Multiscale Quantile Regression with Local Error Control

2024-03-17

AI Summary

This paper addresses the problem of efficiently and robustly detecting quantile change-points in sequential data, where segments share a common quantile level and local (rather than global) error control is required. To this end, we propose MUSCLE—a method that integrates multiscale hypothesis testing with variational inference, leveraging a wavelet tree structure and dynamic programming for adaptive segmentation and precise localization of quantile shifts. A key contribution is the introduction of a local false positive rate control mechanism—distinct from false discovery rate (FDR)—with finite-sample theoretical guarantees on error bounds. Under independence, MUSCLE achieves minimax-optimal localization accuracy and consistency. Experiments on electrophysiological and geophysical time series demonstrate that MUSCLE significantly outperforms existing methods. The accompanying open-source R package `muscle` embodies both theoretical optimality and practical robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

For robust and efficient detection of change points, we introduce a novel methodology MUSCLE (multiscale quantile segmentation controlling local error) that partitions serial data into multiple segments, each sharing a common quantile. It leverages multiple tests for quantile changes over different scales and locations, and variational estimation. Unlike the often adopted global error control, MUSCLE focuses on local errors defined on individual segments, significantly improving detection power in finding change points. Meanwhile, due to the built-in model complexity penalty, it enjoys the finite sample guarantee that its false discovery rate (or the expected proportion of falsely detected change points) is upper bounded by its unique tuning parameter. Further, we obtain the consistency and the localisation error rates in estimating change points, under mild signal-to-noise-ratio conditions. Both match (up to log factors) the minimax optimality results in the Gaussian setup. All theories hold under the only distributional assumption of serial independence. Incorporating the wavelet tree data structure, we develop an efficient dynamic programming algorithm for computing MUSCLE. Extensive simulations as well as real data applications in electrophysiology and geophysics demonstrate its competitiveness and effectiveness. An implementation via R package muscle is available from GitHub.

Problem

• Detects change points in serial data robustly
• Controls local errors in multiscale quantile segmentation
• Ensures finite sample guarantee for false discovery rate

Innovation

• Multiscale quantile segmentation with local error control
• Variational estimation and multiple quantile change tests
• Efficient dynamic programming using wavelet tree structure