Related papers: Distributions associated with general runs and pat…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
From a mathematical and statistical point of view, a segment of a DNA strand can be viewed as a sequence of four-state (A, C, G, T) trials. We consider distributions of runs and patterns related to run lengths of multi-state sequences,…
This paper is concerned with statistical methods for the segmental classification of linear sequence data where the task is to segment and classify the data according to an underlying hidden discrete state sequence. Such analysis is…
Various and ubiquitous information systems are being used in monitoring, exchanging, and collecting information. These systems are generating massive amount of event sequence logs that may help us understand underlying phenomenon. By…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
We present a new algorithm for discovering patterns in time series and other sequential data. We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior…
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…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other…
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…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
Developing satisfactory methodology for the analysis of Markov random field is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical…
The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent random variables this method is here extended to functions of…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…