Related papers: Accelerating Power Methods for Higher-order Markov…
Nonnegative tensors arise very naturally in many applications that involve large and complex data flows. Due to the relatively small requirement in terms of memory storage and number of operations per step, the (shifted) higher-order power…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…
We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free…
We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…
We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric…
Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
Strong and weak simulation relations have been proposed for Markov chains, while strong simulation and strong probabilistic simulation relations have been proposed for probabilistic automata. However, decision algorithms for strong and weak…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…
A commonly used technique for the higher-order PageRank problem is the power method that is computationally intractable for large-scale problems. The truncated power method proposed recently provides us with another idea to solve this…
We present two new methods for estimating the order (memory depth) of a finite alphabet Markov chain from observation of a sample path. One method is based on entropy estimation via recurrence times of patterns, and the other relies on a…
The main goal of the paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate a decomposition procedure for the…
We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
Planning problems where effects of actions are non-deterministic can be modeled as Markov decision processes. Planning problems are usually goal-directed. This paper proposes several techniques for exploiting the goal-directedness to…
The Importance Markov chain is a novel algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain…