Perfect sampling for nonhomogeneous Markov chains and hidden Markov models

Perfect Sampling for Nonhomogeneous Markov Chains and Hidden Markov Models By

An Interruptible Algorithm for Perfect Sampling via Markov Chains Short Title: Perfect Sampling via Markov Chains

For a large class of examples arising in statistical physics known as attractive spin systems (e.g., the Ising model), one seeks to sample from a probability distribution π on an enormously large state space, but elementary sampling is ruled out by the infeasibility of calculating an appropriate normalizing constant. The same difficulty arises in computer science problems where one seeks to sam...

Taylor Expansion for the Entropy Rate of Hidden Markov Chains

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

Perfect Sampling of Harris Recurrent Markov Chains

We develop an algorithm for simulating \perfect" random samples from the invariant measure of a Harris recurrent Markov chain. The method uses backward coupling of embedded regeneration times, and works most eeectively for nite chains and for stochas-tically monotone chains even on continuous spaces, where paths may be sandwiched below \upper" and \lower" processes. Examples show that more naiv...

Boltzmann Chains and Hidden Markov Models

We propose a statistical mechanical framework for the modeling of discrete time series. Maximum likelihood estimation is done via Boltzmann learning in one-dimensional networks with tied weights. We call these networks Boltzmann chains and show that they contain hidden Markov models (HMMs) as a special case. Our framework also motivates new architectures that address particular shortcomings of ...