arXiv subjects

Changliang Zou

Publications and source records attributed to Changliang Zou.

At least 37 records · Page 2Linked to original sources

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.

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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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arXiv2025

Error-quantified Conformal Inference for Time Series

Uncertainty quantification in time series prediction is challenging due to the temporal dependence and distribution shift on sequential data. Conformal inference provides a pivotal and flexible instrument for assessing the uncertainty of machine learning models through prediction sets. Recently, a series of online conformal inference methods updated thresholds of prediction sets by performing online gradient descent on a sequence of quantile loss functions. A drawback of such methods is that they only use the information of revealed non-conformity scores via miscoverage indicators but ignore error quantification, namely the distance between the non-conformity score and the current threshold. To accurately leverage the dynamic of miscoverage error, we propose \textit{Error-quantified Conformal Inference} (ECI) by smoothing the quantile loss function. ECI introduces a continuous and adaptive feedback scale with the miscoverage error, rather than simple binary feedback in existing methods. We establish a long-term coverage guarantee for ECI under arbitrary dependence and distribution shift. The extensive experimental results show that ECI can achieve valid miscoverage control and output tighter prediction sets than other baselines.

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arXiv2025

Simultaneous Detection and Localization of Mean and Covariance Changes in High Dimensions

Existing methods for high-dimensional changepoint detection and localization typically focus on changes in either the mean vector or the covariance matrix separately. This separation reduces detection power and localization accuracy when both parameters change simultaneously. We propose a simple yet powerful method that jointly monitors shifts in both the mean and covariance structures. Under mild conditions, the test statistics for detecting these shifts jointly converge in distribution to a bivariate standard normal distribution, revealing their asymptotic independence. This independence enables the combination of the individual p-values using Fisher's method, and the development of an adaptive p-value-based estimator for the changepoint. Theoretical analysis and extensive simulations demonstrate the superior performance of our method in terms of both detection power and localization accuracy.

math.ST↗

arXiv2025

e-GAI: e-value-based Generalized $α$-Investing for Online False Discovery Rate Control

Online multiple hypothesis testing has attracted a lot of attention in many applications, e.g., anomaly status detection and stock market price monitoring. The state-of-the-art generalized $α$-investing (GAI) algorithms can control online false discovery rate (FDR) on p-values only under specific dependence structures, a situation that rarely occurs in practice. The e-LOND algorithm (Xu & Ramdas, 2024) utilizes e-values to achieve online FDR control under arbitrary dependence but suffers from a significant loss in power as testing levels are derived from pre-specified descent sequences. To address these limitations, we propose a novel framework on valid e-values named e-GAI. The proposed e-GAI can ensure provable online FDR control under more general dependency conditions while improving the power by dynamically allocating the testing levels. These testing levels are updated not only by relying on both the number of previous rejections and the prior costs, but also, differing from the GAI framework, by assigning less $α$-wealth for each rejection from a risk aversion perspective. Within the e-GAI framework, we introduce two new online FDR procedures, e-LORD and e-SAFFRON, and provide strategies for the long-term performance to address the issue of $α$-death, a common phenomenon within the GAI framework. Furthermore, we demonstrate that e-GAI can be generalized to conditionally super-uniform p-values. Both simulated and real data experiments demonstrate the advantages of both e-LORD and e-SAFFRON in FDR control and power.

