Conformal prediction (CP) has attracted broad attention as a simple and flexible framework for uncertainty quantification through prediction sets. In this work, we study how to deploy CP under differential privacy (DP) in a statistically efficient manner. We first introduce differential CP, a non-splitting conformal procedure that avoids the efficiency loss caused by data splitting and serves as a bridge between oracle CP and private conformal inference. By exploiting the stability properties of DP mechanisms, differential CP establishes a direct connection to oracle CP and inherits corresponding validity behavior. Building on this idea, we develop Differentially Private Conformal Prediction (DPCP), a fully private procedure that combines DP model training with a private quantile mechanism for calibration. We establish the end-to-end privacy guarantee of DPCP and investigate its coverage properties under additional regularity conditions. We further study the efficiency of both differential CP and DPCP under empirical risk minimization and general regression models, showing that DPCP can produce tighter prediction sets than existing private split conformal approaches under the same privacy budget. Numerical experiments on synthetic and real datasets demonstrate the practical effectiveness of the proposed methods.

Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing conditional validity is challenging, as standard stratification methods suffer from the curse of dimensionality. We propose Conformal Prediction Assessment (CPA), a framework that reframes the evaluation of conditional coverage as a supervised learning task by training a reliability estimator that predicts instance-level coverage probabilities. Building on this estimator, we introduce the Conditional Validity Index (CVI), which decomposes reliability into safety (undercoverage risk) and efficiency (overcoverage cost). We establish convergence rates for the reliability estimator and prove the consistency of CVI-based model selection. Extensive experiments on synthetic and real-world datasets demonstrate that CPA effectively diagnoses local failure modes and that CC-Select, our CVI-based model selection algorithm, consistently identifies predictors with superior conditional coverage performance.

The author contributed to this paper during an internship at the Max Planck Institute for Software Systems.

Surrogate models (including deep neural networks and other machine learning algorithms in supervised learning) are capable of approximating arbitrarily complex, high-dimensional input-output problems in science and engineering, but require a thorough data-agnostic uncertainty quantification analysis before these can be deployed for any safety-critical application. The standard approach for data-agnostic uncertainty quantification is to use conformal prediction (CP), a well-established framework to build uncertainty models with proven statistical guarantees that do not assume any shape for the error distribution of the surrogate model. However, since the classic statistical guarantee offered by CP is given in terms of bounds for the marginal coverage, for small calibration set sizes (which are frequent in realistic surrogate modelling that aims to quantify error at different regions), the potentially strong dispersion of the coverage distribution around its average negatively impacts the relevance of the uncertainty model's statistical guarantee, often obtaining coverages below the expected value, resulting in a less applicable framework. After providing a gentle presentation of uncertainty quantification for surrogate models for machine learning practitioners, in this paper we bridge the gap by proposing a new statistical guarantee that offers probabilistic information for the coverage of a single conformal predictor. We show that the proposed framework converges to the standard solution offered by CP for large calibration set sizes and, unlike the classic guarantee, still offers relevant information about the coverage of a conformal predictor for small data sizes. We validate the methodology in a suite of examples, and implement an open access software solution that can be used alongside common conformal prediction libraries to obtain uncertainty models that fulfil the new guarantee.

Conformal prediction is a model-agnostic approach to generating prediction sets that cover the true class with a high probability. Although its prediction set size is expected to capture aleatoric uncertainty, there is a lack of evidence regarding its effectiveness. The literature presents that prediction set size can upper-bound aleatoric uncertainty or that prediction sets are larger for difficult instances and smaller for easy ones, but a validation of this attribute of conformal predictors is missing. This work investigates how effectively conformal predictors quantify aleatoric uncertainty, specifically the inherent ambiguity in datasets caused by overlapping classes. We perform this by measuring the correlation between prediction set sizes and the number of distinct labels assigned by human annotators per instance. We further assess the similarity between prediction sets and human-provided annotations. We use three conformal prediction approaches to generate prediction sets for eight deep learning models trained on four datasets. The datasets contain annotations from multiple human annotators (ranging from five to fifty participants) per instance, enabling the identification of class overlap. We show that the vast majority of the conformal prediction outputs show a very weak to weak correlation with human annotations, with only a few showing moderate correlation. These findings underscore the necessity of critically reassessing the prediction sets generated using conformal predictors. While they can provide a higher coverage of the true classes, their capability in capturing aleatoric uncertainty and generating sets that align with human annotations remains limited.

