# Fast Sequence Segmentation using Log-Linear Models

## TL;DR

This paper introduces a pruning technique for dynamic programming in sequence segmentation with log-linear models, significantly reducing computation time while maintaining optimality.

## Contribution

It presents a theoretical pruning method that accelerates the dynamic programming approach for sequence segmentation using log-linear models.

## Key findings

- Significant reduction in computational time demonstrated empirically.
- Pruning method maintains optimal segmentation results.
- Applicable to a broad class of distributions within log-linear models.

## Abstract

Sequence segmentation is a well-studied problem, where given a sequence of elements, an integer K, and some measure of homogeneity, the task is to split the sequence into K contiguous segments that are maximally homogeneous. A classic approach to find the optimal solution is by using a dynamic program. Unfortunately, the execution time of this program is quadratic with respect to the length of the input sequence. This makes the algorithm slow for a sequence of non-trivial length. In this paper we study segmentations whose measure of goodness is based on log-linear models, a rich family that contains many of the standard distributions. We present a theoretical result allowing us to prune many suboptimal segmentations. Using this result, we modify the standard dynamic program for one-dimensional log-linear models, and by doing so reduce the computational time. We demonstrate empirically, that this approach can significantly reduce the computational burden of finding the optimal segmentation.