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arXiv2025

Change-Points Detection and Support Recovery for Spatially Indexed Functional Data

Large volumes of spatiotemporal data, characterized by high spatial and temporal variability, may experience structural changes over time. Unlike traditional change-point problems, each sequence in this context consists of function-valued curves observed at multiple spatial locations, with typically only a small subset of locations affected. This paper addresses two key issues: detecting the global change-point and identifying the spatial support set, within a unified framework tailored to spatially indexed functional data. By leveraging a weakly separable cross-covariance structure -- an extension beyond the restrictive assumption of space-time separability -- we incorporate functional principal component analysis into the change-detection methodology, while preserving common temporal features across locations. A kernel-based test statistic is further developed to integrate spatial clustering pattern into the detection process, and its local variant, combined with the estimated change-point, is employed to identify the subset of locations contributing to the mean shifts. To control the false discovery rate in multiple testing, we introduce a functional symmetrized data aggregation approach that does not rely on pointwise p-values and effectively pools spatial information. We establish the asymptotic validity of the proposed change detection and support recovery method under mild regularity conditions. The efficacy of our approach is demonstrated through simulations, with its practical usefulness illustrated in an application to China's precipitation data.

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arXiv2025

Power Enhancement of Permutation-Augmented Partial-Correlation Tests via Fixed-Row Permutations

Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate of interest. We remedy this by fixing a design-driven subset of rows and permuting only the remainder. The fixed rows are chosen by a greedy algorithm that maximizes a lower bound on power. This strategy reduces covariate-permutation collinearity while preserving worst-case Type I error control. Simulations confirm that this refinement maintains nominal size and delivers substantial power gains over original unrestricted permutations, especially in high-collinearity regimes.

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arXiv2025

Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach

Conformal prediction is a powerful tool for constructing prediction intervals for black-box models, providing a finite sample coverage guarantee for exchangeable data. However, this exchangeability is compromised when some entries of the test feature are contaminated, such as in the case of cellwise outliers. To address this issue, this paper introduces a novel framework called detect-then-impute conformal prediction. This framework first employs an outlier detection procedure on the test feature and then utilizes an imputation method to fill in those cells identified as outliers. To quantify the uncertainty in the processed test feature, we adaptively apply the detection and imputation procedures to the calibration set, thereby constructing exchangeable features for the conformal prediction interval of the test label. We develop two practical algorithms, PDI-CP and JDI-CP, and provide a distribution-free coverage analysis under some commonly used detection and imputation procedures. Notably, JDI-CP achieves a finite sample $1-2α$ coverage guarantee. Numerical experiments on both synthetic and real datasets demonstrate that our proposed algorithms exhibit robust coverage properties and comparable efficiency to the oracle baseline.

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arXiv2025

LoCA: Location-Aware Cosine Adaptation for Parameter-Efficient Fine-Tuning

Low-rank adaptation (LoRA) has become a prevalent method for adapting pre-trained large language models to downstream tasks. However, the simple low-rank decomposition form may constrain the hypothesis space. To address this limitation, we introduce Location-aware Cosine Adaptation (LoCA), a novel frequency-domain parameter-efficient fine-tuning method based on inverse Discrete Cosine Transform (iDCT) with selective locations of learnable components. We begin with a comprehensive theoretical comparison between frequency-domain and low-rank decompositions for fine-tuning pre-trained large models. Our analysis reveals that frequency-domain decomposition with carefully selected frequency components can surpass the expressivity of traditional low-rank-based methods. Furthermore, we demonstrate that iDCT offers a more efficient implementation compared to inverse Discrete Fourier Transform (iDFT), allowing for better selection and tuning of frequency components while maintaining equivalent expressivity to the optimal iDFT-based adaptation. By employing finite-difference approximation to estimate gradients for discrete locations of learnable coefficients on the DCT spectrum, LoCA dynamically selects the most informative frequency components during training. Experiments on diverse language and vision fine-tuning tasks demonstrate that LoCA offers enhanced parameter efficiency while maintains computational feasibility comparable to low-rank-based methods.

cs.LG↗

arXiv2025

Robust Multi-Source Domain Adaptation under Label Shift

As the volume of data continues to expand, it becomes increasingly common for data to be aggregated from multiple sources. Leveraging multiple sources for model training typically achieves better predictive performance on test datasets. Unsupervised multi-source domain adaptation aims to predict labels of unlabeled samples in the target domain by using labeled samples from source domains. This work focuses on robust multi-source domain adaptation for multi-category classification problems against the heterogeneity of label shift and data contamination. We investigate a domain-weighted empirical risk minimization framework for robust estimation of the target domain's class proportion. Inspired by outlier detection techniques, we propose a refinement procedure within this framework. With the estimated class proportion, robust classifiers for the target domain can be constructed. Theoretically, we study the finite-sample error bounds of the domain-weighted empirical risk minimization and highlight the improvement of the refinement step. Numerical simulations and real-data applications demonstrate the superiority of the proposed method.

