Labeled Optimal Partitioning

TL;DR

This paper introduces Labeled Optimal Partitioning (LOPART), a dynamic programming method for changepoint detection that accurately fits labeled training data and predicts unlabeled test changepoints, improving over existing methods.

Contribution

The paper presents a novel optimal changepoint detection model and algorithm that guarantees label fitting in training data while predicting in unlabeled test regions, with theoretical and empirical validation.

Findings

LOPART outperforms existing baselines in label error metrics.

The algorithm has manageable time complexity relative to data size and label count.

Empirical results demonstrate improved accuracy in both train and test changepoint detection.

Abstract

In data sequences measured over space or time, an important problem is accurate detection of abrupt changes. In partially labeled data, it is important to correctly predict presence/absence of changes in positive/negative labeled regions, in both the train and test sets. One existing dynamic programming algorithm is designed for prediction in unlabeled test regions (and ignores the labels in the train set); another is for accurate fitting of train labels (but does not predict changepoints in unlabeled test regions). We resolve these issues by proposing a new optimal changepoint detection model that is guaranteed to fit the labels in the train data, and can also provide predictions of unlabeled changepoints in test data. We propose a new dynamic programming algorithm, Labeled Optimal Partitioning (LOPART), and we provide a formal proof that it solves the resulting non-convex optimization problem. We provide theoretical and empirical analysis of the time complexity of our algorithm, in terms of the number of labels and the size of the data sequence to segment. Finally, we provide empirical evidence that our algorithm is more accurate than the existing baselines, in terms of train and test label error.