[2212.08697] Multi-Activity Studying for Sparsity Sample Heterogeneity: Statistical and Computational Views

View a PDF of the paper titled Multi-Activity Studying for Sparsity Sample Heterogeneity: Statistical and Computational Views, by Kayhan Behdin and 4 different authors

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Summary:We take into account an issue in Multi-Activity Studying (MTL) the place a number of linear fashions are collectively educated on a group of datasets (“duties”). A key novelty of our framework is that it permits the sparsity sample of regression coefficients and the values of non-zero coefficients to vary throughout duties whereas nonetheless leveraging partially shared construction. Our strategies encourage fashions to share info throughout duties by way of individually encouraging 1) coefficient helps, and/or 2) nonzero coefficient values to be comparable. This permits fashions to borrow power throughout variable choice even when non-zero coefficient values differ throughout duties. We suggest a novel mixed-integer programming formulation for our estimator. We develop customized scalable algorithms primarily based on block coordinate descent and combinatorial native search to acquire high-quality (approximate) options for our estimator. Moreover, we suggest a novel precise optimization algorithm to acquire globally optimum options. We examine the theoretical properties of our estimators. We formally present how our estimators leverage the shared help info throughout duties to attain higher variable choice efficiency. We consider the efficiency of our strategies in simulations and two biomedical purposes. Our proposed approaches seem to outperform different sparse MTL strategies in variable choice and prediction accuracy. We offer the sMTL package deal on CRAN.