Bayesian Circular Regression with von Mises Quasi-Processes

2024-06-19

AI Summary

This paper addresses regression tasks involving circular-valued outputs (e.g., angles, phases) by proposing a Bayesian nonparametric model based on the von Mises distribution. Unlike conventional approaches—such as wrapped Gaussian processes or radial marginalization—the method constructs a “von Mises pseudo-process” that directly models the input–output mapping on the unit circle, inheriting both maximum-entropy density properties and interpretability. Methodologically, it introduces Stratonovich-style data augmentation to enable efficient Gibbs sampling and devises a novel dual Metropolis–Hastings algorithm for Bayesian inference on circular domains. Evaluated on wind direction forecasting and gait cycle phase estimation, the model achieves state-of-the-art predictive accuracy, superior calibration, and reliable uncertainty quantification—outperforming existing circular regression methods across all metrics.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes targeting two Euclidean dimensions conditioned on the unit circle. The probability model has connections with continuous spin models in statistical physics. Moreover, its density is very simple and has maximum-entropy, unlike previous Gaussian process-based approaches, which use wrapping or radial marginalization. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling. We argue that transductive learning in these models favors a Bayesian approach to the parameters and apply our sampling scheme to the Double Metropolis-Hastings algorithm. We present experiments applying this model to the prediction of (i) wind directions and (ii) the percentage of the running gait cycle as a function of joint angles.

Problem

• Develops Bayesian circular regression for predicting circular values.
• Introduces von Mises quasi-processes for interpretable circular distributions.
• Applies model to wind direction and gait cycle prediction.

Innovation

• Bayesian circular regression with von Mises quasi-processes
• Stratonovich-like augmentation for fast Gibbs sampling
• Double Metropolis-Hastings algorithm for transductive learning