Related papers: A Markov chain representation of the Perron-Froben…
In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability…
In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
Markov chain models are used in various fields, such behavioral sciences or econometrics. Although the goodness of fit of the model is usually assessed by large sample approximation, it is desirable to use conditional tests if the sample…
The conventional perspective on Markov chains considers decision problems concerning the probabilities of temporal properties being satisfied by traces of visited states. However, consider the following query made of a stochastic system…
In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…
The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases. We formulate irreducibility and symmetry properties of a…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
We introduce a new definition of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of…
We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many…
In spite of remarkable progress in machine learning techniques, the state-of-the-art machine learning algorithms often keep machines from real-time learning (online learning) due in part to computational complexity in parameter…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
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 study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…
Markov chain analysis is a key technique in formal verification. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not --…
Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d\times d$ matrix. Motivated by [4], we define a similar class of matrices which are a generalization of…