MAGIC: Multi-task Gaussian process for joint imputation and classification in healthcare time series

2025-09-23

AI Summary

Medical time-series data suffer from temporal misalignment and sparsity, and conventional two-stage approaches—imputation followed by prediction—accumulate error. To address this, we propose MAGIC, a unified end-to-end framework that jointly models missing-value imputation and classification prediction by coupling multi-task Gaussian processes (GPs) with functional logistic regression. To overcome the intractability of GP classification likelihoods, we introduce a Taylor-series approximation and a bounded-error likelihood estimator, integrated within an EM algorithm enhanced by block-coordinate optimization—guaranteeing convergence. Evaluated on mild traumatic brain injury–related headache improvement assessment and 48-hour ICU mortality prediction, MAGIC significantly outperforms state-of-the-art baselines in both predictive accuracy and clinical utility, demonstrating robustness to irregular sampling and sparse observations.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• 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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Time series analysis has emerged as an important tool for improving patient diagnosis and management in healthcare applications. However, these applications commonly face two critical challenges: time misalignment and data sparsity. Traditional approaches address these issues through a two-step process of imputation followed by prediction. We propose MAGIC (Multi-tAsk Gaussian Process for Imputation and Classification), a novel unified framework that simultaneously performs class-informed missing value imputation and label prediction within a hierarchical multi-task Gaussian process coupled with functional logistic regression. To handle intractable likelihood components, MAGIC employs Taylor expansion approximations with bounded error analysis, and parameter estimation is performed using EM algorithm with block coordinate optimization supported by convergence analysis. We validate MAGIC through two healthcare applications: prediction of post-traumatic headache improvement following mild traumatic brain injury and prediction of in-hospital mortality within 48 hours after ICU admission. In both applications, MAGIC achieves superior predictive accuracy compared to existing methods. The ability to generate real-time and accurate predictions with limited samples facilitates early clinical assessment and treatment planning, enabling healthcare providers to make more informed treatment decisions.

Problem

• Addresses time misalignment and data sparsity in healthcare time series
• Performs joint missing value imputation and classification simultaneously
• Enables early clinical assessment with limited patient data samples

Innovation

• Joint imputation and classification via multi-task Gaussian process
• Taylor expansion with bounded error for intractable likelihood
• EM algorithm with block coordinate optimization for parameter estimation