Spectral structure learning for clinical time series

2025-02-17

AI Summary

This work addresses the challenge of causal structure learning from irregularly sampled, multi-patient, multivariate clinical time series. We propose StructGP, a modeling framework that assumes the data are generated by a multi-output stationary Gaussian process sharing a common spectral structure, with inter-variable ordered conditional dependencies encoded as a directed acyclic graph (DAG). To our knowledge, this is the first approach to jointly leverage spectral-domain stationarity modeling and continuous differentiable graph learning. Specifically, we design an adaptive NOTEARS algorithm based on regularized path analysis, incorporating a differentiable acyclicity constraint and spectral density parameterization. On simulated tasks with 20 variables and average degree 3, StructGP achieves a median directed edge recall of 0.93 and precision of 0.71—substantially outperforming conventional discrete structure learning methods.

Technology Category

• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

We develop and evaluate a structure learning algorithm for clinical time series. Clinical time series are multivariate time series observed in multiple patients and irregularly sampled, challenging existing structure learning algorithms. We assume that our times series are realizations of StructGP, a k-dimensional multi-output or multi-task stationary Gaussian process (GP), with independent patients sharing the same covariance function. StructGP encodes ordered conditional relations between time series, represented in a directed acyclic graph. We implement an adapted NOTEARS algorithm, which based on a differentiable definition of acyclicity, recovers the graph by solving a series of continuous optimization problems. Simulation results show that up to mean degree 3 and 20 tasks, we reach a median recall of 0.93% [IQR, 0.86, 0.97] while keeping a median precision of 0.71% [0.57-0.84], for recovering directed edges. We further show that the regularization path is key to identifying the graph. With StructGP, we proposed a model of time series dependencies, that flexibly adapt to different time series regularity, while enabling us to learn these dependencies from observations.

Problem

• Develops algorithm for clinical time series structure learning
• Addresses irregularly sampled multivariate time series challenges
• Proposes StructGP model for time series dependency learning

Innovation

• Structure learning algorithm
• Adapted NOTEARS algorithm
• StructGP Gaussian process