Deviation Rate Function for Finite State <scp>M</scp>arkov Chains

Vidyasagar, M.

doi:10.1002/asjc.806

Cited by 28 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is called the edge measure pertaining to P. Observe that the map from an irreducible transition matrix P to its edge measure is one-toone (see, e.g., [8]) and that the set of all edge measures Q(X , E) can be expressed as…”

Section: Irreducible Markov Chainsmentioning

confidence: 99%

Information geometry of Markov Kernels: a survey

Wolfer

Watanabe

2023

Front. Phys.

View full text Add to dashboard Cite

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. We attempt to provide a self-contained treatment of the foundations without requiring a solid background in differential geometry. We present the core concepts of information geometry of Markov chains, including information projections and the pivotal information geometric construction of Nagaoka. We then delve into recent advances in the field, such as geometric structures arising from time reversibility, lumpability of Markov chains, or tree models. Finally, we highlight practical applications of this framework, such as parameter estimation, hypothesis testing, large deviation theory, and the maximum entropy principle.

show abstract

Section: Irreducible Markov Chainsmentioning

confidence: 99%

Information geometry of Markov Kernels: a survey

Wolfer

Watanabe

2023

Front. Phys.

View full text Add to dashboard Cite

show abstract

“…Let the set of all possible types of length-L, stationary, third-order Markov sequences be P L . The cardinality of P L is upper-bounded by (L + 1) 4 as shown in [22]. The type class, T L , of a given type, p ∈ P L , is then defined as the set of all length-L sequences whose types are equal to p:…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…We now use some Large Deviations theory to make an argument about the probability of error in the hypothesis test. 1) Large Deviations Principle: Vidyasagar [22] provides an extensive analysis of large deviations theory for Markov processes. Theorems 3 and 4, shown below, utilize this analysis along with [23, Lemma 1], which allows us to make an argument about the probability of error for the subsequent hypothesis test.…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

The Metagenomic Binning Problem: Clustering Markov Sequences

Greenberg

Shomorony

2019

2019 IEEE Information Theory Workshop (ITW)

View full text Add to dashboard Cite

The goal of metagenomics is to study the composition of microbial communities, typically using high-throughput shotgun sequencing. In the metagenomic binning problem, we observe random substrings (called contigs) from a mixture of genomes and want to cluster them according to their genome of origin. Based on the empirical observation that genomes of different bacterial species can be distinguished based on their tetranucleotide frequencies, we model this task as the problem of clustering N sequences generated by M distinct Markov processes, where M N . Utilizing the large-deviation principle for Markov processes, we establish the information-theoretic limit for perfect binning. Specifically, we show that the length of the contigs must scale with the inverse of the Chernoff Information between the two most similar species. Our result also implies that contigs should be binned using the conditional relative entropy as a measure of distance, as opposed to the Euclidean distance often used in practice.

show abstract

“…Finite‐state fading channel (FSFC) models are widely adopted for modeling wireless flat‐fading channels. The Gilbert‐Elliott channel (GEC) model can be considered as the rudiment of FSFC models, where a two‐state (good and bad) Markov network state determines the channel error probability.…”

Section: Introductionmentioning

confidence: 99%

State Feedback Stabilization Over Finite‐State Fading Channels

Xiao¹,

Niu²,

Xie³

2015

Asian Journal of Control

View full text Add to dashboard Cite

This paper studies state feedback stabilization over finite-state fading channels, where the stochastic characteristic of time-varying fading channels is assumed to be driven by a finite-state random process. The finite-state process is used to represent different channel fading amplitudes and/or to model different configurations of the overall physical environment. A series of necessary and sufficient conditions are given for stabilization over finite-state Markov fading channels. In the case of finite-state independent and identially distributed fading channels, explicit network requirements for stabilization are presented for both single-input case and multi-input case. It is shown that our results cover some existing results as special cases. Finally, the results are applied to stabilization of a single-input plant over a Gilbert-Elliott channel demonstrated by numerical simulations.

show abstract

An Elementary Derivation of the Large Deviation Rate Function for Finite State Markov Chains

Cited by 28 publications

References 29 publications

Information geometry of Markov Kernels: a survey

Information geometry of Markov Kernels: a survey

The Metagenomic Binning Problem: Clustering Markov Sequences

State Feedback Stabilization Over Finite‐State Fading Channels

Contact Info

Product

Resources

About