PGP-Clinical-TimeKAN: Prior-Guided Joint Probabilistic Forecasting of Clinical Trajectories

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.

Clinical irregular multivariate time series are shaped not only by physiological dynamics but also by the measurement process that determines when and what to observe. In event-centric models, however, co-timestamp structure can be flattened too early: measurements acquired at the same timestamp are embedded as isolated nodes, leaving local patient-state context unavailable until later message-passing layers. We study this pre-propagation representation bottleneck and address it by restoring co-timestamp context before message passing begins. We propose MissHyper, a missingness-guided hypergraph forecasting model with pre-propagation synchronicity restoration. MissHyper augments each event with a local support-density cue, aggregates co-timestamp records to recover patient-state context, and uses a missingness-guided gate to adaptively fuse node-specific evidence with the recovered context. Across PhysioNet 2012, MIMIC-III, and MIMIC-IV, MissHyper achieves consistent gains in multi-step forecasting and outperforms a strong hypergraph baseline. These results suggest that improving event initialization can benefit sparse clinical forecasting without requiring a redesigned downstream propagation architecture. Ablations indicate that snapshot restoration, adaptive fusion, and support-density encoding all contribute, pointing to event initialization as a critical design axis for sparse clinical forecasting.

Joint-embedding predictive architectures (JEPA) learn representations by predicting in latent space, as in computer vision; retaining the action-conditioned predictor at inference turns them into latent world models, enabling planning in robotics (V-JEPA 2-AC). Bringing this design to EHR patient trajectories---a predictor that simulates a patient's trajectory in latent space---has not been explored. We use an LLM as the encoder, reading the hourly record as text, avoiding feature engineering and vocabulary harmonisation. But an LLM adapted by supervised fine-tuning does not organise its latent space around physiological dynamics, and freezing it to train the predictor, as in V-JEPA 2-AC, leaves the encoder unaware of the rollout signal: the predictor degrades under rollout. We instead co-train encoder and predictor under one latent-prediction objective, grounding the encoder in the dynamics its predictor must follow. Naïve co-training, however, is unstable: the untrained predictor drags the encoder toward collapse, and the predictor's rollout diverges as its target space moves. We present Clin-JEPA, a five-phase curriculum that stably co-trains an LLM encoder with a latent trajectory predictor on MIMIC-IV. Three evaluations support the design: (1) under 48-hour autoregressive rollout the co-trained predictor degrades least (predictor degradation $\times$1.06, against $\times$1.23--1.36 for two-stage designs and $\times$6.3--66 for curriculum ablations) while the co-trained encoder resolves the progression of patient state most sharply (largest state displacement); (2) the co-trained encoder separates deteriorating from stable patients in its latent space with Cohen's $d{=}1.59$, against $\leq$0.50 for two-stage encoders; (3) one set of embeddings serves 34 downstream tasks across three benchmarks, outperforming strong per-task tuned baselines and a pretrained EHR foundation model.