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arXiv2025

Patch Triplet Similarity Purification for Guided Real-World Low-Dose CT Image Denoising

Image denoising of low-dose computed tomography (LDCT) is an important problem for clinical diagnosis with reduced radiation exposure. Previous methods are mostly trained with pairs of synthetic or misaligned LDCT and normal-dose CT (NDCT) images. However, trained with synthetic noise or misaligned LDCT/NDCT image pairs, the denoising networks would suffer from blurry structure or motion artifacts. Since non-contrast CT (NCCT) images share the content characteristics to the corresponding NDCT images in a three-phase scan, they can potentially provide useful information for real-world LDCT image denoising. To exploit this aspect, in this paper, we propose to incorporate clean NCCT images as useful guidance for the learning of real-world LDCT image denoising networks. To alleviate the issue of spatial misalignment in training data, we design a new Patch Triplet Similarity Purification (PTSP) strategy to select highly similar patch (instead of image) triplets of LDCT, NDCT, and NCCT images for network training. Furthermore, we modify two image denoising transformers of SwinIR and HAT to accommodate the NCCT image guidance, by replacing vanilla self-attention with cross-attention. On our collected clinical dataset, the modified transformers trained with the data selected by our PTSP strategy show better performance than 15 comparison methods on real-world LDCT image denoising. Ablation studies validate the effectiveness of our NCCT image guidance and PTSP strategy. We will publicly release our data and code.

eess.IV↗

arXiv2025

ART: Distribution-Free and Model-Agnostic Changepoint Detection with Finite-Sample Guarantees

We introduce ART, a distribution-free and model-agnostic framework for changepoint detection that provides finite-sample guarantees. ART transforms independent observations into real-valued scores via a symmetric function, ensuring exchangeability in the absence of changepoints. These scores are then ranked and aggregated to detect distributional changes. The resulting test offers exact Type-I error control, agnostic to specific distributional or model assumptions. Moreover, ART seamlessly extends to multi-scale settings, enabling robust multiple changepoint estimation and post-detection inference with finite-sample error rate control. By locally ranking the scores and performing aggregations across multiple prespecified intervals, ART identifies changepoint intervals and refines subsequent inference while maintaining its distribution-free and model-agnostic nature. This adaptability makes ART as a reliable and versatile tool for modern changepoint analysis, particularly in high-dimensional data contexts and applications leveraging machine learning methods.

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arXiv2024

Conditional Testing based on Localized Conformal p-values

In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies.

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arXiv2024

TUNE: Algorithm-Agnostic Inference after Changepoint Detection

In multiple changepoint analysis, assessing the uncertainty of detected changepoints is crucial for enhancing detection reliability -- a topic that has garnered significant attention. Despite advancements through selective p-values, current methodologies often rely on stringent assumptions tied to specific changepoint models and detection algorithms, potentially compromising the accuracy of post-detection statistical inference. We introduce TUNE (Thresholding Universally and Nullifying change Effect), a novel algorithm-agnostic approach that uniformly controls error probabilities across detected changepoints. TUNE sets a universal threshold for multiple test statistics, applicable across a wide range of algorithms, and directly controls the family-wise error rate without the need for selective p-values. Through extensive theoretical and numerical analyses, TUNE demonstrates versatility, robustness, and competitive power, offering a viable and reliable alternative for model-agnostic post-detection inference.

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