2,284 research outputs found
Limit theorems for the sample entropy of hidden Markov chains
The Shannon-McMillan-Breiman theorem asserts that the sample entropy of a stationary and ergodic stochastic process converges to the entropy rate of the same process (as the sample size tends to infinity) almost surely. In this paper, we restrict our attention to the convergence behavior of the sample entropy of hidden Markov chains. Under certain positivity assumptions, we prove that a central limit theorem (CLT) with some Berry-Esseen bound for the sample entropy of a hidden Markov chain, and we use this CLT to establish a law of iterated logarithm (LIL) for the sample entropy. © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Symposium on Information Theory (ISIT), St. Petersburg, Russia, 31 July-5 August 2011. In Proceedings of ISIT, 2011, p. 3009-301
A Randomized Algorithm for the Capacity of Finite-State Channels
Inspired by ideas from the field of stochastic approximation, we propose a ran- domized algorithm to compute the capacity of a finite-state channel with a Markovian input. When the mutual information rate of the channel is concave with respect to the chosen parameterization, the proposed algorithm proves to be convergent to the ca- pacity of the channel almost surely with the derived convergence rate. We also discuss the convergence behavior of the algorithm without the concavity assumption.published_or_final_versio
Consistency of Feature Markov Processes
We are studying long term sequence prediction (forecasting). We approach this
by investigating criteria for choosing a compact useful state representation.
The state is supposed to summarize useful information from the history. We want
a method that is asymptotically consistent in the sense it will provably
eventually only choose between alternatives that satisfy an optimality property
related to the used criterion. We extend our work to the case where there is
side information that one can take advantage of and, furthermore, we briefly
discuss the active setting where an agent takes actions to achieve desirable
outcomes.Comment: 16 LaTeX page
How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos
Symbolic dynamics has proven to be an invaluable tool in analyzing the
mechanisms that lead to unpredictability and random behavior in nonlinear
dynamical systems. Surprisingly, a discrete partition of continuous state space
can produce a coarse-grained description of the behavior that accurately
describes the invariant properties of an underlying chaotic attractor. In
particular, measures of the rate of information production--the topological and
metric entropy rates--can be estimated from the outputs of Markov or generating
partitions. Here we develop Bayesian inference for k-th order Markov chains as
a method to finding generating partitions and estimating entropy rates from
finite samples of discretized data produced by coarse-grained dynamical
systems.Comment: 8 pages, 1 figure; http://cse.ucdavis.edu/~cmg/compmech/pubs/hrct.ht
Information Geometry Approach to Parameter Estimation in Markov Chains
We consider the parameter estimation of Markov chain when the unknown
transition matrix belongs to an exponential family of transition matrices.
Then, we show that the sample mean of the generator of the exponential family
is an asymptotically efficient estimator. Further, we also define a curved
exponential family of transition matrices. Using a transition matrix version of
the Pythagorean theorem, we give an asymptotically efficient estimator for a
curved exponential family.Comment: Appendix D is adde
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