Related papers: Identifying combinatorially symmetric Hidden Marko…
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…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…
A method of constructing Markov chains on finite state spaces is provided. The chain is specified by three constraints: stationarity, dependence and marginal distributions. The generalized Pythagorean theorem in information geometry plays a…
The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard HMM learning…
Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph $G=(V,…
We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to…
The identifiability of latent variable models has received increasing attention due to its relevance in interpretability and out-of-distribution generalisation. In this work, we study the identifiability of Switching Dynamical Systems,…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
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 prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
In this paper a new proof is given for the supermodularity of information content. Using the decomposability of the information content an algorithm is given for discovering the Markov network graph structure endowed by the pairwise Markov…
This paper introduces a new parsimonious structure for mixture of autoregressive models. the weighting coefficients are determined through latent random variables, following a hidden Markov model. We propose a dynamic programming algorithm…
We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
This report introduces a parsimonious structure for mixture of autoregressive models, where the weighting coefficients are determined through latent random variables as functions of all past observations. These variables follow a hidden…
We consider symmetric Markov chains on $\Bbb Z^d$ where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper…
We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…
We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at…
We consider the problem of finding the transition rates of a continuous-time homogeneous Markov chain under the empirical condition that the state changes at most once during a time interval of unit length. It is proven that this…
For a Markov chain both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical…