# Variational Inference of Joint Models using Multivariate Gaussian Convolution Processes

arXiv: https://arxiv.org/abs/1903.03867 · HTML: https://mlsanity.com/paper/1903.03867/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2019.

## Built on by (most cited first, 4 of 4)

- [Fed-Joint: Joint Modeling of Nonlinear Degradation Signals and Failure Events for Remaining Useful Life Prediction using Federated Learning](https://mlsanity.com/paper/2503.13404/) (2025)
- [Bayesian Joint Model of Multi-Sensor and Failure Event Data for Multi-Mode Failure Prediction](https://mlsanity.com/paper/2506.17036/) (2025)
- [General Value Functions for Remaining Useful Life and Failure-Mode Prediction](https://mlsanity.com/paper/2607.22268/) (2026)
- [Collaborative System Failure Prognostics via Federated Longitudinal-Survival Modeling](https://mlsanity.com/paper/2607.26038/) (2026)

## Abstract (arXiv)

We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the evolution of longitudinal signals and a Cox model to map time-to-event data with longitudinal data modeled through the MGCP. Taking advantage of the unique structure imposed by convolved processes, we provide a variational inference framework to simultaneously estimate parameters in the joint MGCP-Cox model. This significantly reduces computational complexity and safeguards against model overfitting. Experiments on synthetic and real world data show that the proposed framework outperforms state-of-the art approaches built on two-stage inference and strong parametric assumptions.