arXiv subjects

Ruben Zamar

Publications and source records attributed to Ruben Zamar.

6 recordsLinked to original sources

arXiv2022

Multi-Model Subset Selection

The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the L0-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield interpretable models, in terms of prediction accuracy they are often outperformed by "blackbox" multi-model ensemble methods. A regression ensemble is introduced which combines the interpretability of sparse methods with the high prediction accuracy of ensemble methods. An algorithm is proposed to solve the joint optimization of the corresponding L0-penalized regression models by extending recent developments in L0-optimization for sparse methods to multi-model regression ensembles. The sparse and diverse models in the ensemble are learned simultaneously from the data. Each of these models provides an explanation for the relationship between a subset of predictors and the response variable. Empirical studies and theoretical knowledge about ensembles are used to gain insight into the ensemble method's performance, focusing on the interplay between bias, variance, covariance, and variable selection. In prediction tasks, the ensembles can outperform state-of-the-art competitors on both simulated and real data. Forward stepwise regression is also generalized to multi-model regression ensembles and used to obtain an initial solution for the algorithm. The optimization algorithms are implemented in publicly available software packages.

stat.ME↗

arXiv2022

Robust graphical lasso based on multivariate Winsorization

We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr-Muller-Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux-Ollerer's precision matrix estimator, our proposed estimator attains the maximum finite sample breakdown point of 0.5 under cellwise contamination. We conduct an extensive Monte Carlo simulation study to assess the performance of ours and the currently existing proposals. We find that ours has a competitive behavior, regarding the the estimation of the precision matrix and the recovery of the graph. We demonstrate the usefulness of the proposed methodology in a real application to breast cancer data.

stat.ME↗

arXiv2021

Data-Driven Logistic Regression Ensembles With Applications in Genomics

Advances in data collecting technologies in genomics have significantly increased the need for tools designed to study the genetic basis of many diseases. Effective statistical methods should excel in both prediction accuracy and biomarker identification. We introduce a novel approach to high-dimensional binary classification that integrates regularization with ensembling techniques. The method constructs compact ensembles of interpretable models derived by optimizing a global objective function. In medical genomics applications, the proposed approach identifies critical biomarkers overlooked by competing methods. We develop a variable importance ranking system to help researchers prioritize promising genes. The method's asymptotic properties are established, and an efficient computational algorithm is provided. Through extensive simulations across complex scenarios and analysis of cancer genomics datasets, we demonstrate strong predictive performance. Based on the numerical experiments, we offer practical guidelines for determining optimal ensemble size.

stat.ME↗

arXiv2019

Split Regularized Regression

We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by minimizing an objective function that encourages sparsity within each group and diversity among them. The estimated coefficients are then pooled together to form the final fit. Our procedure works on top of a given penalized linear regression estimator (e.g., Lasso, elastic net) by fitting it to possibly overlapping groups of features, encouraging diversity among these groups to reduce the correlation of the corresponding predictions. For the case of two groups, elastic net penalty and orthogonal predictors, we give a closed form solution for the regression coefficients in each group. We establish the consistency of our method with the number of predictors possibly increasing with the sample size. An extensive simulation study and real-data applications show that in general the proposed method improves the prediction accuracy of the base estimator used in the procedure. Possible extensions to GLMs and other models are discussed. The supplemental material for this article, available online, contains the proofs of our theoretical results and the full results of our simulation study.

stat.ME↗

arXiv2018

Objective-Driven Ensembles: Bridging the Gap Between Interpretable Sparsity and Algorithmic Prediction

Sparse methods (e.g., Best Subset Selection, Elastic Net) are the standard approach for obtaining interpretable models, but they can suffer from high variance and vulnerability to spurious correlations. Alternatively, algorithmic ensembles (e.g., Random Forests, Gradient Boosting) achieve high prediction accuracy but yield uninterpretable black boxes driven by randomization or sequential residual fitting. In recent years, a unifying paradigm has emerged: Objective-Driven Ensembles. By generalizing best subset selection into a joint mathematical optimization problem, this approach generates interpretable ensembles by optimally splitting predictors across a small number of diverse models. In this paper, we synthesize this growing body of literature and illustrate the statistical principles driving its empirical success. Specifically, we utilize finite-sample bounds to demonstrate how penalizing predictor overlap controls ensemble covariance and provides a mathematical hedge against spurious correlations. We evaluate these mechanics using an exact combinatorial oracle, and review how recent computational approximations have successfully scaled this framework to a variety of domains, including high-dimensional data, classification tasks, and settings with casewise or cellwise contamination, achieving machine-learning-level accuracy while retaining the interpretability of sparse models.

stat.ME↗

arXiv2012

A robust and sparse K-means clustering algorithm

In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this paper we show that a small proportion of atypical observations might have serious adverse effects on the solutions found by the sparse clustering algorithm of Witten and Tibshirani (2010). We propose a robustification of their sparse K-means algorithm based on the trimmed K-means algorithm of Cuesta-Albertos et al. (1997) Our proposal is also able to handle datasets with missing values. We illustrate the use of our method on microarray data for cancer patients where we are able to identify strong biological clusters with a much reduced number of genes. Our simulation studies show that, when there are outliers in the data, our robust sparse K-means algorithm performs better than other competing methods both in terms of the selection of features and also the identified clusters. This robust sparse K-means algorithm is implemented in the R package RSKC which is publicly available from the CRAN repository.

stat.ML↗