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

arXiv: https://arxiv.org/abs/2509.19577 · HTML: https://mlsanity.com/paper/2509.19577/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 49 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Common Voice: A Massively-Multilingual Speech Corpus](https://mlsanity.com/paper/1912.06670/) (2019)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [rVAD: An Unsupervised Segment-Based Robust Voice Activity Detection Method](https://mlsanity.com/paper/1906.03588/) (2019)
- [Deep Imputation of Missing Values in Time Series Health Data: A Review with Benchmarking](https://mlsanity.com/paper/2302.10902/) (2023)
- [Functional Regression](https://mlsanity.com/paper/1406.4068/) (2014)
- [MAGMA: Inference and Prediction with Multi-Task Gaussian Processes](https://mlsanity.com/paper/2007.10731/) (2020)
- [Cluster-Specific Predictions with Multi-Task Gaussian Processes](https://mlsanity.com/paper/2011.07866/) (2020)

## Abstract (arXiv)

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.