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About

About

I am a professor at the Scientific Area of Mathematics in the School of Technology and Management of the Polytechnic Institute of Viana do Castelo (ESTG-IPVC) and member of the Laboratory in Artificial Intelligence and Decision Support (LIAAD – INESC TEC) of the University of Porto. I have a Msc in Mathematics by the University of Minho and a PhD in Applied Mathematics by the University of Porto in 2014.

My main research lines are Data Analysis; Symbolic Data Analysis (Analysis of multidimensional complex data) and Linear regression models. I work in the development and application of methods adapted to data carrying a lot of information. This research is included in the framework of Symbolic Data Analysis.

Moreover, I collaborate with bio-informaticians and chemistry researchers for the development of mathematical models applied to agent-based modelling. 

Interest
Topics
Details

Details

Publications

2017

Off the beaten track: A new linear model for interval data

Authors
Dias, S; Brito, P;

Publication
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH

Abstract
We propose a new linear regression model for interval-valued variables. The model uses quantile functions to represent the intervals, thereby considering the distributions within them. In this paper we study the special case where the Uniform distribution is assumed in each observed interval, and we analyze the extension to the Symmetric Triangular distribution. The parameters of the model are obtained solving a constrained quadratic optimization problem that uses the Mallows distance between quantile functions. As in the classical case, a goodness-of-fit measure is deduced. Two applications on up-to-date fields are presented: one predicting duration of unemployment and the other allowing forecasting burned area by forest fires.

2015

Linear regression model with histogram-valued variables

Authors
Dias, S; Brito, P;

Publication
Statistical Analysis and Data Mining

Abstract
Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear regression models for this type of data are necessarily more complex than a simple generalization of the classical model: the parameters cannot be negative; still the linear relation between the variables must be allowed to be either direct or inverse. In this work, we propose a new linear regression model for histogram-valued variables that solves this problem, named Distribution and Symmetric Distribution Regression Model. To determine the parameters of this model, it is necessary to solve a quadratic optimization problem, subject to non-negativity constraints on the unknowns; the error measure between the predicted and observed distributions uses the Mallows distance. As in classical analysis, the model is associated with a goodness-of-fit measure whose values range between 0 and 1. Using the proposed model, applications with real and simulated data are presented. © 2015 Wiley Periodicals, Inc.

Supervised
thesis

2017

Modelos de Regressão Linear para Variáveis Intervalares: Uma extensão do modelo ID

Author
Pedro Jorge Correia Malaquias

Institution
UP-FEP