Related papers: Construction of local structure maps for cellular …
We study Markov chains generated by iterated Lipschitz functions systems with possibly place dependent probabilities. Under general conditions, we prove uniqueness of the invariant probability measure for the associated Markov chain, by…
This work introduces the IB-score, a family of independence-based score functions for robust learning of Markov networks independence structures. Markov networks are a widely used graphical representation of probability distributions, with…
We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an…
In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
Learning Markov blanket (MB) structures has proven useful in performing feature selection, learning Bayesian networks (BNs), and discovering causal relationships. We present a formula for efficiently determining the number of MB structures…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
We consider the task of estimating a structural model of dynamic decisions by a human agent based upon the observable history of implemented actions and visited states. This problem has an inherent nested structure: in the inner problem, an…
We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a…
We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of the system within a prescribed basis. We estimate the…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a "single" (i.e. common to all points in the…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…