Related papers: Markov bases and subbases for bounded contingency …
Mutually unbiased bases plays a central role in quantum mechanics and quantum information processing. As an important class of mutually unbiased bases, mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have attracted…
Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant…
The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.\ when the goal is to decide if two common independent sets suffice or not.…
Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov…
In this paper we show that the agglomeration of rows or columns of a contingency table with a hierarchical clustering algorithm yields statistical models defined through toric ideals. In particular, starting from the classical independence…
We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued…
Continuous-time Bayesian networks (CTBNs) are graphical representations of multi-component continuous-time Markov processes as directed graphs. The edges in the network represent direct influences among components. The joint rate matrix of…
We define a triangular change of basis in which the form is diagonal and explicitly compute the diagonal entries of this matrix as products of quotients of Chebyshev polynomials, corroborating the determinant computation of Ko and…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal…
We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they…
We compute some dependence coefficients for the stationary Markov chain whose transition kernel is the Perron-Frobenius operator of an expanding map $T$ of $[0, 1]$ with a neutral fixed point. We use these coefficients to prove a central…
We present new scalar and matrix Chernoff-style concentration bounds for a broad class of probability distributions over the binary hypercube $\{0,1\}^n$. Motivated by recent tools developed for the study of mixing times of Markov chains on…
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
In this paper we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
We propose a general framework of computing interfacial structures between two modulated phases. Specifically we propose to use a computational box consisting of two half spaces, each occupied by a modulated phase with given position and…
An important step in the Markov reward approach to error bounds on stationary performance measures of Markov chains is to bound the bias terms. Affine functions have been successfully used for these bounds for various models, but there are…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
We review Markov models of surplus in life insurance based on a counting process following Norberg (1991), uniting probabilistic theory with elements of practice largely drawn from UK experience. First, we organize models systematically…