Interpretable Hybrid-Rule Temporal Point Processes

TL;DR

This work tackles the interpretability–accuracy gap in Temporal Point Processes for medical event data by introducing HRTPP, a hybrid framework that unifies a basic intensity, a rule-based intensity encoding temporal logic rules, and a numerical feature intensity. The final intensity is given by $\\lambda(t|\\mathcal{H}_t) = \\text{Softplus}(\\lambda_{\\text{base}}(t) + \\lambda_{\\text{rule}}(t) + \\lambda_{\\text{num}}(t))$, with $\\lambda_{\\text{rule}}(t) = \\sum_{R_j} \\alpha_j e_j(t)$ and $\\lambda_{\\text{num}}(t) = \\sum_k \\beta_k g_k(t)$, enabling expressive yet interpretable modeling. A two-phase rule mining strategy with Bayesian optimization selects a compact, clinically meaningful rule set, and evaluation on four MIMIC-IV disease datasets demonstrates superior predictive performance and interpretability against state-of-the-art interpretable TPPs. The results reveal rules aligned with medical knowledge, providing transparent progression insights and supporting clinical decision-making. Together, these contributions offer a practical framework for interpretable, data-driven medical event modeling with real-time diagnostic support.

Abstract

Temporal Point Processes (TPPs) are widely used for modeling event sequences in various medical domains, such as disease onset prediction, progression analysis, and clinical decision support. Although TPPs effectively capture temporal dynamics, their lack of interpretability remains a critical challenge. Recent advancements have introduced interpretable TPPs. However, these methods fail to incorporate numerical features, thereby limiting their ability to generate precise predictions. To address this issue, we propose Hybrid-Rule Temporal Point Processes (HRTPP), a novel framework that integrates temporal logic rules with numerical features, improving both interpretability and predictive accuracy in event modeling. HRTPP comprises three key components: basic intensity for intrinsic event likelihood, rule-based intensity for structured temporal dependencies, and numerical feature intensity for dynamic probability modulation. To effectively discover valid rules, we introduce a two-phase rule mining strategy with Bayesian optimization. To evaluate our method, we establish a multi-criteria assessment framework, incorporating rule validity, model fitting, and temporal predictive accuracy. Experimental results on real-world medical datasets demonstrate that HRTPP outperforms state-of-the-art interpretable TPPs in terms of predictive performance and clinical interpretability. In case studies, the rules extracted by HRTPP explain the disease progression, offering valuable contributions to medical diagnosis.

Figures (4)

• Figure 1: The framework of model. In the HRTPP component, given a candidate rule set and event sequences, the model can compute the likelihood of the intensity function. The model integrates three key intensity components: basic intensity, rule-based intensity, and numerical feature intensity, which together determine the overall event intensity function $\lambda(t | \mathcal{H}_t)$. The numerical feature intensity captures the influence of continuous-valued attributes using a numerical feature encoder and a masking mechanism. The rule-based intensity encodes temporal dependencies through predefined rule set. In the rule set mining and optimizing component, Bayesian optimization iteratively refines the rule set by utilizing HRTPP computed likelihoods to guide the sampling distribution over the search space. The selected rules provide interpretable explanations of critical events via their impact on the intensity function dynamics.
• Figure 2: Hierarchical relationships of CAD indicators. The indicators in green boxes are direct indicators, and those in blue boxes are indirect indicators. Arrows denote dependencies between indicators in a cause-effect manner.
• Figure 3: Frequency of direct rules in five runs.
• Figure 4: Overall intensity over time for a CAD patient. The red curve represents the intensity of the target variable, reflecting the probability of death. Key events affecting the mortality are annotated below the curve, while the timing of logic rules is marked above. The entire figure illustrates the patient's full clinical progression in the ICU.