arXiv subjects

Changliang Zou

Publications and source records attributed to Changliang Zou.

At least 19 recordsLinked to original sources

arXiv2026

Enhanced localized conformal prediction with imperfect auxiliary information

There is growing interest in constructing conformal prediction sets that provide approximate or asymptotic conditional coverage guarantees, capturing local data heterogeneity. However, methods like localized conformal prediction (LCP) may face challenges in ensuring reliable prediction sets in regions with sparse calibration data. This paper introduces Enhanced Localized Conformal Prediction (ELCP), a novel approach that incorporates auxiliary data to refine localized prediction sets while preserving finite-sample marginal coverage guarantees. By utilizing a density-ratio-weighted kernel estimator, ELCP seamlessly integrates auxiliary and calibration data, accommodating potential distributional shifts and improving the local reliability of prediction sets. Theoretical analysis confirms that ELCP maintains marginal coverage and enhances asymptotic test-conditional coverage. Simulation results demonstrate its superior local coverage and smaller prediction sets compared to standard LCP, highlighting its effectiveness in settings with limited calibration data but available auxiliary information from related tasks.

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arXiv2026

Efficient Federated Estimation and Inference for High-Dimensional Tail Index Regression

Tail index regression studies how covariates affect tail heaviness in heavy-tailed data. In many applications, data are distributed across heterogeneous sources, where direct pooling is infeasible due to privacy or regulatory constraints. Existing methods mainly focus on single-dataset analysis and do not address heterogeneous federated settings. We develop a personalized federated framework for high-dimensional tail index regression that accommodates client heterogeneity while exploiting latent similarities across clients. The proposed estimator combines sparsity regularization with nonconcave fusion penalties to perform coefficient estimation, variable selection, and group recovery. We establish non-asymptotic convergence rates and show that the estimator enjoys an oracle property by consistently recovering the underlying grouping structure. For computation, we develop an ADMM-based federated algorithm with adaptive gradient updates and establish its convergence guarantees. We further propose a debiased federated inference procedure based on adaptive weighted aggregation across related clients, yielding valid confidence intervals and hypothesis tests with improved efficiency over target-only inference. Simulation studies and real-data analysis demonstrate the effectiveness of the proposed methods.

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arXiv2026

Unified Conformalized Multiple Testing with Full Data Efficiency

Conformalized multiple testing offers a model-free way to control predictive uncertainty in decision-making. Existing methods typically use only part of the available data to build score functions tailored to specific settings. We propose a unified framework that puts data utilisation at the centre: it uses all available data-null, alternative, and unlabelled-to construct scores and calibrate p-values through a full permutation strategy. This unified use of all available data significantly improves power by enhancing non-conformity score quality and maximising calibration set size while rigorously controlling the false discovery rate. Crucially, our framework provides a systematic design principle for conformal testing and enables automatic selection of the best conformal procedure among candidates without extra data splitting. Extensive numerical experiments demonstrate that our enhanced methods deliver superior efficiency and adaptability across diverse scenarios.

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arXiv2026

Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization

Achieving valid conditional coverage in conformal prediction is challenging due to the theoretical difficulty of satisfying pointwise constraints in finite samples. Building upon the characterization of conditional coverage through marginal moment restrictions, we introduce Minimax Optimization Predictive Inference (MOPI), a framework that generalizes prior work by optimizing over a flexible class of set-valued mappings during the calibration phase, rather than simply calibrating a fixed sublevel set. This minimax formulation effectively circumvents the structural constraints of predefined score functions, achieving superior shape adaptivity while maintaining a principled connection to the minimization of mean squared coverage error. Theoretically, we provide non-asymptotic oracle inequalities and show that the convergence rate of the coverage error attains the optimal order under regular conditions. The MOPI also enables valid inference conditional on sensitive attributes that are available during calibration but unobserved at test time. Empirical results on complex, non-standard conditional distributions demonstrate that MOPI produces more efficient prediction sets than existing baselines.

