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面向稀疏模式异质性的多任务学习：统计与计算视角AI 解读

Abstract We consider a problem in multi-task learning (MTL) where multiple linear models are jointly trained on a collection of datasets (‘tasks’). A key novelty of our framework is that it allows the sparsity pattern of regression coefficients and the values of non-zero coefficients to differ across tasks while still leveraging partially shared structure. Our methods encourage models to share information across tasks through separately encouraging (1) coefficient supports,…

稀疏主成分分析：基于整数规划的可扩展新估计量AI 解读

We consider the sparse principal component analysis (SPCA) problem under the well-known spiked covariance model. Recent work has shown that the SPCA problem can be reformulated as a mixed integer program (MIP) and can be solved to global optimality, leading to estimators that are known to enjoy optimal statistical properties. However, prior MIP algorithms for SPCA appear to be limited in terms of scalability to up to a thousand features or so. In this paper we propose a new…

通过精确融合与稀疏正则化对类别特征建模AI 解读

Abstract We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a) clustering of the regression coefficients to collapse some of the categorical levels together; and (b) sparsity of the regression coefficients. We present novel mixed integer programming formulations for our estimator, and develop a custom…