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

arXiv: https://arxiv.org/abs/2003.02808 · HTML: https://mlsanity.com/paper/2003.02808/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2020.

## Built on by (most cited first, 1 of 1)

- [Optimizing ROC Curves with a Sort-Based Surrogate Loss Function for Binary Classification and Changepoint Detection](https://mlsanity.com/paper/2107.01285/) (2021)

## Abstract (arXiv)

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.