Fair Conformal Prediction

Fairness in conformal prediction is often pursued through Mondrian calibration, which provides finite-sample coverage guarantees separately across groups. These guarantees, however, are coarse: substantial disparities can remain within finer strata. This coarse-to-fine fairness issue raises two questions: how severe can such disparities be, and how can they be mitigated? Aggregate disparities can depend on how groups are distributed across strata. For severity assessment, we introduce propensity standardization to examine the effect of population composition, and show how group composition can induce disagreement between aggregate and finer-stratum comparisons. For mitigation, we develop Tilted Mondrian to improve fairness compared to group-Mondrian at a finer level without additional model training. Tilted Mondrian retains groupwise coverage guarantees and mitigates coverage and prediction set size disparities within finer strata. Finally, we derive a method-agnostic bound that quantifies how much reduction in finer-stratum coverage disparity can be achieved.

Conformal prediction offers a distribution-free coverage guarantee, making it especially attractive for clinical applications. Standard conformal prediction, however, provides such guarantees only at the population level, and its prediction sets can exhibit coverage disparities across clinically important subgroups. A natural remedy is to calibrate within predefined groups. However, this can require access to sensitive subgroup attributes and is prone to a worst-group bottleneck: protecting the most difficult subgroup can inflate prediction sets for all, increasing cognitive burden on decision makers. To this end, we propose Stochastic Grouping Conformal Prediction (SGCP), a conformal framework for subgroup-reliable uncertainty quantification. It learns a stochastic grouping map that allows each sample to draw calibration information from others with similar calibration behavior, yielding a local score law that boosts reliability across subpopulations. We prove that SGCP retains the standard coverage guarantee. Experiments on synthetic and real-world benchmarks show that it consistently reduces subgroup coverage gaps while achieving smaller or comparable prediction set sizes relative to existing baselines.

We introduce Rolling Conformal Prediction (rolling-CP), a distribution-free predictive inference method for the setting of sequential model training. Specifically, given a data stream $(X_1,Y_1),(X_2,Y_2),\dots$, at each time $n$ the trained model may depend on the observed history $\{(X_i,Y_i)\}_{i<n}$. This setting arises naturally in modern sequential training, including one-pass training over massive datasets and continual fine-tuning or test-time adaptation of language models during deployment. Rolling-CP first calibrates each incoming observation against the current predictor and then rolls it into future training. In this way, we avoid the need for data splitting. Remarkably, although the models at times $n=1,2,\dots$ may have entirely different properties and accuracy levels, for exchangeable data it is nonetheless possible to establish a guarantee of marginal coverage, with a familiar universal factor-two guarantee (a worst case guarantee of $1-2α$ coverage, as compared to the target level $1-α$), without any assumptions of stability or any restrictions on the model training process. For i.i.d. data streams, we further prove high-probability training-conditional validity uniformly over time; under stability conditions, coverage guarantees sharpen towards $1-α$. Numerical experiments on sequential regression, multiclass SGD, and one-pass neural-network training further demonstrate the practical effectiveness of rolling-CP.

Neural operators provide fast surrogate models for approximating operators between function spaces, but their predictions often lack uncertainty quantification. We develop a split conformal framework to guarantee that a calibrated pointwise band around the neural operator output contains the true solution on at least a $1-γ$ fraction of the evaluation domain, with probability at least $1-α$ over test and calibration inputs, where $α,γ\in(0,1)$. Our method reduces a normalized residual field to its spatial $(1-γ)$-quantile and computes a scaling factor using a held-out calibration dataset. We prove marginal coverage guarantees for measurable residual fields defined on arbitrary probability spaces, covering both continuum domains and fixed discretizations. Under mild assumptions on the data distribution, we show that the coverage conditional on the calibration set follows a Beta distribution, which we verify with numerical experiments on Darcy flow and Navier--Stokes equations, where our calibration yields bands consistently tighter than existing corrections while retaining the target coverage.

Safe motion planning in dynamic environments requires reasoning about the uncertainty in predicted obstacle motion without sacrificing real-time performance. Existing conformal approaches conformalize a scalar score that aggregates per-obstacle prediction errors, losing spatial coherence and scaling poorly with scene density. We instead conformalize the entire predicted distance field at once. This functional conformal prediction (FCP) framework yields a distribution-free, field-level lower bound, from which safety follows uniformly: any trajectory satisfying the resulting constraint is certified safe, independent of how the control space is sampled. The key enabler is that the residual distance field is empirically low-rank and approximately time-invariant, which makes the bound decomposable in coefficient space. An envelope is fitted offline via functional PCA and a Gaussian-mixture inductive conformal procedure, then refined online by a lightweight adaptive functional conformal (AFCP) update on a low-dimensional vector. This keeps the per-step cost largely insensitive to obstacle count and retains long-run field coverage under distribution shift. We embed the envelope as a tightened safety constraint in a sampling-based model predictive controller, FCP-MPC. On the ETH--UCY pedestrian benchmarks and a dense 3D quadrotor task with up to 280 dynamic obstacles, FCP-MPC attains a favorable balance of safety, feasibility, and efficiency, reaching goals where pointwise and egocentric conformal baselines become too conservative or too expensive, while keeping per-step computation far below online uncertainty-reasoning baselines.

Long-horizon tasks are common in real-world robotic deployments, yet failure detection for such tasks remains underexplored. Detecting failures in long-horizon robotic tasks is particularly challenging because failure onset is often ambiguous and dense temporal annotations are typically unavailable. We present Foresight, a failure detection framework that monitors manipulation trajectories using latent representations from an action-conditioned world model. Foresight is trained using only final task-level success or failure labels. By leveraging predictive world-model embeddings, our method provides a unified framework for failure detection across different policies. We further use functional conformal prediction (FCP) to calibrate detection thresholds adaptively. We evaluate Foresight with state-of-the-art vision-language-action policies in simulation on LIBERO-Long, ManiSkill-Long, and BEHAVIOR-1K, compare it against state-of-the-artfailure detection methods, and validate it on real robots with three long-horizon tasks on a ReactorX-200 arm and one task on a Franka arm. Our results suggest that action-conditioned world-model embeddings provide a scalable representation for reliable failure monitoring in long-horizon manipulation.

Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.

Conformal prediction methods provide statistically rigorous marginal coverage guarantees for machine learning models, but such guarantees fail to account for algorithmic biases, thereby undermining fairness and trust. This paper introduces a fair conformal inference framework for classification tasks. The proposed method constructs prediction sets that guarantee conditional coverage on adaptively identified subgroups, which can be implicitly defined through nonlinear feature combinations. By balancing effectiveness and efficiency in producing compact, informative prediction sets and ensuring adaptive equalized coverage across unfairly treated subgroups, our approach paves a practical pathway toward trustworthy machine learning. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of the framework.

Quantifying uncertainty in clinical predictions is critical for high-stakes diagnosis tasks. Conformal prediction offers a principled approach by providing prediction sets with theoretical coverage guarantees. However, in practice, patient distribution shifts violate the i.i.d. assumptions underlying standard conformal methods, leading to poor coverage in healthcare settings. In this work, we evaluate several conformal prediction approaches on EEG seizure classification, a task with known distribution shift challenges and label uncertainty. We demonstrate that personalized calibration strategies can improve coverage by over 20 percentage points while maintaining comparable prediction set sizes. Our implementation is available via PyHealth, an open-source healthcare AI framework: https://github.com/sunlabuiuc/PyHealth.