Related papers: Analyticity of Entropy Rates of Continuous-State H…
We prove that under certain mild assumptions, the entropy rate of a hidden Markov chain, observed when passing a finite-state stationary Markov chain through a discrete-time continuous-output channel, is jointly analytic as a function of…
We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
Let $K = \{0,1,...,q-1\}$. We use a special class of translation invariant measures on $K^\mathbb{Z}$ called algebraic measures to study the entropy rate of a hidden Markov processes. Under some irreducibility assumptions of the Markov…
We consider a hidden Markov model with multiple observation processes, one of which is chosen at each point in time by a policy---a deterministic function of the information state---and attempt to determine which policy minimises the…
Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…
This paper considers the asymptotic properties of the recursive maximum likelihood estimation in hidden Markov models. The paper is focused on the asymptotic behavior of the log-likelihood function and on the point-convergence and…
We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
I formulate an entropy-rate maximization problem at the observable level for stochastic processes observed through an information-reducing observation map. For a visible stationary law, the map determines an observational fiber of hidden…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
Determining entropy rates of stochastic processes is a fundamental and difficult problem, with closed-form solutions known only for specific cases. This paper pushes the state-of-the-art by solving the problem for Hidden Markov Models…
This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…
Mixtures of Hidden Markov Models (MHMMs) are frequently used for clustering of sequential data. An important aspect of MHMMs, as of any clustering approach, is that they can be interpretable, allowing for novel insights to be gained from…
Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…
We demonstrate an efficient formula to compute the entropy rate $H(\mu)$ of a hidden Markov process with $q$ output symbols where at least one symbol is unambiguously received. Using an approximation to $H(\mu)$ to the first $N$ terms we…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and…
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…
This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behaviour of different types of systems by observing their outputs. With the aim of measuring the stability…