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arXiv2026

A Unified Theory of Conditional Coverage in Conformal Prediction with Applications

Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing methods targeting conditional coverage are largely analyzed case by case, leaving limited general theory for understanding where conditional miscoverage comes from, how different procedures should be compared, and how such guarantees can be extended beyond i.i.d.~data. We address these gaps through a unified framework and theory for conformal methods targeting conditional coverage. Our central contribution is a non-asymptotic decomposition of conditional miscoverage into three interpretable components: score-estimation error, finite-sample calibration error, and intrinsic conditional-mismatch error. This decomposition clarifies the mechanisms behind asymptotic conditional validity and places existing methods within a common analytical lens. Building on this framework, we derive principled guidance for conditional-coverage-oriented model selection, and develop localized methods with asymptotic conditional guarantees under covariate shift. Finally, we extend the framework to structured data, with concrete applications to graph-structured and hierarchical settings. Numerical experiments corroborate the theory and demonstrate the effectiveness of the proposed procedures.

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arXiv2026

Learning U-Statistics with Active Inference

$U$-statistics play a central role in statistical inference. In many modern applications, however, acquiring the labels required for $U$-statistics is costly. Motivated by recent advances in active inference, we develop an active inference framework for $U$-statistics that selectively queries informative labels to improve estimation efficiency under a fixed labeling budget, while preserving valid statistical inference. Our approach is built on the augmented inverse probability weighting $U$-statistic, which is designed to incorporate the sampling rule and machine learning predictions. We characterize the optimal sampling rule that minimizes its variance and design practical sampling strategies. We further extend the framework to $U$-statistic-based empirical risk minimization. Experiments on real datasets demonstrate substantial gains in estimation efficiency over baseline methods, while maintaining target coverage.

stat.ML↗

arXiv2026

Generalized Boundary FDR Control under Arbitrary Dependence: An Approach on Closure Principle

False discovery rate (FDR) is a cornerstone of modern multiple testing. However, it often fails to guarantee the reliability of "marginal" discoveries that lie at the boundary of the rejection set, which are often crucial in high-precision applications. While recent works (Soloff et al., 2024; Xiang et al., 2025) introduced the boundary false discovery rate (bFDR) to control the error probability at the marginal discovery, their method relies on restrictive assumptions such as independence or specific prior distributions. In this paper, we first propose $k$-bFDR, a novel generalization that controls the error probability of the $k$ least significant discoveries. We then provide a systematic investigation into the theoretical relationship between $k$-bFDR and existing error metrics. Furthermore, building upon the closure principle, we develop Domino, a unified framework that guarantees $k$-bFDR control under arbitrary dependence, applicable for both p-values and e-values. We prove the theoretical validity of the proposed Domino algorithm and demonstrate through extensive numerical experiments that it consistently achieves rigorous $k$-bFDR control while identifying trustworthy marginal discoveries. Analyses of real data reveal that $k$-bFDR control yields higher-quality rejection sets with greater practical significance.

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arXiv2026

Reliever: Relieving the Burden of Costly Model Fits for Changepoint Detection

Changepoint detection typically relies on a grid-search strategy for optimal data segmentation. When model fitting itself is expensive, repeatedly fitting a model on every candidate segment dominates the computation. Existing approaches mitigate this by pruning the grid, thus reducing the number of segments (and model fits). We propose Reliever, which instead cuts the number of model fits directly and nests seamlessly within standard grid-search routines. Reliever fits a small, deterministic collection of proxy models and reuses them wherever they apply, making it compatible with a wide range of existing algorithms. For high-dimensional regression with changepoints, coupling Reliever with an optimal grid-search method yields changepoint and coefficient estimators that are rate-optimal up to a logarithmic factor. Extensive numerical experiments demonstrate that Reliever rapidly and accurately detects changepoints across a wide range of high-dimensional and nonparametric models.

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arXiv2026

Changepoint Detection in Complex Models: Cross-Fitting Is Needed

Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or hyperparameter tuning -- this strategy can lead to inaccurate changepoint estimation due to over-adaptivity biases. To mitigate this issue, we propose a novel cross-fitting methodology based on out-of-sample loss evaluations, which decouples model fitting from changepoint search. We establish a general theoretical framework for consistent changepoint estimation under mild conditions, and further extend it to temporally dependent data. A key implication of the theory is that consistency depends primarily on the models' predictive accuracy over nearly homogeneous segments. Numerical experiments show that the proposed method substantially improves the reliability and adaptability of changepoint detection in complex scenarios.