Conformal Prediction (CP) is a popular method for uncertainty quantification with machine learning models. While conformal prediction provides probabilistic guarantees regarding the coverage of the true label, these guarantees are agnostic to the presence of sensitive attributes within the dataset. In this work, we formalize \textit{Conformal Fairness}, a notion of fairness using conformal predictors, and provide a theoretically well-founded algorithm and associated framework to control for the gaps in coverage between different sensitive groups. Our framework leverages the exchangeability assumption (implicit to CP) rather than the typical IID assumption, allowing us to apply the notion of Conformal Fairness to data types and tasks that are not IID, such as graph data. Experiments were conducted on graph and tabular datasets to demonstrate that the algorithm can control fairness-related gaps in addition to coverage aligned with theoretical expectations.

Conformal Prediction (CP) is a widely used technique for quantifying uncertainty in machine learning models. In its standard form, CP offers probabilistic guarantees on the coverage of the true label, but it is agnostic to sensitive attributes in the dataset. Several recent works have sought to incorporate fairness into CP by ensuring conditional coverage guarantees across different subgroups. One such method is Conformal Fairness (CF). In this work, we extend the CF framework to the Federated Learning setting and discuss how we can audit a federated model for fairness by analyzing the fairness-related gaps for different demographic groups. Ensuring model fairness is a critical thrust of trustworthy machine learning (ML). ML models, when not calibrated for fairness, are prone to developing biases at each stage of an ML pipeline, as reflected by their predictions Mehrabi et al. (2021). We define bias as disparate performance (i.e., accuracy for classification) between different sub-populations. In the data collection phase, measurement bias may occur due to disproportionate data collection on sub-populations, while representation bias manifests from a lack of training data on specific strata. During training, these biases are inductively learned by the model-leading to incorrect predictions in safety-critical tasks. These models are also susceptible to algorithmic bias, resulting from regularization and optimization techniques during model training, which incorrectly generalize for marginal-ized groups. To mitigate these risks, many ML models must adhere to regulations placed by local governing bodies (Hirsch et al., 2023). Towards model compliance, Komala et al. (2024); Agrawal et al. (2024); Jones et al. (2025) have proposed approaches to enhance model fairness in varying tasks, including federated graph learning and representation learning.

Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed confidence. We demonstrate a fundamental trade-off between confidence and efficiency in transductive methods, where efficiency is measured by the size of the prediction sets. Specifically, we derive a strict finite-sample bound showing that any non-trivial confidence level leads to exponential growth in prediction set size for data with inherent uncertainty. The exponent scales linearly with the number of samples and is proportional to the conditional entropy of the data. Additionally, the bound includes a second-order term, dispersion, defined as the variance of the log conditional probability distribution. We show that this bound is achievable in an idealized setting. Finally, we examine a special case of transductive prediction where all test data points share the same label. We show that this scenario reduces to the hypothesis testing problem with empirically observed statistics and provide an asymptotically optimal confidence predictor, along with an analysis of the error exponent.

Conformal prediction (CP) is a powerful framework for quantifying uncertainty in machine learning models, offering reliable predictions with finite-sample coverage guarantees. When applied to classification, CP produces a prediction set of possible labels that is guaranteed to contain the true label with high probability, regardless of the underlying classifier. However, standard CP treats classes as flat and unstructured, ignoring domain knowledge such as semantic relationships or hierarchical structure among class labels. This paper presents hierarchical conformal classification (HCC), an extension of CP that incorporates class hierarchies into both the structure and semantics of prediction sets. We formulate HCC as a constrained optimization problem whose solutions yield prediction sets composed of nodes at different levels of the hierarchy, while maintaining coverage guarantees. To address the combinatorial nature of the problem, we formally show that a much smaller, well-structured subset of candidate solutions suffices to ensure coverage while upholding optimality. An empirical evaluation on three new benchmarks consisting of audio, image, and text data highlights the advantages of our approach, and a user study shows that annotators significantly prefer hierarchical over flat prediction sets.