On sparse ensemble methods: An application to short-term predictions of the evolution of COVID-19.

Since the seminal paper by Bates and Granger in 1969, a vast number of ensemble methods that combine different base regressors to generate a unique one have been proposed in the literature. The so-obtained regressor method may have better accuracy than its components, but at the same time it may overfit, it may be distorted by base regressors with low accuracy, and it may be too complex to understand and explain. This paper proposes and studies a novel Mathematical Optimization model to build a sparse ensemble, which trades off the accuracy of the ensemble and the number of base regressors used.

Mathematical optimization in classification and regression trees.

Classification and regression trees, as well as their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous Optimization and the Mixed-Integer Linear Optimization paradigms to develop novel formulations in this research area. We compare those in terms of the nature of the decision variables and the constraints required, as well as the optimization algorithms proposed.

Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization.

Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors' interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called , which may include in particular the set of observed variables.

On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization.

In this article we develop a novel online framework to visualize news data over a time horizon. First, we perform a Natural Language Processing analysis, wherein the words are extracted, and their attributes, namely the importance and the relatedness, are calculated. Second, we present a Mathematical Optimization model for the visualization problem and a numerical optimization approach.

A sparsity-controlled vector autoregressive model.

Vector autoregressive (VAR) models constitute a powerful and well studied tool to analyze multivariate time series. Since sparseness, crucial to identify and visualize joint dependencies and relevant causalities, is not expected to happen in the standard VAR model, several sparse variants have been introduced in the literature. However, in some cases it might be of interest to control some dimensions of the sparsity, as e.