Related papers: Loss of memory of hidden Markov models and Lyapuno…
We present two examples of finite-alphabet, infinite excess entropy processes generated by invariant hidden Markov models (HMMs) with countable state sets. The first, simpler example is not ergodic, but the second is. It appears these are…
In order to steer e-commerce users towards making a purchase, marketers rely upon predictions of when users exit without purchasing. Previously, such predictions were based upon hidden Markov models (HMMs) due to their ability of modeling…
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by "controlled" Markov noise. In particular, the faster and slower recursions have non-additive controlled Markov noise…
The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to…
We study several related aspects of reflectionless Jacobi matrices. Our first set of results deals with the singular part of reflectionless measures. We then introduce and discuss Lyapunov exponents, density of states measures, and other…
We establish large deviation type estimates for i.i.d. products of two dimensional random matrices with finitely supported probability distribution. The estimates are stable under perturbations and require no irreducibility assumptions. In…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however,…
Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of…
This paper deals with parameter estimation in pair hidden Markov models (pair-HMMs). We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model being biologically motivated, some…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
We study the redundancy of universally compressing strings $X_1,\dots, X_n$ generated by a binary Markov source $p$ without any bound on the memory. To better understand the connection between compression and estimation in the Markov…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
We consider a nonlinear discrete stochastic control system, and our goal is to design a feedback control policy in order to lead the system to a prespecified state. We adopt a stochastic approximation viewpoint of this problem. It is known…
This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive model able to generate sequences with a given autocorrelation structure. While a first-order Markov Chain model generates new…
Let \xi_0,\xi_1,...,\xi_{\omega-1} be observations from the hidden Markov model with probability distribution P^{\theta_0}, and let \xi_{\omega},\xi_{\omega+1},... be observations from the hidden Markov model with probability distribution…
We study a hidden Markov process which is the result of a transmission of the binary symmetric Markov source over the memoryless binary symmetric channel. This process has been studied extensively in Information Theory and is often used as…
We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses.…
Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the…
We study strange non-chaotic attractors in a class of quasiperiodically forced monotone interval maps known as pinched skew products. We prove that the probability of positive time-N Lyapunov exponents, with respect to the unique physical…