arXiv subjects

Antonio Galves

Publications and source records attributed to Antonio Galves.

25 records · Page 2Linked to original sources

arXiv2010

Perfect simulation of a coupling achieving the $\bar{d}$-distance between ordered pairs of binary chains of infinite order

We explicitly construct a coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of iid sequence of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.

math.PR↗

arXiv2009

Perfect simulation of infinite range Gibbs measures and coupling with their finite range approximations

In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a perfect simulation algorithm for the measure and for the coupled measures. The algorithm works for general Gibbsian interaction under requirements on the tails of the interaction. As a consequence we obtain an upper bound for the error we make when sampling from a finite range approximation instead of the true infinite range measure.

math.PR↗

arXiv2008

Exponential inequalities for empirical unbounded context trees

In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the context tree of a Variable Length Markov Chain. As a consequence of the exponential bounds we obtain a strong consistency result. We generalize in this way several previous results in the field.

math.ST↗

arXiv2008

Detecting phylogenetic relations out from sparse context trees

The goal of this paper is to study the similarity between sequences using a distance between the \emph{context} trees associated to the sequences. These trees are defined in the framework of \emph{Sparse Probabilistic Suffix Trees} (SPST), and can be estimated using the SPST algorithm. We implement the Phyl-SPST package to compute the distance between the sparse context trees estimated with the SPST algorithm. The distance takes into account the structure of the trees, and indirectly the transition probabilities. We apply this approach to reconstruct a phylogenetic tree of protein sequences in the globin family of vertebrates. We compare this tree with the one obtained using the well-known PAM distance.

stat.AP↗

arXiv2008

Stochastic chains with memory of variable length

Stochastic chains with memory of variable length constitute an interesting family of stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a finite suffix of the past, called context, is enough to predict the next symbol. These models were first introduced in the information theory literature by Rissanen (1983) as a universal tool to perform data compression. Recently, they have been used to model up scientific data in areas as different as biology, linguistics and music. This paper presents a personal introductory guide to this class of models focusing on the algorithm Context and its rate of convergence.

math.PR↗

arXiv2007

Random perturbations of stochastic chains with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

math.PR↗

arXiv1998

Decay of correlations for non Hölderian dynamics. A coupling approach

We present an upper bound on the mixing rate of the equilibrium state of a dynamical systems defined by the one-sided shift and a non Hölder potential of summable variations. The bound follows from an estimation of the relaxation speed of chains with complete connections with summable decay, which is obtained via a explicit coupling between pairs of chains with different histories.

math.PR↗