Balancing Interpretability and Flexibility in Modeling Diagnostic Trajectories with an Embedded Neural Hawkes Process Model

TL;DR

This work addresses the tradeoff between interpretability and flexibility in modeling diagnostic trajectories with Hawkes processes. It introduces the Embedded Neural Hawkes Process (ENHP), which learns a neural impact kernel in a low-dimensional event embedding space to capture complex dependencies while preserving additive, nonnegative intensity and interpretability. A contextualized variant (ENHP-C) using transformer encoders is offered to trade interpretability for extra flexibility, though results show the base kernel often suffices. Applied to large-scale EHR datasets, ENHP yields clinically meaningful topic-level interactions and temporal impact functions $\phi_{i,j}(t)$ that illuminate how early events influence later diagnoses, enabling hypothesis generation and interpretability alongside competitive predictive performance.

Abstract

The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected to understand how each event modulates the intensity of others. Neural network-based HPs offer greater flexibility, resulting in improved fit and prediction performance, but at the cost of interpretability, which is often critical in healthcare. In this work, we aim to understand and improve upon this tradeoff. We propose a novel HP formulation in which impact functions are modeled by defining a flexible impact kernel, instantiated as a neural network, in event embedding space, which allows us to model large-scale event sequences with many event types. This approach is more flexible than traditional HPs yet more interpretable than other neural network approaches, and allows us to explicitly trade flexibility for interpretability by adding transformer encoder layers to further contextualize the event embeddings. Results show that our method accurately recovers impact functions in simulations, achieves competitive performance on MIMIC-IV procedure dataset, and gains clinically meaningful interpretation on Duke-EHR with children diagnosis dataset even without transformer layers. This suggests that our flexible impact kernel is often sufficient to capture self-reinforcing dynamics in EHRs and other data effectively, implying that interpretability can be maintained without loss of performance.

Figures (8)

• Figure 1: Architecture of the ENHP and ENHP-C. Without the event embedding and transformer encoder, the impact function follows formula\ref{['eq:method_eij']}. Without the transformer encoder, it follows formula\ref{['eq:method_embed']}. With all components, it corresponds to formula\ref{['eq:method_TF']}.
• Figure 2: Fitted triggering kernel using ENHP
• Figure 3: Performance comparison across datasets and models based on log-likelihood
• Figure 4: Heatmap of different datasets with regard to impact function or kernel function.
• Figure 5: Recovered impact functions $\phi_{i,j}(t)$ where $j$ is the ADHD diagnosis, $i$ is developmental disorders of speech and language (blue line), conduct disorder (green line), and autistic disorder (red line), respectively