BUSCADOR RECOLECTA

The present paper presents some results that allow us to perform with High Relative Accuracy linear algebra operations with correlation and covariance matrices of Gaussian Markov Random Fields over graphs of paths. Some numerical experiments are carried out showing the computational benefits of this approach.

Gaussian Markov Random Fields are a popular statistical model that has been used successfully in many fields of application. Recent work has studied conditions under which the covariance matrix of a Gaussian Markov Random Field over a graph of paths is totally positive. In such case, many linear algebra operations concerning the covariance matrix can be performed with High Relative Accuracy (the relative error is of order of machine precision). Unfortunately, classical estimators of the covariance matrix do not necessarily yield a totally positive matrix, even when the population covariance matrix is totally positive. Essentially, this inconvenience prevents the available High Relative Accuracy methods to be used with real-life data. Here, we present a method for the estimation of the covariance matrix of a Gaussian Markov Random Field over a graph of paths assuring the estimated covariance matrix (or its inverse) is totally positive.

Aggregation operators are unvaluable tools when different pieces of information have to be taken into account with respect to the same object. They allow to obtain a unique outcome when different evaluations are available for the same element/object. In this contribution we assume that the opinions are not given in form of isolated values, but intervals. We depart from two “classical” aggregation functions and define a new operator for aggregating intervals based on the two original operators. We study under what circumstances this new function is well defined and we provide a general characterization for monotonicity. We also study the behaviour of this operator when the departing functions are the most common aggregation operators. We also provide an illustrative example demonstrating the practical application of the theoretical contribution to ensemble deep learning models., Authors would like to thank for the support of the Spanish Ministry of Science and Innovation projects PID2022-139886NB-I00 (S. Diaz-Vazquez, E. Torres-Manzanera, N. Rico, I. Diaz and S. Montes) and Ministerio de Educación y Formación Profesional PID2022-136627NB-I00 (I. Rodriguez-Martinez and H. Bustince).