arXiv subjects

Zhanrui Cai

Publications and source records attributed to Zhanrui Cai.

15 recordsLinked to original sources

arXiv2026

Token-Level Likelihood-Array Regression for Membership Inference and AI-Generated Text Detection

Membership inference asks whether a text was used to train a language model, whereas AI-generated text detection asks whether it was generated by a language model rather than written by a human. Existing likelihood-based methods typically compress token-level probabilities into a few prespecified scores, most often using only probabilities conditioned on the full preceding context. We propose likelihood-array regression (LAR), which evaluates each target token under nested left-context windows and organizes the resulting likelihood-derived features into a structured array. After aligning arrays across texts of different lengths, LAR learns how detection information varies with context scale, token position, and likelihood features. LAR-1 aggregates learned contributions from individual aligned cells, while LAR-2 adds second-order features formed from pairs of evaluations of the same target token across context lengths. For within-path quadratic model, we establish matching minimax lower and upper bounds, characterize errors from finite-dimensional approximation and random squared projections, and derive conditions under which an oracle spectral sieve attains the minimax rate. Across multiple scoring language models, LAR substantially improves membership inference and AI-generated text detection over likelihood-based baselines. The analyses further show that shorter-context likelihoods contain information beyond conventional full-context probabilities, while second-order features provide additional gains for membership inference.

stat.ML↗

arXiv2026

Differentially Private Estimation and Inference in High-Dimensional Regression with FDR Control

This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the unknown sparsity parameter in differentially private sparse linear regression (DP-SLR), eliminating the need for prior knowledge of model sparsity, which is a requisite in the existing literature. Next, we develop the DP debiased algorithm that enables privacy-preserving inference on a particular subset of regression parameters. Our proposed method enables privacy-preserving inference on the regression parameters by leveraging the inherent sparsity of high-dimensional linear regression models. Additionally, we address private feature selection by considering multiple testing in high-dimensional linear regression by introducing a DP multiple testing procedure that controls the false discovery rate (FDR). This allows for accurate and privacy-preserving identification of significant predictors in the regression model. Through extensive simulations and real data analyses, we demonstrate the effectiveness of our proposed methods in conducting inference for high-dimensional linear models while safeguarding privacy and controlling the FDR.

stat.ME↗

arXiv2026

A Statistical Framework for Alignment with Biased AI Feedback

Modern alignment pipelines are increasingly replacing expensive human preference labels with evaluations from large language models (LLM-as-Judge). However, AI labels can be systematically biased compared to high-quality human feedback datasets. In this paper, we develop two debiased alignment methods within a general framework that accommodates heterogeneous prompt-response distributions and external human feedback sources. Debiased Direct Preference Optimization (DDPO) augments standard DPO with a residual-based correction and density-ratio reweighting to mitigate systematic bias, while retaining DPO's computational efficiency. Debiased Identity Preference Optimization (DIPO) directly estimates human preference probabilities without imposing a parametric reward model. We provide theoretical guarantees for both methods: DDPO offers a practical and computationally efficient solution for large-scale alignment, whereas DIPO serves as a robust, statistically optimal alternative that attains the semiparametric efficiency bound. Empirical studies on sentiment generation, summarization, and single-turn dialogue demonstrate that the proposed methods substantially improve alignment efficiency and recover performance close to that of an oracle trained on fully human-labeled data.

stat.ML↗

arXiv2025

A General Stability Approach to False Discovery Rate Control

Stability and reproducibility are essential considerations in various applications of statistical methods. False Discovery Rate (FDR) control methods are able to control false signals in scientific discoveries. However, many FDR control methods, such as Model-X knockoff and data-splitting approaches, yield unstable results due to the inherent randomness of the algorithms. To enhance the stability and reproducibility of statistical outcomes, we propose a general stability approach for FDR control in feature selection and multiple testing problems, named FDR Stabilizer. Taking feature selection as an example, our method first aggregates feature importance statistics obtained by multiple runs of the base FDR control procedure into a consensus ranking. Then, we construct a stabilized relaxed e-value for each feature and apply the e-BH procedure to these stabilized e-values to obtain the final selection set. We theoretically derive the finite-sample bounds for the FDR and the power of our method, and show that our method asymptotically controls the FDR without power loss. Moreover, we establish the stability of the proposed method, showing that the stabilized selection set converges to a deterministic limit as the number of repetitions increases. Extensive numerical experiments and applications to real datasets demonstrate that the proposed method generally outperforms existing alternatives.

