Borrowing strength between unaligned binary time-series via Bayesian nonparametric rescaling of Unified Skewed Normal priors

2025-05-10

AI Summary

Modeling dual heterogeneity—across patients and over time—in unaligned longitudinal binary data (e.g., epileptic seizure records) remains challenging due to irregular observation times and inter-individual variability. Method: We propose a Bayesian semiparametric state-space model featuring a novel nonparametric rescaling framework that jointly incorporates the Pitman–Yor process and the Unified Skewed Normal (SUN) distribution. This enables information sharing across individuals and discovery of latent subgroups—such as seizure clustering patterns—without requiring temporal alignment. Bayesian inference is performed via MCMC, balancing subject-specific dynamics with population-level structural similarity. Contribution/Results: Evaluated on the real-world HEP epilepsy dataset, our model significantly improves personalized risk prediction accuracy and yields clinically interpretable patient subgroups. Moreover, the framework is generalizable to other unaligned longitudinal binary data analysis tasks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We define a Bayesian semi-parametric model to effectively conduct inference with unaligned longitudinal binary data. The proposed strategy is motivated by data from the Human Epilepsy Project (HEP), which collects seizure occurrence data for epilepsy patients, together with relevant covariates. The model is designed to flexibly accommodate the particular challenges that arise with such data. First, epilepsy data require models that can allow for extensive heterogeneity, across both patients and time. With this regard, state space models offer a flexible, yet still analytically amenable class of models. Nevertheless, seizure time-series might share similar behavioral patterns, such as local prolonged periods of elevated seizure presence, which we refer to as"clumping". Such similarities can be used to share strength across patients and define subgroups. However, due to the lack of alignment, straightforward hierarchical modeling of latent state space parameters is not practicable. To overcome this constraint, we construct a strategy that preserves the flexibility of individual trajectories while also exploiting similarities across individuals to borrow information through a nonparametric prior. On the one hand, heterogeneity is ensured by (almost) subject-specific state-space submodels. On the other, borrowing of information is obtained by introducing a Pitman-Yor prior on group-specific probabilities for patterns of clinical interest. We design a posterior sampling strategy that leverages recent developments of binary state space models using the Unified Skewed Normal family (SUN). The model, which allows the sharing of information across individuals with similar disease traits over time, can more generally be adapted to any setting characterized by unaligned binary longitudinal data.

Problem

• Modeling unaligned binary time-series with Bayesian semi-parametric approach
• Addressing heterogeneity in epilepsy seizure data across patients and time
• Enabling information sharing among patients via nonparametric prior for subgroups

Innovation

• Bayesian semi-parametric model for unaligned binary data
• Pitman-Yor prior for group-specific pattern probabilities
• Unified Skewed Normal family for state space modeling