A Parametric Simplex Approach to Statistical Learning Problems
نویسندگان
چکیده
In this paper, we show that the parametric simplex method is an efficient algorithm for solving various statistical learning problems that can be written as linear programs parametrized by a so-called regularization parameter. The parametric simplex method offers significant advantages over other methods: (1) it finds the complete solution path for all values of the regularization parameter by solving the problem only once; (2) it provides an accurate dual certificate stopping criterion; (3) for Lasso-type problems, it produces the sparse solutions in very few iterations. The learning problems we looked at include Dantzig selector estimation, LAD-Lasso, constrained `1 minimization estimation (CLIME) for sparse precision matrix, linear programming discriminant rule for sparse linear discriminant analysis (LDA) as well as differential network estimation. We provide details on how to apply the parametric simplex method to these problems. Numerical performance of our method applied to these learning problems is investigated using simulated data.
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