conformal risk control

This work addresses a critical limitation of traditional conformal prediction, which only guarantees average error control over a fixed calibration set and fails to ensure validity at arbitrary time points as calibration data dynamically accumulate. To overcome this, the authors propose a dynamic conformal prediction framework grounded in quantile analysis, which provides high-probability risk control for prediction sets at any time during ongoing calibration—even under distributional shifts. The method establishes, for the first time, theoretical validity guarantees for all time points in a dynamic calibration setting, proves an asymptotically tight lower bound, and demonstrates robustness and practical utility in non-stationary environments through both simulation studies and real-world data experiments.

This work addresses the challenge of jointly achieving scenario optimization and conformal prediction with rigorous safety guarantees under limited sample sizes, while appropriately allocating risk across multi-output or multi-stage tasks. From a systems and control perspective, we introduce—for the first time—a natural integration of a sample removal mechanism into the conformal prediction framework, treating discarded samples as acceptable exceptions. We propose a modular risk allocation rule that composes multiple local calibration certificates to construct a unified joint guarantee. The approach leverages exchangeability to derive an average violation law and incorporates multi-step tube-based calibration, making it suitable for multi-output prediction and finite-horizon control. Numerical experiments demonstrate that the proposed strategy effectively balances performance and safety in constraint tightening problems.

Traditional conformal prediction employs a fixed coverage level, often yielding overly conservative or even empty prediction sets, and lacks sample-wise adaptivity. To address this, we propose an adaptive conformal prediction framework that dynamically adjusts the coverage level per sample based on estimated difficulty. Our method is the first to integrate e-values with posterior conformal inference, leveraging a neural network trained on a calibration set to learn data-dependent coverage policies. It employs leave-one-out training and variable-coverage optimization, ensuring strict marginal coverage guarantees while substantially reducing prediction set size. Experiments across diverse classification and regression tasks demonstrate consistent improvements over fixed-coverage baselines—achieving greater flexibility, computational efficiency, and theoretical rigor without compromising statistical validity.

To address the issue of excessively large prediction sets and limited practicality of conformal prediction in high-risk applications, this paper proposes a two-stage Selective Conformal Risk Control (SCRC) framework: first, selective classification filters high-confidence samples; second, calibrated risk control is applied only on the selected subset. SCRC unifies conformal prediction with selective classification for the first time, yielding two novel algorithms—SCRC-T, which guarantees exact coverage under finite-sample settings, and SCRC-I, which provides PAC-style risk guarantees with improved computational efficiency. Both algorithms are theoretically proven to satisfy the target coverage level and a user-specified risk threshold. Empirical evaluation on two public benchmark datasets confirms strict adherence to coverage and risk constraints; SCRC-I achieves comparable predictive performance to SCRC-T while offering superior computational efficiency and more conservative risk control. The core contribution lies in jointly ensuring statistical reliability, prediction set compactness, and computational feasibility.

Existing conformal prediction methods treat the modeling pipeline as a black box, preventing decomposition of the overall prediction error across individual modules and thus hindering uncertainty attribution to specific pipeline stages. Method: We propose the first modular, calibration-preserving framework for conformal prediction, introducing residual decomposition to enable multi-stage uncertainty溯源 and interpretable selection of risk parameters in sequential models. Our approach integrates two-stage calibration, family-wise error rate (FWER) control, and an adaptive update mechanism to ensure long-term coverage validity under non-stationary data streams. Results: Evaluated on synthetic data and real-world supply chain and stock market datasets, our framework significantly improves coverage stability under distribution shift compared to baseline methods. It further enables stage-wise uncertainty quantification and principled uncertainty attribution—advancing both reliability and interpretability in sequential conformal prediction.

This work addresses a critical limitation of existing conformal prediction methods, which guarantee only marginal coverage and fail to characterize key operational metrics—such as decision frequency, error exposure, and rejection rate—and their inherent trade-offs in real-world deployment. To overcome this, the authors propose an operational certification framework that goes beyond coverage by introducing a calibration-audit two-stage mechanism to quantify and guarantee the statistical properties of system behavior under finite-sample settings. Key innovations include Small-Sample Beta Correction (SSBC) for finite-sample coverage guarantees, reusable confidence envelopes for operational metrics, and the revelation of geometric couplings and trade-off boundaries among these metrics under conformal partitioning. The framework successfully generates auditable operational configuration menus on Tox21 and AquaSolDB benchmarks, explicitly delineating performance boundaries and uncertainties across different calibration strategies.

This work addresses the limitation of traditional conformal prediction, which relies on a fixed sample size and thus fails to provide valid coverage guarantees at arbitrary time points in streaming data settings. The authors extend conformal prediction and the PAC framework to the sequential setting, achieving— for the first time—time-uniform prediction sets that remain valid under dynamically updated models and even when evaluation occurs at data-dependent stopping times. Their approach integrates time-uniform conformal theory, sequential hypothesis testing, and probabilistic inequalities to construct prediction intervals with guaranteed coverage at any stopping time. Empirical evaluations on both synthetic and real-world datasets demonstrate the method’s theoretical soundness and practical utility.

Traditional conformal prediction relies on the exchangeability assumption, which fails in time series due to temporal dependence and distributional shift, undermining nominal coverage guarantees. To address this, we propose the first unified conformal prediction framework for non-exchangeable time series, establishing finite-sample theoretical guarantees for split conformal prediction under weak dependence conditions. We systematically categorize, model, and compare three mainstream strategies—reweighting, dynamic updating, and adaptive hyperparameter tuning—and integrate residual reweighting, online distribution calibration, and coverage-adaptive adjustment. Extensive experiments on diverse synthetic and real-world time series demonstrate that our method significantly narrows prediction intervals while strictly maintaining target coverage. Crucially, we quantitatively characterize the fundamental trade-off between interval width and predictive stability—the first such result—thereby providing both theoretical foundations and practical tools for reliable uncertainty quantification in nonstationary time series.

Existing online conformal prediction methods typically support only a single confidence level, making it difficult to simultaneously ensure validity and nested prediction sets across multiple coverage levels, thereby failing to accommodate heterogeneous user risk preferences requiring full-spectrum uncertainty calibration. This work proposes two novel online conformal prediction approaches that, for the first time, incorporate nesting constraints into an online framework. By jointly estimating quantiles at multiple coverage levels and leveraging cross-quantile information sharing, non-crossing constraints, and low-regret online optimization, the proposed methods enable synchronized and efficient uncertainty quantification across the entire risk spectrum. Experiments on both synthetic and real-world data demonstrate that the methods achieve strict nesting, stable empirical coverage, and significantly improved prediction efficiency compared to existing baselines.

This work addresses the selection bias inherent in selective inference when inference is performed only on high-informativeness prediction sets, which can compromise false coverage rate (FCR) control. Under an idealized setting, the authors derive an oracle strategy that maximizes statistical power while maintaining FCR guarantees. They then develop a finite-sample calibration mechanism grounded in conformal prediction and probability calibration to adapt this optimal strategy to practical settings. The resulting procedure rigorously controls FCR while achieving substantially higher power than existing methods. Empirical evaluations on both synthetic and real-world classification datasets demonstrate consistent superiority over current approaches in terms of statistical efficiency without sacrificing FCR control.