Rough-Fuzzy CPD: A Gradual Change Point Detection Algorithm

TL;DR

This paper introduces a novel fuzzy rough set theory-based algorithm for detecting gradual changepoints in time series data, outperforming existing methods in accuracy and robustness, with practical applications demonstrated on real datasets.

Contribution

The paper presents a new fuzzy rough set approach for gradual changepoint detection, including a mathematical framework, statistical testing, and a Python package for implementation.

Findings

Outperforms existing fuzzy and crisp methods in simulations

Robust to noise, fuzziness, and hyperparameter variations

Successfully applied to real-world datasets including Covid-19

Abstract

Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint detection problem, although there is not much work devoted towards gradual changepoints as compared to abrupt ones. Here we present a new approach to solve changepoint detection problem using fuzzy rough set theory which is able to detect such gradual changepoints. An expression for the rough-fuzzy estimate of changepoints is derived along with its mathematical properties concerning fast computation. In a statistical hypothesis testing framework, asymptotic distribution of the proposed statistic on both single and multiple changepoints is derived under null hypothesis enabling multiple changepoint detection. Extensive simulation studies have been performed to investigate how simple crude statistical measures of disparity can be subjected to improve their efficiency in estimation of gradual changepoints. Also, the said rough-fuzzy estimate is robust to signal-to-noise ratio, high degree of fuzziness in true changepoints and also to hyper parameter values. Simulation studies reveal that the proposed method beats other fuzzy methods and also popular crisp methods like WBS, PELT and BOCD in detecting gradual changepoints. The applicability of the estimate is demonstrated using multiple real-life datasets including Covid-19. We have developed the python package "roufcp" for broader dissemination of the methods.