A cost-sensitive constrained Lasso

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. The latter is controlled by means of a regularization term that penalizes regressors with a poor individual performance. Our approach is flexible to incorporate desirable properties one may have on the ensemble, such as controlling the performance of the ensemble in critical groups of records, or the costs associated with the base regressors involved in the ensemble. We illustrate our approach with real data sets arising in the COVID-19 context.

Robust optimal classification trees under noisy labels

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. The motivation of this new methodology is based on the superaditive effect of combining together margin based classifiers and outlier detection techniques. Our approach rests on two main elements: (1) the splitting rules for the classification trees are designed to maximize the separation margin between classes applying the paradigm of SVM; and (2) some of the labels of the training sample are allowed to be changed during the construction of the tree trying to detect the label noise. Both features are considered and integrated together to design the resulting Optimal Classification Tree. We present a Mixed Integer Non Linear Programming formulation for the problem, suitable to be solved using any of the available off-the-shelf solvers. The model is analyzed and tested on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of our approach. Our computational results show that in most cases the new methodology outperforms both in accuracy and AUC the results of the benchmarks provided by OCT and OCT-H.