GARLIC: Graph Attention-based Relational Learning of Multivariate Time Series in Intensive Care

The paper introduces GARLIC (Graph Attention-based Relational Learning for Intensive Care), a novel neural network architecture designed to address challenges in analyzing Intensive Care Unit (ICU) data. The authors note that Healthcare data, such as Intensive Care Unit (ICU) records, comprise heterogeneous multivariate time series sampled at irregular intervals with pervasive missingness. The work is motivated by two key challenges: "First, the inherent irregularity and heterogeneity of clinical measurements render standard sequence models (e.g., RNNs, Transformers) suboptimal: naïve imputation biases downstream tasks, while specialized approaches often ignore inter-sensor dependencies. Second, interpretability is paramount in healthcare, but prevalent post-hoc methods demand extra computation and can yield inconsistent explanations."

GARLIC is described as a unified framework that simultaneously addresses irregular sampling, missingness, and the need for transparent decision making. The architecture consists of three main components:

The model uses a decay-based latent feature encoder with an exponential-decay mechanism to handle missing data. The imputed value is calculated as: x̂k,t = γt xk,t′ + (1 − γt)x̄k, where γt = exp −max(0, wk∆t + bk). The model constructs an augmented input at each time step to retain both the observed or imputed value and the missingness indicator. Each signal is processed through a dedicated two-layer MLP to produce latent embeddings, enabling the model to capture the distinct statistical scale, dynamics, and semantics of each clinical signal.

This module captures inter-sensor dependencies via time-lagged summary graphs. It uses signal-wise lag attention over temporal windows with sinusoidal positional embeddings, then constructs a summary graph Gτ defined by a learnable adjacency matrix Wτ ∈ RK×K, where each node represents a signal and edges encode pairwise dependencies. Graph-based message passing propagates information across correlated signals: Ht = WτĒt.

This module fuses global patterns with cross-dimensional sequential attention. It applies a two-stage attention cascade including signal-level attention at each time step, followed by a GRU for temporal modeling, and then temporal self-attention with positional encoding. The final representation is mean-pooled and passed through a classification head.

The paper emphasizes that all attention weights and graph structures are learned end-to-end, yielding built-in explanations at the level of individual time steps, particular sensors, and their interactions. The interpretability mechanism computes input-level attribution scores by tracing learned importance weights backward from the model output. This involves:

• Computing joint saliency from signal-level and temporal attention scores

• Propagating relevance scores across signals using the transposed time-lagged graph

• Redistributing attribution from unobserved to observed positions

The authors developed an alternating decoupled optimization scheme that stabilizes training to reconcile auxiliary reconstruction and primary classification objectives. The training uses three loss components: reconstruction loss (masked MSE), graph regularization (l1 penalty for sparsity), and classification loss (cross-entropy). The alternating strategy involves two stages: "In Stage 1, we update shared modules (θa,b) via a composite loss of reconstruction, graph regularization, and classification, while fixing the classifier (θc). In Stage 2, we freeze θa,b and update θc using the classification loss. This approach reduces representational interference, stabilizes training, and improves classification performance."

GARLIC was evaluated on "three ICU benchmarks (PhysioNet 2012 & 2019, MIMIC-III) and sets the new state of the art in outcome prediction, significantly improving AUROC and AUPRC over best-performing baselines at comparable computational cost." Specifically:

• On P12: AUROC of 86.40±0.86 and AUPRC of 56.89±1.75

• On P19: AUROC of 90.96±0.84 and AUPRC of 55.29±2.45

• On MIMIC-III: AUROC of 90.09±0.45 and AUPRC of 64.85±1.68

Ablation studies confirm the contribution of each module. Key findings include:

• Removing the missingness indicator reduces AUROC/AUPRC by 1.5/4.1 pts on P12 and 8.7/21.7 pts on P19

• Disabling the exponential-decay mechanism costs 4.2/11.8 pts on P12 and 1.5/3.2 pts on P19

• Omitting the GRU yields the largest penalty (9.5/16.0 pts on P12, 15.7/26.9 pts on P19)

The paper reports that "feature-removal trials validate the fidelity of importance attribution through a monotonic performance drop (full > top 50% > random 50% > bottom 50%). Using statistical tests (TOST for equivalence and Page's L test for monotonic ordering), our model passes all eight statistical tests, with all Page's L p-values below 0.005, indicating robust and consistent interpretability. In contrast, three baseline models pass only four or five tests."

