Healthcare data, such as Intensive Care Unit (ICU) records, comprise heterogeneous multivariate time series sampled at irregular intervals with pervasive missingness. However, clinical applications demand predictive models that are both accurate and interpretable. We present our Graph Attention-based Relational Learning for Intensive Care (GARLIC) model, a novel neural network architecture that imputes missing data through a learnable exponential-decay encoder, captures inter-sensor dependencies via time-lagged summary graphs, and fuses global patterns with cross-dimensional sequential attention. All attention weights and graph edges are learned end-to-end to serve as built-in observation-, signal-, and edge-level explanations. To reconcile auxiliary reconstruction and primary classification objectives, we developed an alternating decoupled optimization scheme that stabilizes training. On three ICU benchmarks (PhysioNet 2012 & 2019, MIMIC-III), GARLIC sets the new state of the art in outcome prediction, significantly improving AUROC and AUPRC over best-performing baselines at comparable computational cost. Ablation studies confirm the contribution of each module, and feature-removal trials validate the fidelity of importance attribution through a monotonic performance drop (full > top 50% > random 50% > bottom 50%). Real-time case studies demonstrate actionable risk warnings with transparent explanations, marking a significant advance toward accurate, explainable deep learning for irregularly sampled ICU time series data. Moreover, we demonstrated \proposed{}'s superiority in data imputation and classification on various time-series datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks.
In healthcare, multimodal time series tasks often operate on incomplete observations in practice, for example when ECG segments are lost because electrodes detach or an entire respiratory channel is unavailable during overnight monitoring. Such missingness typically appears in two structurally distinct patterns: within-modality missing, where values are absent within an otherwise observed modality, and modality-level missing, where an entire modality is unavailable. Existing methods typically represent unobserved data implicitly through masks or missing embeddings, without learning instance-specific missing information, and most are designed for only one missingness pattern. A natural approach is to explicitly estimate the missing data; however, existing imputation methods treat missingness uniformly despite their different structural priors, and the imputation process is often isolated from downstream tasks, preventing downstream tasks from guiding imputation toward more informative representations. To address these limitations, we present PAMF, a multimodal time-series framework that explicitly handles different missingness patterns while coupling imputation with downstream prediction through prior-aware flow matching and weight sharing. Specifically, the method initializes the flow-matching source state with type-specific priors to distinguish two missing types. It further connects imputation and classification through architecturally matched encoders with weight sharing, transferring task-relevant representations into the imputation process. Experiments on multiple multimodal healthcare time-series benchmarks show that the proposed method achieves the strongest overall downstream performance across diverse datasets and missing settings compared with existing baselines.