A pruned dynamic programming algorithm to recover the best segmentations with $1$ to $K_{max}$ change-points

TL;DR

This paper introduces a pruned dynamic programming algorithm for efficiently recovering segmentations with up to Kmax change-points, improving computational speed over traditional methods especially with quadratic loss.

Contribution

The authors develop a novel pruning algorithm based on functional cost representation, reducing the complexity of change-point detection to match existing algorithms and demonstrating empirical efficiency.

Findings

Algorithm has worst-case complexity of O(Kmax n^2)

Pruning is effective even without change-points in the data

Empirically faster than the segment neighbourhood algorithm for quadratic loss

Abstract

A common computational problem in multiple change-point models is to recover the segmentations with $1$ to $K_{max}$ change-points of minimal cost with respect to some loss function. Here we present an algorithm to prune the set of candidate change-points which is based on a functional representation of the cost of segmentations. We study the worst case complexity of the algorithm when there is a unidimensional parameter per segment and demonstrate that it is at worst equivalent to the complexity of the segment neighbourhood algorithm: $\mathcal{O}(K_{max} n^2)$. For a particular loss function we demonstrate that pruning is on average efficient even if there are no change-points in the signal. Finally, we empirically study the performance of the algorithm in the case of the quadratic loss and show that it is faster than the segment neighbourhood algorithm.