Neighborhood radius estimation in Variable-neighborhood Random Fields

We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region it is necessary to inspect a random number of neighborhood symbols which might change according to the value of them. In analogy to the one dimensional setting we call these neighborhood symbols the context of the region. This framework is a natural extension, to d-dimensional fields, of the notion of variable-length Markov chains introduced by Rissanen (1983) in his classical paper. We define an algorithm to estimate the radius of the smallest ball containing the context based on a realization of the field. We prove the consistency of this estimator. Our proofs are constructive and yield explicit upper bounds for the probability of wrong estimation of the radius of the context

A View Of The Em Algorithm That Justifies Incremental, Sparse, And Other Variants

. The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible. 1. Introduction The Expectation-Maximization (EM) algorithm finds maximum likelihood parameter estimates in problems where some variables were unobserved. Special cases of the algorithm date back several dec..

The moment-corrected phi-divergence test statistics for symmetry

In this paper we consider the family of phi-divergence test statistics, T-n(phi,S), for the problem of symmetry in I x I contingency tables whose asymptotic distribution is chi-square with I (I - 1)/2 degrees of freedom and we propose a moment-corrected phi-divergence test statistic in order to improve the accuracy of the chi-square approximation of the distribution of T,T-n(phi,S) under the hypothesis of symmetry