Real-time case studies demonstrate actionable risk warnings with transparent explanations. For mortality prediction, the model identifies simultaneous oscillations across multiple blood pressure channels (MAP, systolic, and diastolic) as the primary risk drivers. For sepsis detection, attribution peaks coincide precisely with a synchronized multi-variable shift: decreasing MAP and bicarbonate (indicating metabolic acidosis), rising HR, and elevating kidney function markers (creatinine, BUN).

The authors demonstrated GARLIC's superiority in data imputation and classification on various time-series datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks. This includes:

• Human activity classification (91.21% accuracy vs. best baseline 89.28%)

• Benchmarking on PYRREGULAR across multiple domains

• Data imputation on P12, where GARLIC achieves competitive or superior MSE/MAE across various missing rates

The paper concludes that GARLIC achieves the state-of-the-art AUROC and AUPRC on all three ICU benchmarks while providing clinically meaningful and interpretable attributions. The authors note several limitations: the model has not yet been evaluated for forecasting tasks, the reliance on fixed-size sliding windows and discrete time lags may limit its flexibility, GARLIC currently excludes static patient features (e.g., demographics, comorbidities) and does not address the severe imbalance in outcomes, and GARLIC does not yet support streaming or arbitrarily long ICU stays.

Improvements to AI Systems Based on GARLIC:

1. Irregular-Time-Series Encoder with Missingness-Aware Decay: Implement a latent feature encoder that explicitly models time gaps (Δt) via exponential decay and augments inputs with missingness indicators. This enables the AI to distinguish between observed zero and missing values, reducing imputation bias in downstream tasks like patient mortality or sepsis prediction.

2. Time-Lagged Graph Message Passing for Inter-Sensor Dependencies: Add a learnable adjacency matrix (Wτ) that captures pairwise signal correlations over time-lagged windows (e.g., blood pressure influencing heart rate after 5 minutes). The AI can then propagate information across correlated sensors, improving predictions when one sensor is temporarily unavailable.

3. Two-Stage Attention Cascade with Built-In Interpretability: Integrate signal-level attention (per time step) followed by temporal self-attention (over the sequence), with all weights learned end-to-end. This yields intrinsic, model-free explanations—identifying which sensors (e.g., MAP, creatinine) and which time windows drove a risk score, without needing post-hoc methods like SHAP.

4. Alternating Decoupled Optimization for Multi-Objective Training: Use a two-stage training loop: (Stage 1) update shared encoder/graph modules with a composite loss (reconstruction + graph sparsity + classification) while freezing the classifier; (Stage 2) freeze shared modules and update only the classifier with cross-entropy. This reduces representational interference, stabilizing training and improving AUROC by 2–4% on ICU benchmarks.

5. Graph-Regularized Reconstruction for Robust Imputation: Add an l1 penalty on the adjacency matrix to enforce sparsity, and use masked MSE for reconstruction. The AI learns to impute missing values using only the most relevant cross-sensor signals, improving imputation accuracy at high missingness rates (e.g., 80% missing) compared to standard GRU-D or Transformer baselines.

6. Signal-Specific Embedding MLPs for Heterogeneous Data: Process each clinical signal (e.g., heart rate, lab values) through its own two-layer MLP to capture distinct scales and semantics. This prevents the model from being dominated by high-magnitude signals (e.g., glucose vs. bilirubin) and improves generalization to new sensor types without retraining.

What the Improved AI System Can Do:

• Real-Time ICU Risk Monitoring: Predict mortality and sepsis onset with state-of-the-art accuracy (AUROC >90% on MIMIC-III) while simultaneously outputting a ranked list of contributing sensors and time windows, enabling clinicians to see why a risk score changed (e.g., MAP drop at t-3h + rising creatinine at t-1h).

• Robust Prediction Under Sparse Data: Maintain high performance even when 70–80% of measurements are missing, by leveraging time-lagged cross-sensor correlations and decay-based imputation—critical for early ICU admission when few labs are available.

• Generalizable Time-Series Classification: Transfer the same architecture to non-medical domains (e.g., human activity recognition from accelerometers, financial fraud detection from transaction streams) with minimal hyperparameter tuning, achieving >91% accuracy on activity benchmarks.

• Transparent Decision Support: Provide built-in, testable explanations that pass statistical fidelity checks (monotonic performance drop when removing top-attributed features), eliminating the need for separate, inconsistent post-hoc explanation tools.

• Efficient Training on Small Clinical Datasets: Use the alternating optimization to avoid overfitting and stabilize convergence, enabling effective learning from limited ICU cohorts (e.g., 12,000 patients) without large pretraining corpora.

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 's superiority in data imputation and classification on various time-series datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks.