Rethinking Irregular Time Series Forecasting from the Perspective of Basis Functions

Irregular time series forecasting is crucial in many domains, such as healthcare and meteorological observation. However, due to the inherent characteristics of irregular time series, including sparse observations and non-uniform sampling, accurately predicting future dynamics remains challenging. In light of these two characteristics, many existing methods aggregate irregular observations into fixed-dimensional estimated response coefficients through predefined basis functions and use these coefficients as sequence representations. Nevertheless, this modeling paradigm still suffers from two key limitations: (i) a potential non-vanishing asymptotic bias caused by ignoring the sampling density of timestamps; and (ii) the limited adaptability of predefined basis functions to diverse temporal patterns. In this study, we propose a Debiased Neural Basis-Function Network (DNBNet) to address these challenges. Its core is a debiased neural basis-function response mechanism, which corrects asymptotic bias through importance sampling while parameterizing basis functions with neural networks to adapt to diverse temporal patterns. In addition, considering the sparsity of irregular data, we design a novel multi-scale decomposition module based on average pooling, together with a mass-aware fusion mechanism, to obtain richer representations. Finally, a dual-branch decoder is employed for forecasting. Extensive experiments on multiple real-world datasets demonstrate the effectiveness of DNBNet and its strong generalizability across diverse irregular time series scenarios. Our code can be obtained at https://github.com/hnu-vis/DNBNet.

Intervention-Aware Clinical World Model for Post-Op Outcome Forecasting in Cardiology

Many clinical prediction models treat post-intervention outcomes as a one-step mapping from baseline measurements to a future endpoint. However, recovery after a procedure often unfolds as an irregular trajectory: clinical observations, medication changes, repeat interventions, and physiological measurements are recorded asynchronously and can change risk assessment over time. We propose an intervention-aware clinical world model that represents each patient with a structured latent state and evolves it through time-ordered post-intervention events. The model first encodes baseline imaging into a 3D spatial latent state. It then updates this state using procedural context, static covariates, elapsed time, and peri-event physiological embeddings. Follow-up imaging provides training-only supervision through a latent forecasting objective. We apply the framework to atrial fibrillation ablation. During the 90-day recovery window, irregular post-procedure records provide clinically meaningful evidence for long-term recurrence risk. In repeated internal cross-validation on DECAAF-II, our model achieves AUROC 0.756 and AUPRC 0.777 for recurrence prediction. It also achieves a scar-extent MAE of 2.971 percentage points without requiring follow-up MRI intensities at inference. The learned state supports recurrence-risk queries at different horizons and retrospective input editing of blanking-period records.

CT-HEG: A Bidirectional, Timestamp-Attributed Event Graph for ICU In-Hospital Mortality Prediction - An Architectural Ablation Study

Accurate ICU mortality prediction requires modeling irregular clinical observations across heterogeneous entity types. Existing sequence models handle irregular sampling but ignore typed relational structure; existing graph models assume fixed-interval inputs. We introduce the Continuous-Time Heterogeneous EHR Graph (CT-HEG) schema and evaluate which architectural choices drive predictive performance. CT-HEG encodes each ICU stay as a typed, timestamped graph with three node types (visit, vital, lab_event) and 2D edge attributes (t_hours/48, value_norm) encoding timing and value without imputation. We instantiate CT-HEG as CHIRP-Net, a four-layer heterogeneous GATv2Conv network, evaluated on MIMIC-IV v3.1 (31,142 ICU stays, LOS>=48h, 13.4% mortality) with five seeds and bootstrapped confidence intervals, against logistic regression, mTAND, a Transformer, and GRU-D, plus an ablation study. CHIRP-Net achieved 5-seed mean AUROC 0.8449+/-0.0071 (AUPRC 0.4958+/-0.0209); the ensemble achieved AUROC 0.8618 (95% CI: 0.8485-0.8745). Removing reverse edges disconnected observation nodes from the visit readout, cutting AUROC by 0.1968+/-0.0073. Time-attentive edge features contributed 0.0247+/-0.0093 AUROC. Collapsing heterogeneous edge types into one relation (7x fewer parameters) outperformed the full model on all seeds. Post-calibration ECE was 0.0307. Temporal and demographic subgroup analyses were explored but not reported here, pending follow-up work. Bidirectional connectivity was necessary for the model to use its inputs at all, and CT-HEG was reasonably well calibrated after validation-fitted temperature scaling. These results support CT-HEG for irregular EHR data, while external validation, a pre-specified temporal evaluation, and a demographic fairness audit remain necessary before any claim of robustness. Code: https://github.com/nasiruddinstudents-ctrl/chirp-net-mimic-iv.

