Clinical Risk: wavelet reconstruction networks for marked point processes

Jeremy C. Weiss

Abstract: Timestamped sequences of events, pervasive in domains with data logs, e.g., health records, are often modeled as point processes with rate functions over time. Leading classical methods for risk scores such as Cox and Hawkes processes use such data but make strong assumptions about the shape and form of multivariate influences, resulting in time-to-event distributions irreflective of many real world processes. Recent methods in point processes and recurrent neural networks capably model rate functions but may be complex and difficult to interrogate. Our work develops a high-performing, interrogable model. We introduce wavelet reconstruction networks, a multivariate point process with a sparse wavelet reconstruction kernel to model rate functions from marked, timestamped data. We show they achieve improved performance and interrogability over baselines in forecasting complications and scheduled care visits in patients with diabetes.

TL;DR: Wavelet reconstructions on relative time, used in absolute-time point process models, improve risk prediction of complications and adherence in diabetes.

Keywords: point processes, wavelets, temporal neural networks, Hawkes processes