Differentiable latent structure discovery for interpretable forecasting in clinical time series

arXiv cs.LG / 5/1/2026

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Key Points

The paper introduces StructGP, a continuous-time multi-task Gaussian process that learns a sparse, ordered dependency structure as a directed acyclic graph (DAG) for interpretable forecasting from irregular EHR time series.
It further proposes LP-StructGP, adding latent pathway components modeled with temporally shifted, subject-specific coupling filters and softmax gating to capture cross-patient progression patterns.
Both models are trained with sparsity and acyclicity constraints (via augmented Lagrangian) using scalable low-rank updates, enabling practical optimization with Adam.
In simulations, StructGP reliably recovers the ground-truth graphs and pathway assignments, and on real datasets (MIMIC-IV septic shock and PhysioNet Challenge) it improves forecasting accuracy and calibration of uncertainty compared with independent-task and unstructured-kernel baselines.
The results suggest that structured process convolutions plus latent pathway modeling can provide interpretable, scalable, and well-calibrated clinical forecasting for irregular time series.

Abstract

Background: Timely, uncertainty-aware forecasting from irregular electronic health records (EHR) can support critical-care decisions, yet most approaches either impute to a grid or sacrifice interpretability. We introduce StructGP, a continuous-time multi-task Gaussian process that couples process convolutions with differentiable structure learning to uncover a sparse, ordered directed acyclic graph (DAG) of inter-variable dependencies while preserving principled uncertainty. We further propose LP-StructGP, which augments StructGP with latent pathways-shared, temporally shifted trajectories inferred via subject-specific coupling filters and a softmax gating mechanism-to capture cross-patient progression patterns. Both models are trained under sparsity and acyclicity constraints (augmented Lagrangian, Adam) using scalable low-rank updates. Results: In simulations, the approach reliably recovers ground-truth graphs (Structural Hamming Distance approaching 0 as cohorts grow) and pathway assignments (high Adjusted Rand Index). On a MIMIC-IV septic shock cohort (n=1,008; norepinephrine, creatinine, mean arterial pressure), StructGP improves short-horizon (6 h) forecasting over independent-task baselines (average RMSE 0.68 [95%CI: 0.63--0.74] vs. 0.88 [0.83-0.94]) and, with 15 additional inputs, markedly outperforms unstructured kernels (0.63 [0.58-0.69] vs. 3.02 [2.85-3.18]) with superior calibration (coverage 0.96 vs. 0.84). On the PhysioNet Challenge (12k patients, 41 variables), StructGP attains competitive accuracy (MAE 3.72e-2) relative to a state-of-the-art graph neural model while maintaining calibrated uncertainty. Conclusion: These results show that structured process convolutions with latent pathways deliver interpretable, scalable, and well-calibrated forecasting for irregular clinical time series.