Linear time dynamic programming for the exact path of optimal models selected from a finite set

Abstract

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a finite set of models. The fastest existing algorithm for computing the breakpoints in the regularization path is quadratic in the number of models, so it scales poorly to high dimensional problems. We provide new formal proofs that a dynamic programming algorithm can be used to compute the breakpoints in linear time. Empirical results on changepoint detection problems demonstrate the improved accuracy and speed relative to grid search and the previous quadratic time algorithm.

arXiv comment14 pages

References in corpus (5)

• Nearly unbiased variable selection under minimax concave penalty
• Optimal detection of changepoints with a linear computational cost
• Selective review of offline change point detection methods
• Data-driven calibration of penalties for least-squares regression
• SparseStep: Approximating the Counting Norm for Sparse Regularization

Cited by in corpus (1)

• Optimizing ROC Curves with a Sort-Based Surrogate Loss Function for Binary Classification and Changepoint Detection