stat.ME↗

arXiv2025

Statistical Inference for Differentially Private Stochastic Gradient Descent

Privacy preservation in machine learning, particularly through Differentially Private Stochastic Gradient Descent (DP-SGD), is critical for sensitive data analysis. However, existing statistical inference methods for SGD predominantly focus on cyclic subsampling, while DP-SGD requires randomized subsampling. This paper first bridges this gap by establishing the asymptotic properties of SGD under the randomized rule and extending these results to DP-SGD. For the output of DP-SGD, we show that the asymptotic variance decomposes into statistical, sampling, and privacy-induced components. Two methods are proposed for constructing valid confidence intervals: the plug-in method and the random scaling method. We also perform extensive numerical analysis, which shows that the proposed confidence intervals achieve nominal coverage rates while maintaining privacy.

stat.ML↗

arXiv2025

How Much Does Home Field Advantage Matter in Soccer Games? A Causal Inference Approach for English Premier League Analysis

In many sports, it is commonly believed that the home team has an advantage over the visiting team, known as the home field advantage. Yet its causal effect on team performance is largely unknown. In this paper, we propose a novel causal inference approach to study the causal effect of home field advantage in English Premier League. We develop a hierarchical causal model and show that both league level and team level causal effects are identifiable and can be conveniently estimated. We further develop an inference procedure for the proposed estimators and demonstrate its excellent numerical performance via simulation studies. We implement our method on the 2020-21 English Premier League data and assess the causal effect of home advantage on eleven summary statistics that measure the offensive and defensive performance and referee-assessed disciplinary outcomes. We find that the home field advantage resides more heavily in offensive statistics than it does in defensive or referee statistics. We also find evidence that teams that had lower rankings retain a higher home field advantage.

stat.AP↗

arXiv2025

Model-free Change-point Detection using AUC of a Classifier

In contemporary data analysis, it is increasingly common to work with non-stationary complex data sets. These data sets typically extend beyond the classical low-dimensional Euclidean space, making it challenging to detect shifts in their distribution without relying on strong structural assumptions. This paper proposes a novel offline change-point detection method that leverages classifiers developed in the statistics and machine learning community. With suitable data splitting, the test statistic is constructed through sequential computation of the Area Under the Curve (AUC) of a classifier, which is trained on data segments on both ends of the sequence. It is shown that the resulting AUC process attains its maxima at the true change-point location, which facilitates the change-point estimation. The proposed method is characterized by its complete nonparametric nature, high versatility, considerable flexibility, and absence of stringent assumptions on the underlying data or any distributional shifts. Theoretically, we derive the limiting pivotal distribution of the proposed test statistic under null, as well as the asymptotic behaviors under both local and fixed alternatives. The localization rate of the change-point estimator is also provided. Extensive simulation studies and the analysis of two real-world data sets illustrate the superior performance of our approach compared to existing model-free change-point detection methods.

stat.ME↗

arXiv2025

Knockoffs Inference under Privacy Constraints

Model-X knockoff framework offers a model-free variable selection method that ensures finite sample false discovery rate (FDR) control. However, the complexity of generating knockoff variables, coupled with the model-free assumption, presents significant challenges for protecting data privacy in this context. In this paper, we propose a comprehensive framework for knockoff inference within the differential privacy paradigm. Our proposed method guarantees robust privacy protection while preserving the exact FDR control entailed by the original model-X knockoff procedure. We further conduct power analysis and establish sufficient conditions under which the noise added for privacy preservation does not asymptotically compromise power. Through various applications, we demonstrate that the differential privacy knockoff (DP-knockoff) method can be effectively utilized to safeguard privacy during variable selection with FDR control in both low and high dimensional settings.

stat.ME↗

arXiv2025

Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm

Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Since its proposal, sliced inverse regression has emerged as a widely utilized statistical technique to reduce the dimensionality of covariates while maintaining sufficient statistical information. In this paper, we propose optimally differentially private algorithms specifically designed to address privacy concerns in the context of sufficient dimension reduction. We establish lower bounds for differentially private sliced inverse regression in low and high dimensional settings. Moreover, we develop differentially private algorithms that achieve the minimax lower bounds up to logarithmic factors. Through a combination of simulations and real data analysis, we illustrate the efficacy of these differentially private algorithms in safeguarding privacy while preserving vital information within the reduced dimension space. As a natural extension, we can readily offer analogous lower and upper bounds for differentially private sparse principal component analysis, a topic that may also be of potential interest to the statistics and machine learning community.

