Structure-Aware Graph Abstention for Reliable Selective Forecasting

Deep learning methods have achieved state-of-the-art in time series forecasting, yet their accuracy varies considerably across samples, as some instances remain inherently difficult to predict. Reject option mechanisms, which allow models to abstain from high-risk predictions, are well established in classification and regression but underexplored in forecasting. Existing abstention strategies typically rely on proxies, such as the width of the prediction interval or learned confidence scores derived from forecasts. However, these approaches are inherently tied to the training domain, limiting their ability to generalize. We propose a selective forecasting framework that addresses this limitation by modeling the empirical percentile of forecasting errors, that is, a scale-invariant statistic, based on structural characteristics extracted from recent lags via metalearning. By decoupling the rejection decision from the forecast itself and grounding it in domain-agnostic features, the framework enables effective abstention transfer across heterogeneous time series. Experiments in both in-domain and transfer learning settings show that rejecting samples predicted as challenging consistently improves forecasting accuracy across coverage levels.

Standard selective prediction methods typically estimate uncertainty from the output of a single predictive branch. While effective for general uncertainty estimation, these approaches often struggle under partial observability, where local temporal evidence can be contradictory and standard confidence scores become misleading. We introduce CHASE (Competing Hypotheses for Ambiguity-Aware Selective Prediction), a selective prediction framework that explicitly compares structured temporal explanations to determine whether to commit to a decision or abstain. Because genuine ambiguity causes the score gap between competing hypotheses to collapse, CHASE optimizes a ranking-aware selector over these hypothesis margins to globally separate safe commitments from fundamentally uncertain ones. We evaluate this framework on the problem of hidden connectivity inference, utilizing a controlled, physically grounded simulator inspired by the dynamics of giant unilamellar vesicles (GUVs), alongside zero-shot qualitative transfer (without retraining or fine tuning) to representative real GUV videos. Our experiments demonstrate that explicitly reasoning over competing hypotheses provides a superior balance of metrics. Compared to canonical uncertainty baselines, CHASE achieves statistically significant gains in overall no-abstain accuracy, three-way accuracy, and overall ambiguity-aligned abstention (at 80% coverage). Specifically, it yields up to an 11.0% relative mean improvement in overall alignment, alongside up to an 8.8% relative boost in three-way accuracy in the very-high ambiguity regime. By maintaining a selective risk boundary strictly at par with the best baselines at 80% coverage, and reducing overall risk by 9.9% at 90% coverage, this framework offers a more reliable approach to decision-making under structured ambiguity.

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.