  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.