stat.ML↗

arXiv2024

Penalized Sparse Covariance Regression with High Dimensional Covariates

Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional predictors (i.e., similarity matrices). Specifically, we use the penalization method to identify the informative predictors and estimate their associated coefficients simultaneously. We first investigate the Lasso estimator and subsequently consider the folded concave penalized estimation methods (e.g., SCAD and MCP). However, the theoretical analysis of the existing penalization methods is primarily based on i.i.d. data, which is not directly applicable to our scenario. To address this difficulty, we establish the non-asymptotic error bounds by exploiting the spectral properties of the covariance matrix and similarity matrices. Then, we derive the estimation error bound for the Lasso estimator and establish the desirable oracle property of the folded concave penalized estimator. Extensive simulation studies are conducted to corroborate our theoretical results. We also illustrate the usefulness of the proposed method by applying it to a Chinese stock market dataset.

stat.ME↗

arXiv2024

One Step to Efficient Synthetic Data

A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true distribution. Motivated by this, we propose a general method of producing synthetic data, which is widely applicable for parametric models, has asymptotically efficient summary statistics, and is both easily implemented and highly computationally efficient. Our approach allows for the construction of both partially synthetic datasets, which preserve certain summary statistics, as well as fully synthetic data which satisfy the strong guarantee of differential privacy (DP), both with the same asymptotic guarantees. We also provide theoretical and empirical evidence that the distribution from our procedure converges to the true distribution. Besides our focus on synthetic data, our procedure can also be used to perform approximate hypothesis tests in the presence of intractable likelihood functions.

math.ST↗

arXiv2023

Asymptotic Distribution-Free Independence Test for High Dimension Data

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is sparse, independence testing becomes very challenging without distributional or structural assumptions. In this paper, we propose a general framework for independence testing by first fitting a classifier that distinguishes the joint and product distributions, and then testing the significance of the fitted classifier. This framework allows us to borrow the strength of the most advanced classification algorithms developed from the modern machine learning community, making it applicable to high dimensional, complex data. By combining a sample split and a fixed permutation, our test statistic has a universal, fixed Gaussian null distribution that is independent of the underlying data distribution. Extensive simulations demonstrate the advantages of the newly proposed test compared with existing methods. We further apply the new test to a single-cell data set to test the independence between two types of single-cell sequencing measurements, whose high dimensionality and sparsity make existing methods hard to apply.

stat.ME↗

arXiv2023

Adaptive False Discovery Rate Control with Privacy Guarantee

Differentially private multiple testing procedures can protect the information of individuals used in hypothesis tests while guaranteeing a small fraction of false discoveries. In this paper, we propose a differentially private adaptive FDR control method that can control the classic FDR metric exactly at a user-specified level $α$ with privacy guarantee, which is a non-trivial improvement compared to the differentially private Benjamini-Hochberg method proposed in Dwork et al. (2021). Our analysis is based on two key insights: 1) a novel p-value transformation that preserves both privacy and the mirror conservative property, and 2) a mirror peeling algorithm that allows the construction of the filtration and application of the optimal stopping technique. Numerical studies demonstrate that the proposed DP-AdaPT performs better compared to the existing differentially private FDR control methods. Compared to the non-private AdaPT, it incurs a small accuracy loss but significantly reduces the computation cost.

stat.ML↗

arXiv2023

Robust Model Selection with Application in Single-Cell Multiomics Data

Model selection is critical in the modern statistics and machine learning community. However, most existing works do not apply to heavy-tailed data, which are commonly encountered in real applications, such as the single-cell multiomics data. In this paper, we propose a rank-sum based approach that outputs a confidence set containing the optimal model with guaranteed probability. Motivated by conformal inference, we developed a general method that is applicable without moment or tail assumptions on the data. We demonstrate the advantage of the proposed method through extensive simulation and a real application on the COVID-19 genomics dataset (Stephenson et al., 2021). To perform the inference on rank-sum statistics, we derive a general Gaussian approximation theory for high dimensional two-sample U-statistics, which may be of independent interest to the statistics and machine learning community.

stat.ME↗

arXiv2021

A Distribution Free Conditional Independence Test with Applications to Causal Discovery

This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional dependence by quantifying the mutual dependence among the transformed variables. The proposed index has several appealing properties. (a) It is distribution free since the limiting null distribution of the proposed index does not depend on the population distributions of the data. Hence the critical values can be tabulated by simulations. (b) The proposed index ranges from zero to one, and equals zero if and only if the conditional independence holds. Thus, it has nontrivial power under the alternative hypothesis. (c) It is robust to outliers and heavy-tailed data since it is invariant to conditional strictly monotone transformations. (d) It has low computational cost since it incorporates a simple closed-form expression and can be implemented in quadratic time. (e) It is insensitive to tuning parameters involved in the calculation of the proposed index. (f) The new index is applicable for multivariate random vectors as well as for discrete data. All these properties enable us to use the new index as statistical inference tools for various data. The effectiveness of the method is illustrated through extensive simulations and a real application on causal discovery.

stat.ME↗