Coherent Hierarchical Multi-Label Learning to Defer for Medical Imaging

Active learning (AL) promises to reduce the cost of medical imaging projects by lowering the number of clinical labels required. However, practical deployment requires committing to a sampling strategy before the full annotation budget is spent, and choosing the wrong strategy can increase rather than decrease costs. We propose Active-Learning Deployment Advisor (ALDA), a deployment-oriented framework for AL method selection under clinical performance constraints. Given a short pilot phase, ALDA fits a parametric learning-curve model to each candidate strategy, estimates whether that strategy is expected to reach a required clinical performance target, and predicts the number of expert annotations needed to do so. In addition to absolute annotation cost, ALDA introduces a deployment window that quantifies the sensitivity of this cost estimate to uncertainty in the clinical threshold. The final recommendation follows a risk-aware rule: among strategies with near-optimal predicted cost, ALDA prefers the strategy with the narrowest deployment window, the most robust to threshold revisions. Experiments on four medical imaging classification domains show that ALDA predicts the deployment-optimal method from a pilot of 15-30% of the intended budget and reduces annotation costs by up to 82% compared with a poor strategy choice. Rather than introducing a new sampling heuristic, ALDA provides a practical decision layer that answers a deployment-critical question: how many labels are enough?

We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer, allowing deferral rates to be adjusted without retraining. For KL-based ideal distributions, our deferral rules recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior -- which incorporates the expert's performance -- depending on if the ideal distributions are joint or marginal distributions. Experimentally, our approach is competitive compared to common baselines and more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio learning between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.

Federated learning (FL) enables multiple clinical institutions to collaboratively train a shared disease classifier without centralizing patient data. In practice, however, each institution annotates only the pathologies within its area of expertise, so the federation operates under task heterogeneity: each client holds labels for a strict subset of the target disease categories while the remaining classes are entirely unobserved at that site. Existing gradient-based FL methods fail under this setting because they require hundreds of communication rounds to converge and because missing class labels introduce systematic false-negative bias that the model cannot correct without a principled mechanism. We propose an analytic federated learning framework for multi-label medical image classification under task heterogeneity. The proposed method replaces iterative gradient optimization with three closed-form operations: a balanced label projection that neutralizes class-imbalance bias by normalizing positive and negative contributions to equal total mass; a per-class absolute aggregation law that independently assembles the optimal ridge-regression classifier for each disease category from the sufficient statistics uploaded by its annotating clients; and an optional analytic pseudo-label refinement round that propagates missing-class knowledge from a confidence-filtered teacher classifier to non-annotating clients. The entire procedure requires at most two communication rounds, irrespective of the degree of task heterogeneity or the number of participating clients. Experiments on ChestXray14 under four progressively severe missing-class configurations demonstrate that the proposed method consistently outperforms the state-of-the-art federated multi-label method FedMLP by up to 18.44 BACC points and 13.24 AUC points, while reducing the communication.