Robust outlier-adjusted mean-shift estimation of state-space models

2025-11-19

AI Summary

State-space models (SSMs) assume Gaussian observation errors and are thus highly sensitive to additive outliers, leading to non-robust parameter estimation. To address this, we propose ROAMS—a Robust Outlier-Aware Modeling framework—that explicitly incorporates time-point-specific shift parameters into the observation equation to model outliers, while coupling an L₀-type regularization penalty to jointly achieve robust parameter estimation and automatic outlier detection within a unified optimization framework. Our key innovation lies in integrating outlier-shift modeling with sparse regularization, eliminating the need for pre-filtering or iterative outlier removal, and providing BIC path curves for diagnosing outlier structure and guiding hyperparameter selection. In extensive simulations and real-world animal tracking data, ROAMS consistently outperforms classical SSMs, ARIMA, and existing robust benchmarks: it reduces parameter estimation error by 20%–45%, demonstrating both statistical robustness and computational practicality.

Technology Category

• Intelligent Robots: State Estimation
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

State-space models (SSMs) provide a flexible framework for modelling time series data, but their reliance on Gaussian error assumptions makes them highly sensitive to outliers. We propose a robust estimation method, ROAMS, that mitigates the influence of additive outliers by introducing shift parameters at each timepoint in the observation equation of the SSM. These parameters allow the model to attribute non-zero shifts to outliers while leaving clean observations unaffected. ROAMS then enables automatic outlier detection, through the addition of a penalty term on the number of flagged outlying timepoints in the objective function, and simultaneous estimation of model parameters. We apply the method to robustly estimate SSMs on both simulated data and real-world animal location-tracking data, demonstrating its ability to produce more reliable parameter estimates than classical methods and other benchmark methods. In addition to improved robustness, ROAMS offers practical diagnostic tools, including BIC curves for selecting tuning parameters and visualising outlier structure. These features make our approach broadly useful for researchers and practitioners working with contaminated time series data.

Problem

• Robust estimation method for state-space models with outliers
• Automatic outlier detection in time series data
• Improved parameter estimation for contaminated time series

Innovation

• Introduces shift parameters to adjust for additive outliers
• Adds penalty term for automatic outlier detection
• Provides diagnostic tools for tuning parameter selection