Uncertainty estimation is crucial for ensuring the reliability of machine learning models in safety-critical applications. Evidential Deep Learning (EDL) offers a principled framework by modeling predictive uncertainty through Dirichlet distributions over class probabilities. However, existing EDL methods predominantly rely on level-0 hard labels, which supervise an uncertainty-aware model with full certainty. We argue that hard labels not only fail to capture epistemic uncertainty but also obscure the aleatoric uncertainty arising from inherent data noise and label ambiguity. As a result, EDL models often produce degenerate Dirichlet distributions that collapse to near-deterministic outputs. To overcome these limitations, we propose a vicinal risk minimization paradigm for EDL by incorporating level-1 supervision in the form of vicinally smoothed conditional label distributions.

We introduce a novel framework for AI-generated image detection through epistemic uncertainty, aiming to address critical security concerns in the era of generative models. Our key insight stems from the observation that distributional discrepancies between training and testing data manifest distinctively in the epistemic uncertainty space of machine learning models. In this context, the distribution shift between natural and generated images leads to elevated epistemic uncertainty in models trained on natural images when evaluating generated ones. Hence, we exploit this phenomenon by using epistemic uncertainty as a proxy for detecting generated images. This converts the challenge of generated image detection into the problem of uncertainty estimation, underscoring the generalization performance of the model used for uncertainty estimation. Fortunately, advanced large-scale vision models pre-trained on extensive natural images have shown excellent generalization performance for various scenarios. Thus, we utilize these pre-trained models to estimate the epistemic uncertainty of images and flag those with high uncertainty as generated. Extensive experiments demonstrate the efficacy of our method. Code is available at https://github.com/tmlr-group/WePe.

This work introduces a novel approach, Pairwise Epistemic Estimators (PairEpEsts), for epistemic uncertainty estimation in ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). By utilizing the pairwise distances between model components, PaiDEs establish bounds on entropy. We leverage this capability to enhance the performance of Bayesian Active Learning by Disagreement (BALD). Notably, unlike sample-based Monte Carlo estimators, PairEpEsts can estimate epistemic uncertainty up to 100 times faster and demonstrate superior performance in higher dimensions. To validate our approach, we conducted a varied series of regression experiments on commonly used benchmarks: 1D sinusoidal data, Pendulum, Hopper, Ant, and Humanoid, demonstrating PairEpEsts' advantage over baselines in high-dimensional regression active learning.

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty---due to incomplete knowledge---requires richer representations than those offered by classical probability. Imprecise probability (IP) theory offers such models, capturing ambiguity and partial belief. This has driven growing interest in imprecise probabilistic machine learning (IPML), where inference and decision-making rely on broader uncertainty models---highlighting the need for metrics beyond classical probability. This work introduces the Integral Imprecise Probability Metric (IIPM) framework, a Choquet integral-based generalisation of classical Integral Probability Metric to the setting of capacities---a broad class of IP models encompassing many existing ones, including lower probabilities, probability intervals, belief functions, and more. Theoretically, we establish conditions under which IIPM serves as a valid metric and metrises a form of weak convergence of capacities. Practically, IIPM not only enables comparison across different IP models but also supports the quantification of epistemic uncertainty~(EU) within a single IP model. In particular, by comparing an IP model with its conjugate, IIPM gives rise to a new class of epistemic uncertainty measures---Maximum Mean Imprecision (MMI) ---which satisfy key axiomatic properties proposed in the Uncertainty Quantification literature. We validate MMI through selective classification experiments, demonstrating strong empirical performance against established EU measures, and outperforming them when classical methods struggle to scale to a large number of classes.

The interactive task of composed image retrieval aims to retrieve the most relevant images with the bi-modal query, consisting of a reference image and a modification sentence. Despite significant efforts to bridge the heterogeneous gap within the bi-modal query and leverage contrastive learning to reduce the disparity between positive and negative triplets, prior methods often fail to ensure reliable matching due to aleatoric and epistemic uncertainty. Specifically, the aleatoric uncertainty stems from underlying semantic correlations within candidate instances and annotation noise, and the epistemic uncertainty is usually caused by overconfidence in dominant semantic categories. In this paper, we propose Robust UNcertainty Calibration (RUNC) to quantify the uncertainty and calibrate the imbalanced semantic distribution. To mitigate semantic ambiguity in similarity distribution between fusion queries and targets, RUNC maximizes the matching evidence by utilizing a high-order conjugate prior distribution to fit the semantic covariances in candidate samples. With the estimated uncertainty coefficient of each candidate, the target distribution is calibrated to encourage balanced semantic alignment. Additionally, we minimize the ambiguity in the fusion evidence when forming the unified query by incorporating orthogonal constraints on explicit textual embeddings and implicit queries, to reduce the representation redundancy. Extensive experiments and ablation analysis on benchmark datasets FashionIQ and CIRR verify the robustness of RUNC in predicting reliable retrieval results from a large image gallery.

