Universidade Federal do Ceará
Mestrado e Doutorado em Ciências da Computação

Título: Bayesian Regression Models for Interval-Valued Data

Data: 22/08/2025
Horário: 14h
Local: Sala de Seminários – Bloco 952 e Google Meet (meet.google.com/zqq-nxwo-efk)

Resumo:

Solving regression problems with interval-valued datasets is a challenging task that may arise in many real world applications. Motivated by this fact, many researchers have proposed regression methods to handle interval-valued data in recent years. Bayesian models provide a powerful framework for regression, mainly, due to their ability to lead with uncertainty. However, their application to interval data remains underexplored. In this work, we propose Bayesian regression models for interval-valued data. The first approach is a linear conjugate model, while the second operates in a nonlinear context, where we adapt a standard Gaussian Process (GP) and a multi-task GP to handle interval-valued data, also establishing a dependency structure between the lower and upper bounds of the predicted intervals. Both approaches ensure that the predicted intervals are mathematically valid. In the linear case, we compare our proposed method with two Bayesian and one non-Bayesian linear models. In the nonlinear case, we evaluated our proposed method against five state-of-the-art approaches, one of which is Bayesian. We verify the analysis results through numerical experiments. Across both linear and nonlinear settings, our models demonstrated competitive performance, particularly in terms of the log-likelihood metric, notably achieving the highest scores across all datasets. Moreover, in synthetic datasets where a direct relationship exists between inputs and outputs, the proposed methods achieved the best results across all evaluated metrics. These results confirm that our models are valid and reliable approaches for interval regression, while also ensuring consistent interval predictions and offering uncertainty quantification.

Banca examinadora: