Variational Inference of Joint Models using Multivariate Gaussian Convolution Processes

Abstract

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.

References in corpus (5)

• Deep Gaussian Processes
• Heterogeneous Multi-output Gaussian Process Prediction
• Rates of Convergence for Sparse Variational Gaussian Process Regression
• Joint Modeling of Event Sequence and Time Series with Attentional Twin Recurrent Neural Networks
• Fast Kernel Approximations for Latent Force Models and Convolved Multiple-Output Gaussian processes

Cited by in corpus (2)

• Weakly-supervised Multi-output Regression via Correlated Gaussian Processes
• The Renyi Gaussian Process: Towards Improved Generalization