# Latent Factor Point Processes for Patient Representation in Electronic Health Records

## TL;DR

This paper introduces a latent factor point process model for EHR data that captures complex temporal structures and underlying disease processes, improving patient representation for classification and clustering tasks.

## Contribution

It proposes a novel low-rank point process model and Fourier-Eigen embedding for efficient, interpretable patient representations from high-dimensional EHR data.

## Key findings

- Effective in capturing subgroup-specific temporal patterns
- Improves classification and clustering of patient data
- Demonstrated on Alzheimer's disease cohort

## Abstract

Electronic health records (EHR) contain valuable longitudinal patient-level information, yet most statistical methods reduce the irregular timing of EHR codes into simple counts, thereby discarding rich temporal structure. Existing temporal models often impose restrictive parametric assumptions or are tailored to code level rather than patient-level tasks. We propose the latent factor point process model, which represents code occurrences as a high-dimensional point process whose conditional intensity is driven by a low dimensional latent Poisson process. This low-rank structure reflects the clinical reality that thousands of codes are governed by a small number of underlying disease processes, while enabling statistically efficient estimation in high dimensions. Building on this model, we introduce the Fourier-Eigen embedding, a patient representation constructed from the spectral density matrix of the observed process. We establish theoretical guarantees showing that these embeddings efficiently capture subgroup-specific temporal patterns for downstream classification and clustering. Simulations and an application to an Alzheimer's disease EHR cohort demonstrate the practical advantages of our approach in uncovering clinically meaningful heterogeneity.