Bayesian Outlier Detection for Matrix-variate Models

2025-03-25

AI Summary

This paper addresses outlier detection in high-dimensional matrix-valued economic and financial time series. Methodologically, it proposes an online Bayesian real-time monitoring framework: (i) extends predictive Bayes factors to matrix-variate models for the first time; (ii) introduces a power discounting prior perturbation mechanism to bypass MCMC sampling and enable closed-form posterior inference; and (iii) derives an uncertainty quantification criterion and designs a robust refinement strategy. Key contributions are: (1) the first sequential Bayesian anomaly detection paradigm specifically designed for matrix-structured data; (2) a statistically rigorous yet computationally efficient approach enabling low-latency streaming analysis; and (3) empirical validation—across macroeconomic and financial benchmark datasets as well as synthetic experiments—demonstrating high detection accuracy, low computational overhead, and strong real-time performance.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Bayes Factor (BF) is one of the tools used in Bayesian analysis for model selection. The predictive BF finds application in detecting outliers, which are relevant sources of estimation and forecast errors. An efficient framework for outlier detection is provided and purposely designed for large multidimensional datasets. Online detection and analytical tractability guarantee the procedure's efficiency. The proposed sequential Bayesian monitoring extends the univariate setup to a matrix--variate one. Prior perturbation based on power discounting is applied to obtain tractable predictive BFs. This way, computationally intensive procedures used in Bayesian Analysis are not required. The conditions leading to inconclusive responses in outlier identification are derived, and some robust approaches are proposed that exploit the predictive BF's variability to improve the standard discounting method. The effectiveness of the procedure is studied using simulated data. An illustration is provided through applications to relevant benchmark datasets from macroeconomics and finance.

Problem

• Detecting anomalies in economic and financial matrix-variate data
• Extending Bayesian outlier detection to multidimensional datasets
• Providing computationally efficient online detection with analytical tractability

Innovation

• Bayesian framework for outlier detection
• Extends univariate to matrix-variate models
• Uses power-discounted priors for tractability