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arXiv2026

Stable Localized Conformal Prediction via Transduction

Existing evaluations of conformal prediction, such as prediction efficiency and test-conditional coverage, are defined in expectation over the calibration data. In practice, when only one calibration set of limited size is available, prediction sets often exhibit high variability in size, especially for methods with localization. We formalize this concern as set stability, defined as the variance of the conditional expectation of the set size given the calibration data. To improve stability without requiring additional target-task labels, we propose Stable Conformal Prediction (StCP), a transfer learning approach that utilizes labeled source-task data and unlabeled target data. Theoretically, we characterize the marginal coverage and stability of StCP; empirically, it delivers more stable prediction sets than standard conformal prediction methods, especially for those with localization, when calibration data are limited.

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arXiv2026

Alignment Imprint: Zero-Shot AI-Generated Text Detection via Provable Preference Discrepancy

Detecting AI-generated text is an important but challenging problem. Existing likelihood-based detection methods are often sensitive to content complexity and may exhibit unstable performance. In this paper, our key insight is that modern Large Language Models (LLMs) undergo alignment (including fine-tuning and preference tuning), leaving a measurable distributional imprint. We theoretically derive this imprint by abstracting the alignment process as a sequence of constrained optimization steps, showing that the log-likelihood ratio can naturally decompose into implicit instructional biases and preference rewards. We refer to this quantity as the Alignment Imprint. Furthermore, to mitigate the instability in high-entropy regions, we introduce Log-likelihood Alignment Preference Discrepancy (LAPD), a standardized information-weighted statistic based on alignment imprint. We provide statistical guarantee that alignment-based statistics dominate Fast-DetectGPT in performance. We also theoretically show that LAPD strictly improves the unweighted alignment scores when the aligned and base models are close in distribution. Extensive experiments show that LAPD achieves an improvement 45.82% relative to the strongest existing baselines, yielding large and consistent gains across all settings.

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arXiv2026

Toward Exact Convergence in Byzantine-Robust Decentralized Learning: A Statistical Identification Approach

To defend against Byzantine attacks in decentralized learning, most existing methods rely on robust aggregation rules to mitigate the influence of malicious machines. However, these strategies inherently introduce bias, leading to inexact convergence with non-vanishing steady-state errors. In this paper, we propose a strategic shift from passive aggregation to active identification by introducing the Decentralized Rescaled Stochastic Gradient Descent with Byzantine Machine Identification (DRSGD-ByMI) framework. The core of our approach is an identification-based ``detect-then-optimize'' pipeline, where a p-value-free detection procedure is developed to accurately prune malicious nodes from the network. By leveraging sample-splitting score statistics, this identification mechanism achieves false discovery rate control without requiring restrictive distributional assumptions. We theoretically demonstrate that this precise identification allows the decentralized network to recover sufficient connectivity among the normal nodes, thereby enabling DRSGD-ByMI to match, even in the presence of Byzantine machines, the same order-optimal convergence rate as standard decentralized stochastic first-order methods. Numerical experiments validate our theoretical results and demonstrate the effectiveness of DRSGD-ByMI for decentralized robust learning problems.

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arXiv2026

Distribution-informed Online Conformal Prediction

Conformal prediction provides a pivotal and flexible technique for uncertainty quantification by constructing prediction sets with a predefined coverage rate. Many online conformal prediction methods have been developed to address data distribution shifts in fully adversarial environments, resulting in overly conservative prediction sets. We propose Conformal Optimistic Prediction (COP), an online conformal prediction algorithm incorporating underlying data pattern into the update rule. Through estimated cumulative distribution function of non-conformity scores, COP produces tighter prediction sets when predictable pattern exists, while retaining valid coverage guarantees even when estimates are inaccurate. We establish a joint bound on coverage and regret, which further confirms the validity of our approach. We also prove that COP achieves distribution-free, finite-sample coverage under arbitrary learning rates and can converge when scores are $i.i.d.$. The experimental results also show that COP can achieve valid coverage and construct shorter prediction intervals than other baselines.

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arXiv2026

Model-Agnostic and Uncertainty-Aware Dimensionality Reduction in Supervised Learning

Dimension reduction is a fundamental tool for analyzing high-dimensional data in supervised learning. Traditional methods for estimating intrinsic order often prioritize model-specific structural assumptions over predictive utility. This paper introduces predictive order determination (POD), a model-agnostic framework that determines the minimal predictively sufficient dimension by directly evaluating out-of-sample predictiveness. POD quantifies uncertainty via error bounds for over- and underestimation and achieves consistency under mild conditions. By unifying dimension reduction with predictive performance, POD applies flexibly across diverse reduction tasks and supervised learners. Simulations and real-data analyses show that POD delivers accurate, uncertainty-aware order estimates, making it a versatile component for prediction-centric pipelines.

