Gaussian Process Regression for Value-Censored Functional and Longitudinal Data

Area of Science:

• Statistics
• Machine Learning
• Bayesian Inference

Background:

• Gaussian process (GP) regression is a powerful tool for non-parametric Bayesian modeling of smooth functions.
• Handling censored data in GP regression is crucial for accurate analysis, especially in longitudinal studies.

Purpose of the Study:

• To develop an exact and closed-form solution for Gaussian process regression with value-based censored observations.
• To extend the method for both single-curve fitting and hierarchical models, accommodating various censoring types (left, right, interval).

Main Methods:

• Derivation of conditional posterior distributions for underlying functions under censoring.
• Application as an empirical Bayes method or integration within Markov-Chain Monte Carlo (MCMC) samplers.
• Validation through extensive simulations and real-world data analysis.

Main Results:

• The proposed method provides exact and closed-form solutions for censored GP regression.
• Demonstrated substantial performance improvement over naive approaches that ignore or misinterpret censored data.
• Successfully applied to longitudinal HIV-1 RNA measurements with left-censored data.

Conclusions:

• The developed Gaussian process regression method effectively handles censored data, offering superior performance.
• This approach provides a robust framework for Bayesian modeling with censored observations in diverse scientific applications.
• The method is valuable for analyzing data with detection limits or other forms of censoring.