Selecting a subset of promising candidates from a large pool is crucial across various scientific and real-world applications. Conformal selection offers a distribution-free and model-agnostic framework for candidate selection with uncertainty quantification. While effective in offline settings, its application to online scenarios, where data arrives sequentially, poses challenges. Notably, conformal selection permits the deselection of previously selected candidates, which is incompatible with applications requiring irreversible selection decisions. This limitation is particularly evident in resource-intensive sequential processes, such as drug discovery, where advancing a compound to subsequent stages renders reversal impractical. To address this issue, we extend conformal selection to an online Accept-to-Reject Changes (ARC) procedure: non-selected data points can be reconsidered for selection later, and once a candidate is selected, the decision is irreversible. Specifically, we propose a novel conformal selection method, Online Conformal Selection with Accept-to-Reject Changes (dubbed OCS-ARC), which incorporates online Benjamini–Hochberg procedure into the candidate selection process. We provide theoretical guarantees that OCS-ARC controls the false discovery rate (FDR) at or below the nominal level at any timestep under both i.i.d. and exchangeable data assumptions. Additionally, we theoretically show that our approach naturally extends to multivariate response settings. Extensive experiments on synthetic and real-world datasets demonstrate that OCS-ARC significantly improves selection power over the baseline while maintaining valid FDR control across all examined timesteps.

Conformal prediction, as an emerging uncertainty quantification technique, typically functions as post-hoc processing for the outputs of trained classifiers. To optimize the classifier for maximum predictive efficiency, Conformal Training rectifies the training objective of base classifiers with a regularization that minimizes the average prediction set size at a specific error rate. However, the regularization term inevitably deteriorates the classification accuracy of classifiers, thereby leading to suboptimal efficiency of conformal predictors. To address this issue, we introduce Conformal Adapter (C-Adapter), an adapter-based tuning method to enhance the efficiency of conformal predictors without sacrificing accuracy. In particular, we implement the adapter as a class of intra order-preserving functions and tune it with our proposed loss that maximizes the discriminability of non-conformity scores between correctly and randomly matched data-label pairs. Using C-Adapter, the model tends to produce higher non-conformity scores for incorrect labels than for correct ones, thereby enhancing predictive efficiency across different coverage rates. Extensive experiments demonstrate that C-Adapter can effectively adapt various classifiers for efficient conformal prediction sets, as well as enhance the conformal training method.

Conformal prediction is a popular framework of uncertainty quantification that constructs prediction sets with coverage guarantees. To uphold the exchangeability assumption, many conformal prediction methods necessitate an additional hold-out set for parameter tuning. Yet, the impact of violating this principle on coverage remains underexplored, making it ambiguous in practical applications. In this work, we empirically find that the tuning bias - the coverage gap introduced by leveraging the same dataset for tuning and calibration, is negligible for simple parameter tuning in many conformal prediction methods. In particular, we observe the scaling law of the tuning bias: this bias increases with parameter space complexity and decreases with calibration set size. Formally, we establish a theoretical framework to quantify the tuning bias and provide rigorous proof for the scaling law of the tuning bias by deriving its upper bound. In the end, we discuss how to reduce the tuning bias, guided by the theories we developed.

Conformal prediction is an emerging technique for uncertainty quantification that constructs prediction sets guaranteed to contain the true label with a predefined probability. Recent work develops online conformal prediction methods that adaptively construct prediction sets to accommodate distribution shifts. However, existing algorithms typically assume *perfect label accuracy* which rarely holds in practice. In this work, we investigate the robustness of online conformal prediction under uniform label noise with a known noise rate. We show that label noise causes a persistent gap between the actual mis-coverage rate and the desired rate $\alpha$, leading to either overestimated or underestimated coverage guarantees. To address this issue, we propose a novel loss function *robust pinball loss*, which provides an unbiased estimate of clean pinball loss without requiring ground-truth labels. Theoretically, we demonstrate that robust pinball loss enables online conformal prediction to eliminate the coverage gap under uniform label noise, achieving a convergence rate of $\mathcal{O}(T^{-1/2})$ for both empirical and expected coverage errors (i.e., absolute deviation of the empirical and expected mis-coverage rate from the target level $\alpha$). This loss offers a general solution to the uniform label noise, and is complementary to existing online conformal prediction methods. Extensive experiments demonstrate that the proposed loss enhances the noise robustness of various online conformal prediction methods by achieving a precise coverage guarantee.

Hyperspectral image (HSI) classification involves assigning unique labels to each pixel to identify various land cover categories. While deep classifiers have achieved high predictive accuracy in this field, they lack the ability to rigorously quantify confidence in their predictions. This limitation restricts their application in critical contexts where the cost of prediction errors is significant, as quantifying the uncertainty of model predictions is crucial for the safe deployment of predictive models. To address this limitation, a rigorous theoretical proof is presented first, which demonstrates the validity of Conformal Prediction, an emerging uncertainty quantification technique, in the context of HSI classification. Building on this foundation, a conformal procedure is designed to equip any pre-trained HSI classifier with trustworthy prediction sets, ensuring that the true labels are included with a user-defined probability (e.g., 95%). Furthermore, a novel framework of Conformal Prediction specifically designed for HSI data, called Spatial-Aware Conformal Prediction (SACP), is proposed. This framework integrates essential spatial information of HSI by aggregating the non-conformity scores of pixels with high spatial correlation, effectively improving the statistical efficiency of prediction sets. Both theoretical and empirical results validate the effectiveness of the proposed approaches. The source code is available at https://github.com/J4ckLiu/SACP.

Subspace learning has been widely applied for joint feature extraction and dimensionality reduction, demonstrating significant efficacy. Numerous subspace learning methods with diverse assumptions regarding the criteria for the target subspaces have been developed to obtain compact and interpretable data representations. However, when applied to image data, existing methods fail to fully exploit the inherent correlations within the image set. This paper proposes a Robust Discriminative t-Linear Subspace Learning model (RDtSL) to tackle this issue using t-product. The model mainly has four strengths: 1) Taking advantage of t-product, RDtSL learns the projection basis directly from the image set while fully exploiting its internal correlations; 2) Based on its energy preservation module, RDtSL retains the primary energy of samples in the learned subspace, maintaining satisfactory performance even with low subspace dimensions; 3) Class-distinctive features are effectively preserved in the learned representations due to the incorporation of the classification module; 4) Relying on its graph embedding module, RDtSL learns an affinity graph of samples adaptively to enrich the data representations with locality and similarity information. The harmonious balance maintained between the three proposed modules helps RDtSL learn discriminative and informative data representations. We also develop an iterative algorithm to solve RDtSL. Extensive experiments on benchmark databases demonstrate the superiority of the proposed model.