Causal Discovery on Irregular Time Series

Causal discovery methods have shown strong performance in temporal systems, but they typically rely on regular and discrete lag structures, limiting their applicability to regularly sampled data. However, many real-world tasks require dealing with irregularly sampled streams of events, such as sensor streams, healthcare data, and financial transactions. In this work, we propose an extension of PCMCI+, a state-of-the-art method for causal discovery on regular multivariate time series, to allow for handling irregular time series. Instead of modelling causal relations through fixed-lag dependencies, our method aggregates causal influence over predefined temporal windows. We evaluate our method on synthetic irregular event streams with known causal structures under different signal-to-noise ratios, showing that it consistently recovers the underlying causal graph and substantially outperforms the standard PCMCI+ on irregularly sampled data.

TRIAGE: Dialectical Reasoning for Explainable Risk Prediction on Irregularly Sampled Medical Time Series with LLMs

Clinical early warning systems built on electronic health records, in which clinical observations are recorded as irregularly sampled medical time series (ISMTS), must deliver both calibrated risk scores for patient triage and interpretable rationales that clinicians can verify. Large Language Models (LLMs) have been explored for this task, yet they collapse graded clinical risk into overconfident binary predictions. This risk polarization undermines both calibration and cross-patient comparability. To address this, we propose TRIAGE, a framework that trains an LLM to generate dialectical reasoning over competing clinical outcomes by eliciting outcome-specific rationales. This dialectical formulation mitigates risk polarization, enabling a single LLM to yield continuous risk scores grounded in explicit clinical reasoning. Evaluated on three ISMTS benchmarks, TRIAGE achieves an average AUPRC improvement of 3.3% and reduces calibration error by 81% compared to the competitive baselines. An LLM-as-a-judge assessment further shows that our rationales surpass post-hoc explanations from the baseline by 20% in clinical reasoning quality. The source code is available at https://github.com/HyeongWon-Jang/TRIAGE .

Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observations

Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance. However, real-world deployment is challenging due to the irregular nature of sensor observations, characterized by asynchronous sampling, burst missingness, and temporal jitter. Compounding this issue, purely data-driven models often generate physically implausible degradation trajectories that violate the irreversible nature of damage accumulation. To address this, we propose PC-MambaSDE, a unified continuous-time framework for robust RUL prediction under irregular observations. Specifically, we design a Mask-Aware Continuous Mamba Encoder that explicitly leverages observation masks to extract context-rich control signals. Furthermore, we introduce a Physics-Guided Latent SDE with parametrically rectified hybrid drift, superimposing a global physical bias to enforce monotonic degradation even amid severe observation gaps. Additionally, we formulate RUL prediction as a boundary value problem via a Terminal Degradation Penalty, which decouples a Health Index dimension and applies a penalty loss to guide trajectories toward the failure state. Theoretically, we prove that our variational objective is mathematically equivalent to minimizing the KL divergence via Girsanov's theorem, and we guarantee the global asymptotic stability of the learned dynamics through Lyapunov analysis. To enable rigorous evaluation, we develop a Hybrid Irregularity Generation Scheme that simulates realistic industrial imperfections. Extensive experiments on public benchmarks demonstrate that PC-MambaSDE significantly outperforms state-of-the-art methods, particularly under extreme observation scarcity, validating the efficacy of embedding physical priors into continuous-time latent dynamics.