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arXiv2025

Optimal Model Selection for Conformalized Robust Optimization

In decision-making under uncertainty, Contextual Robust Optimization (CRO) provides reliability by minimizing the worst-case decision loss over a prediction set. While recent advances use conformal prediction to construct prediction sets for machine learning models, the downstream decisions critically depend on model selection. This paper introduces novel model selection frameworks for CRO that unify robustness control with decision risk minimization. We first propose Conformalized Robust Optimization with Model Selection (CROMS), a framework that selects the model to approximately minimize the averaged decision risk in CRO solutions. Given the target robustness level 1-α, we present a computationally efficient algorithm called E-CROMS, which achieves asymptotic robustness control and decision optimality. To correct the control bias in finite samples, we further develop two algorithms: F-CROMS, which ensures a 1-αrobustness but requires searching the label space; and J-CROMS, which offers lower computational cost while achieving a 1-2αrobustness. Furthermore, we extend the CROMS framework to the individualized setting, where model selection is performed by minimizing the conditional decision risk given the covariates of the test data. This framework advances conformal prediction methodology by enabling covariate-aware model selection. Numerical results demonstrate significant improvements in decision efficiency across diverse synthetic and real-world applications, outperforming baseline approaches.

stat.ML↗

arXiv2025

Empirical Likelihood Meets Prediction-Powered Inference

We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based on labeled outcomes with auxiliary moment conditions built from predictions, and then optimizing empirical likelihood under these joint constraints. The resulting empirical likelihood-based prediction-powered inference (EPI) estimator is asymptotically normal, has asymptotic variance no larger than the fully supervised estimator, and attains the semiparametric efficiency bound when the auxiliary functions span the predictable component of the supervised score. For hypothesis testing and confidence sets, empirical likelihood ratio statistics admit chi-squared-type limiting distributions. As a by-product, the empirical likelihood weights induce a calibrated empirical distribution that integrates supervised and prediction-based information, enabling estimation and uncertainty quantification for general functionals beyond parameters defined by estimating equations. We present two practical implementations: one based on basis expansions in the predictions and covariates, and one that learns an approximately optimal auxiliary function by cross-fitting. In simulations and applications, EPI reduces mean squared error and shortens confidence intervals while maintaining nominal coverage.

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arXiv2025

CAP: A General Algorithm for Online Selective Conformal Prediction with FCR Control

We study the problem of post-selection predictive inference in an online fashion. To avoid devoting resources to unimportant units, a preliminary selection of the current individual before reporting its prediction interval is common and meaningful in online predictive tasks. Since the online selection causes a temporal multiplicity in the selected prediction intervals, it is important to control the real-time false coverage-statement rate (FCR) which measures the overall miscoverage level. We develop a general framework named CAP (Calibration after Adaptive Pick) that performs an adaptive pick rule on historical data to construct a calibration set if the current individual is selected and then outputs a conformal prediction interval for the unobserved label. We provide tractable procedures for constructing the calibration set for popular online selection rules. We proved that CAP can achieve an exact selection-conditional coverage guarantee in the finite-sample and distribution-free regimes. To account for the distribution shift in online data, we also embed CAP into some recent dynamic conformal prediction algorithms and show that the proposed method can deliver long-run FCR control. Numerical results on both synthetic and real data corroborate that CAP can effectively control FCR around the target level and yield more narrowed prediction intervals over existing baselines across various settings.

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arXiv2025

Aggregating Conformal Prediction Sets via α-Allocation

Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet, efficiently leveraging multiple conformity scores to reduce prediction set size remains a major open challenge. Instead of selecting a single best score, this work introduces a principled aggregation strategy, COnfidence-Level Allocation (COLA), that optimally allocates confidence levels across multiple conformal prediction sets to minimize empirical set size while maintaining provable coverage. Two variants are further developed, COLA-s and COLA-f, which guarantee finite-sample marginal coverage via sample splitting and full conformalization, respectively. In addition, we develop COLA-l, an individualized allocation strategy that promotes local size efficiency while achieving asymptotic conditional coverage. Extensive experiments on synthetic and real-world datasets demonstrate that COLA achieves considerably smaller prediction sets than state-of-the-art baselines while maintaining valid coverage.

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