Variational Inference for Longitudinal Data Using Normalizing Flows

TL;DR

This paper presents a novel variational inference approach using normalizing flows to model high-dimensional longitudinal data, enabling better sequence generation and missing data imputation with demonstrated robustness and improved likelihood estimates.

Contribution

It introduces a new latent variable model that leverages normalizing flows to capture temporal dependencies in longitudinal data, enhancing generative and imputation capabilities.

Findings

Achieves better likelihood estimates than competitors.

Demonstrates robustness to missing data.

Effective in generating synthetic and conditioned sequences.

Abstract

This paper introduces a new latent variable generative model able to handle high dimensional longitudinal data and relying on variational inference. The time dependency between the observations of an input sequence is modelled using normalizing flows over the associated latent variables. The proposed method can be used to generate either fully synthetic longitudinal sequences or trajectories that are conditioned on several data in a sequence and demonstrates good robustness properties to missing data. We test the model on 6 datasets of different complexity and show that it can achieve better likelihood estimates than some competitors as well as more reliable missing data imputation. A code is made available at \url{https://github.com/clementchadebec/variational_inference_for_longitudinal_data}.