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It is a well-known fact that the first and last non-trivial coefficients of the characteristic polynomial of a linear operator are respectively its trace and its determinant. This work shows how to compute recursively all the coefficients…

We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…

Complementary product recommendation is a powerful strategy to improve customer experience and retail sales. However, recommending the right product is not a simple task because of the noisy and sparse nature of user-item interactions. In…

In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…

The effectiveness of recommendation systems is pivotal to user engagement and satisfaction in online platforms. As these recommendation systems increasingly influence user choices, their evaluation transcends mere technical performance and…

Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…

The problem of finding completely positive matrices with equal cp-rank and rank is considered. We give some easy-to-check sufficient conditions on the entries of a doubly nonnegative matrix for it to be completely positive with equal…

We consider the problem of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time…

We present the Vector Equivalence technique. This technique allows a simple and systematic calculating of Feynman diagrams involving massive fermions at the matrix element level. As its name suggests, the technique allows two Lorentz…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

Solving multi-objective optimization problems is important in various applications where users are interested in obtaining optimal policies subject to multiple, yet often conflicting objectives. A typical approach to obtain optimal policies…

The independent component model is a latent variable model where the components of the observed random vector are linear combinations of latent independent variables. The aim is to find an estimate for a transformation matrix back to…

Feature selection can efficiently identify the most informative features with respect to the target feature used in training. However, state-of-the-art vector-based methods are unable to encapsulate the relationships between feature samples…

In this paper we introduce a new technique to analyze families of rankings focused on the study of structural properties of a new type of graphs. Given a finite number of elements and a family of rankings of those elements, we say that two…

This paper introduces some efficient initials for a well-known algorithm (an inverse iteration) for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also…

A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…

We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…

In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable somebody to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a…

Spatial networks are a powerful framework for studying a large variety of systems belonging to a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few. Spatial…