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- W2999243450 abstract "We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to solve (to optimality) $ell_0$-regularized regression problems at scales much larger than what was conventionally considered possible. Despite their usefulness, MIP-based global optimization approaches are significantly slower compared to the relatively mature algorithms for $ell_1$-regularization and heuristics for nonconvex regularized problems. We aim to bridge this gap in computation times by developing new MIP-based algorithms for $ell_0$-regularized classification. We propose two classes of scalable algorithms: an exact algorithm that can handle $papprox 50,000$ features in a few minutes, and approximate algorithms that can address instances with $papprox 10^6$ in times comparable to the fast $ell_1$-based algorithms. Our exact algorithm is based on the novel idea of textsl{integrality generation}, which solves the original problem (with $p$ binary variables) via a sequence of mixed integer programs that involve a small number of binary variables. Our approximate algorithms are based on coordinate descent and local combinatorial search. In addition, we present new estimation error bounds for a class of $ell_0$-regularized estimators. Experiments on real and synthetic data demonstrate that our approach leads to models with considerably improved statistical performance (especially, variable selection) when compared to competing methods." @default.
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- W2999243450 date "2020-01-17" @default.
- W2999243450 modified "2023-09-27" @default.
- W2999243450 title "Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives" @default.
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