We introduce a novel framework for AI-generated image detection through epistemic uncertainty, aiming to address critical security concerns in the era of generative models. Our key insight stems from the observation that distributional discrepancies between training and testing data manifest distinctively in the epistemic uncertainty space of machine learning models. In this context, the distribution shift between natural and generated images leads to elevated epistemic uncertainty in models trained on natural images when evaluating generated ones. Hence, we exploit this phenomenon by using epistemic uncertainty as a proxy for detecting generated images. This converts the challenge of generated image detection into the problem of uncertainty estimation, underscoring the generalization performance of the model used for uncertainty estimation. Fortunately, advanced large-scale vision models pre-trained on extensive natural images have shown excellent generalization performance for various scenarios. Thus, we utilize these pre-trained models to estimate the epistemic uncertainty of images and flag those with high uncertainty as generated. Extensive experiments demonstrate the efficacy of our method.

Epistemic uncertainty is often viewed as a reducible uncertainty that vanishes with increasing data. This perspective implicitly assumes parameter identifiability and equates epistemic uncertainty with predictive variability. In overparametrized neural networks, however, model parameters are typically non-identifiable due to symmetries and redundant representations. As a consequence, substantial parameter uncertainty can persist even when the underlying function is fully identified. In this work, we analyze epistemic uncertainty through the lens of non-identifiability and characterize both discrete and continuous sources of residual uncertainty. Focusing on one-hidden-layer ReLU networks, we thoroughly analyze the resulting posterior structure and validate our theoretical insights through empirical studies.

Single-pass uncertainty quantification (UQ) methods for classification represent uncertainty by predicting a tractable distribution over the class probability vector. While existing approaches primarily focus on enhancing the expressiveness of this distribution, they often provide limited insight into how predictive uncertainty is structured and aggregated, resulting in weak interpretability. We introduce the courtroom analogy, which conceptualizes uncertainty-aware classification as a structured debate among class-specific advocates. Each advocate forms a probabilistic opinion, and a final verdict is reached by aggregating these opinions using input-dependent plausibility weights. In this framework, each advocate's opinion is modeled as a Dirichlet distribution whose concentration parameter is decomposed into shared evidence and class-specific advocacy. This yields a structured mixture of Dirichlet distributions with semantically interpretable parameters. To instantiate this formulation, we propose Mixture of Dirichlet EXperts (MoDEX), a single-pass neural architecture that predicts the courtroom parameters, enabling efficient and expressive UQ while explicitly modeling uncertainty aggregation. We demonstrate that MoDEX enjoys strong theoretical properties and achieves state-of-the-art UQ performance across diverse benchmarks, yielding interpretable uncertainty estimates with meaningful semantics.

Reliable deployment of machine learning models requires reasoning under epistemic uncertainty--the ability to recognize when the operating distribution has shifted beyond the scope of what was encountered during training. This challenge is central to test-time adaptation (TTA), a paradigm in which a model pretrained on source distribution Ps receives unlabeled data from a target distribution Pt = Ps at deployment time. Existing TTA methods (Wang et al., 2021; Niu et al., 2023; Zhang et al., 2022a; Yuan et al., 2023; Su et al., 2022) improve accuracy under distribution shift by adapting model parameters using statistics computed from test batches, but they provide no formal guarantees about when predictions should be trusted or how much risk degrades as a function of shift magnitude. This gap is particularly concerning in safety-critical applications such as autonomous driving, medical imaging, and financial risk assessment, where a model that silently degrades under distribution shift can cause significant harm. The inability to quantify how wrong a model's predictions might be in an unseen environment fundamentally limits its trustworthy deployment.

Effective medication management in Parkinson's Disease (PD) is challenging due to heterogeneous disease progression, variable patient response, and medication side effects. While AI models can forecast levodopa equivalent daily dose (LEDD) as a measure of medication needs, standard uncertainty quantification often fails to communicate the reliability of these predictions, treating high and low confidence clinical decisions identically. We introduce CASCADE (Calibrated Adaptive Scaling via Conformal And Distributional Estimation), a novel conformal prediction framework that propagates epistemic uncertainty from a screening classifier to adapt downstream predictions. Unlike standard conformal methods that rely on auxiliary residual regression, we leverage epistemic uncertainty from a primary classification task (identifying whether a medication change is needed) to dynamically scale the prediction intervals of a secondary regression task (predicting how much change). By mapping Venn-Abers multi-probabilistic uncertainty directly to non-conformity scores, our framework achieves continuous risk adaptation. We demonstrate that this ``cascade effect'' produces highly efficient intervals for confident patients (38.9% narrower than standard conformal baselines) while automatically expanding intervals to ensure robust coverage for uncertain cases, bridging the gap between discrete clinical decision-making and continuous dose forecasting in PD.