Robust State-Conditional Feature-Weighted Jump Models for Temporal Clustering

2026-06-11

AI Summary

This study addresses the challenge of dynamic clustering in time series corrupted by outliers by proposing a robust state-conditioned feature-weighted jump model. The method innovatively integrates Tukey’s bisquare loss to enhance robustness against anomalies, incorporates a smoothness penalty on state transitions, and allows feature weights to adaptively vary with latent states. This joint learning framework simultaneously uncovers temporal cluster structures and identifies state-dependent salient features. Experiments on both synthetic data and real-world datasets—including homicide records from the Kosovo conflict and European macroeconomic indicators—demonstrate that the model accurately recovers ground-truth clustering sequences and key features, significantly outperforming existing approaches in the presence of outliers.

Abstract

We propose a robust feature-weighted jump model for time-dependent clustering. A penalty is used to encourage smoothness of transitions over time, while robustness is achieved through the use of a Tukey's biweight loss function. An additional parameter controls the variability of feature weights across states, allowing the model to assign state-specific relevance to each feature. We illustrate in simulation how the method accurately recovers the true cluster sequence and reliably identifies relevant features, outperforming competing approaches, particularly in the presence of outliers. We conclude with two empirical applications, one on the number of conflict-related homicides in Kosovo in the period 1998-2000, and another on macroeconomic performance of twelve European countries in the period 1949-2024.

Problem

• temporal clustering
• feature weighting
• robustness
• state-dependent features
• outliers

Innovation

• feature-weighted jump model
• temporal clustering
• Tukey's biweight loss
• state-dependent feature relevance
• smoothness penalty