Compositionally-warped Gaussian processes.

Area of Science:

• Machine Learning
• Statistical Modeling

Background:

• Gaussian processes (GPs) are flexible nonparametric models but are limited to Gaussian marginal distributions.
• Modeling non-Gaussian data often requires warping GPs (WGPs), which can be computationally intensive due to numerical inverse warping approximations.
• Existing methods like Bayesian WGPs and deep GPs also face computational challenges.

Purpose of the Study:

• To develop a novel Gaussian process model capable of handling non-Gaussian data efficiently.
• To address the computational limitations of existing warped Gaussian process methods.
• To propose a generative model with a deep compositional architecture and analytical inverse warping.

Main Methods:

• Constructed a new class of warpings by composing multiple elementary functions with known explicit inverses.
• Developed the compositionally-warped Gaussian process (CWGP) model.
• Employed a deep compositional architecture for enhanced expressiveness and analytical inverse warping for computational efficiency.

Main Results:

• The proposed CWGP model demonstrated robustness to the choice of warpings.
• Achieved more accurate point predictions compared to standard warped Gaussian processes.
• Resulted in better trained models and significantly shorter computation times.

Conclusions:

• The compositionally-warped Gaussian process (CWGP) offers an efficient and accurate solution for modeling non-Gaussian data.
• CWGP overcomes the computational drawbacks of traditional warped Gaussian processes through analytical inverse warping.
• The model's deep compositional architecture enhances its expressiveness and predictive performance.