Towards Robust Prediction Using The Elliptical Process for Regression

A.B. Al Khabori*, M.T. Alodat and Amadou Sarr

Department of Statistics, Sultan Qaboos University, Al-Khod Muscat, Sultanate of Oman

Abstract:

We present a novel Bayesian family of models, Elliptical Processes (EPs), designed to extend regression modeling framework. Unlike the widely used Gaussian Process (GP) Regression, EPs generalize the GP framework by accommodating non-normal tail distributions and outlier-prone data, where Gaussian assumptions often fail. In this paradigm, the GP is still a special case, but EPs are more accurate, especially when dealing with heavy-tailed data. We use the Laplace approximation technique to ensure scalability and computational efficiency while addressing the analytical complexity inherent in EP inference. We derive the predictive distribution for EPs at new input points and provide a comprehensive performance comparison with GP, T-Process, and other EP models. The proposed EP, particularly under non-Gaussian assumptions, outperform the GP by demonstrating superior performance and flexibility in handling complex data structures across both simulated and real-world scenarios.

Keywords: Bayesian Inference, Elliptical Process, Gaussian Process, Laplace approximation, Predictive distribution, Regression.

Pages: 47 – 85 | Full PDF Paper