Spectral structure learning for clinical time series

TL;DR

The paper develops StructGP, a structured multi-task Gaussian process for learning dependency graphs among irregularly sampled clinical time series across multiple patients. It encodes ordered conditional relations via a sparse impulse-response structure and learns a DAG using a differentiable acyclicity constraint implemented through an augmented Lagrangian framework with proximal gradient updates, combined with grid-search for sparsity selection. Through toy and larger simulation studies, the approach demonstrates capacity to recover the true graph structure with high recall and reasonable precision, while highlighting the importance of the regularization path for graph identification. The work advances scalable, data-driven discovery of temporal dependencies in EHR time series and discusses practical considerations such as standardization sensitivity and potential GPU-enabled scaling.

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.

Figures (4)

• Figure 1: A toy model with 4 tasks We sample a random graph whose adjacency matrix sparsity pattern encodes ordered conditional relations between time series (a). We recover the parameters and order of variables from observations sampled uniformly and independently between tasks (see section \ref{['sec:simstudy']}).
• Figure 2: Average metrics for an increasing number of patients Reports of 'EXP1', increasing the number of patients for 10 tasks and 10 observations per task. The predicted graph (purple dots) is compared with a random graph from the same graph distribution (orange dots). The simulated graphs are random graphs with mean degree 2. Error bars represent bootstrap 95% confidence intervals.
• Figure 3: Average metrics for an increasing number of grid search steps ($n_{\lambda}$) Reports of 'EXP2', an increasing number of grid search steps for 50 patients, 10 tasks, 10 observations per task, and random graph of mean degree 3. The predicted graph (red dots) is compared with a random graph from the same graph distribution (blue dots), and also with a predicted graph directly fitted from a random initialization with the optimal $\lambda_*$ found from grid search (green dots). Error bars represent bootstrap 95% confidence intervals.
• Figure 4: Average metrics for an increasing number of tasks Reports of 'EXP3', an increasing number of tasks for 50 patients, and 10 observations per task. The predicted graph (purple dots) is compared with a random graph from the same graph distribution (orange dots). Error bars represent bootstrap 95% confidence intervals.