arXiv subjects

Lixing Zhu

Publications and source records attributed to Lixing Zhu.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Framework for In-Context Learning with Causal and Masked Language Models

In-context learning (ICL) has emerged as a central capability of pretrained language models, yet its theoretical analysis has focused primarily on causal language models trained by left-to-right autoregressive prediction, such as GPT-style models. Masked language models instead recover masked tokens from bidirectional context, and their role in ICL remains less understood. We develop a statistical learning framework that represents the context examples by their empirical measure and models prediction as a function of the context and the query. This formulation places autoregressive and masked pretraining objectives within a common excess-risk analysis. Under Wasserstein-type regularity conditions, we relate pretraining with T tasks and N samples per task to k-shot excess risk at inference, obtaining same-order upper bounds for masked and autoregressive objectives. We also study task-distribution shift, where pretraining tasks are sampled from P and inference tasks from Q; the resulting bound contains an additional term controlled by the lifted Wasserstein distance between P and Q. The bounds further imply an order-optimal allocation under a fixed pretraining data budget and refined rates under intrinsic low-dimensional structure. Experiments on controlled function-learning tasks show that the Masked Pair Encoder (MPE) can achieve performance comparable to GPT-2-style causal Transformers, suggesting that ICL behavior is not specific to causal language models.

cs.LG↗

arXiv2026

Missingness-Adaptive Factor Identification in High-Dimensional Data

Determining the number of factors in high-dimensional factor models remains a fundamental challenge, particularly when data are incomplete. This paper introduces the concept of identifiable factors, those that can be reliably recovered despite missing observations, and proposes the Missingness-Adaptive Thresholding Estimator (MATE). To our knowledge, MATE is the first missingness-adaptive framework for factor number determination that accommodates both homogeneous and heterogeneous missingness without imposing restrictive assumptions on factor strength. Notably, it operates without data imputation, circumventing the computational burden associated with most existing approaches. We establish a rigorous theoretical foundation for MATE, proving its consistency under a range of structural conditions. Extensive simulations and real-world applications demonstrate that MATE consistently outperforms state-of-the-art methods, exhibiting superior robustness in settings with high missingness rates and weak factor signals.

stat.ME↗

arXiv2026

Empirical Likelihood-Based Fairness Auditing: Distribution-Free Certification and Flagging

Machine learning models in high-stakes applications, such as recidivism prediction and automated personnel selection, often exhibit systematic performance disparities across sensitive subpopulations, raising critical concerns regarding algorithmic bias. Fairness auditing addresses these risks through two primary functions: certification, which verifies adherence to fairness constraints; and flagging, which isolates specific demographic groups experiencing disparate treatment. However, existing auditing techniques are frequently limited by restrictive distributional assumptions or prohibitive computational overhead. We propose a novel empirical likelihood-based (EL) framework that constructs robust statistical measures for model performance disparities. Unlike traditional methods, our approach is non-parametric; the proposed disparity statistics follow asymptotically chi-square or mixed chi-square distributions, ensuring valid inference without assuming underlying data distributions. This framework uses a constrained optimization profile that admits stable numerical solutions, facilitating both large-scale certification and efficient subpopulation discovery. Empirically, the EL methods outperform bootstrap-based approaches, yielding coverage rates closer to nominal levels while reducing computational latency by several orders of magnitude. We demonstrate the practical utility of this framework on the COMPAS dataset, where it successfully flags intersectional biases, specifically identifying a significantly higher positive prediction rate for African-American males under 25 and a systemic under-prediction for Caucasian females relative to the population mean.

stat.ML↗

arXiv2026

Asymptotic Distribution-Free Tests for Ultra-high Dimensional Parametric Regressions via Projected Empirical Processes and $p$-value Combination

This paper develops a novel methodology for testing the goodness-of-fit of sparse parametric regression models based on projected empirical processes and p-value combination, where the covariate dimension may substantially exceed the sample size. In such ultra-high dimensional settings, traditional empirical process-based tests often fail due to the curse of dimensionality or their reliance on the asymptotic linearity and normality of parameter estimators--properties that may not hold under ultra-high dimensional scenarios. To overcome these challenges, we first extend the classic martingale transformation to ultra-high dimensional settings under mild conditions and construct a Cramer-von Mises type test based on a martingale-transformed, projected residual-marked empirical process for any projection on the unit sphere. The martingale transformation renders this projected test asymptotically distribution-free and enables us to derive its limiting distribution using only standard convergence rates of parameter estimators. While the projected test is consistent for almost all projections on the unit sphere under mild conditions, it may still suffer from power loss for specific projections. Therefore, we further employ powerful p-value combination procedures, such as the Cauchy combination, to aggregate p-values across multiple projections, thereby enhancing overall robustness. Furthermore, recognizing that empirical process-based tests excel at detecting low-frequency signals while local smoothing tests are generally superior for high-frequency alternatives, we propose a novel hybrid test that aggregates both approaches using Cauchy combination. The resulting hybrid test is powerful against both low-frequency and high-frequency alternatives. $\cdots$

math.ST↗

arXiv2025

A Two-Step Projection-Based Goodness-of-Fit Test for Ultra-High Dimensional Sparse Regressions

This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders existing goodness-of-fit tests for regressions infeasible, primarily due to the curse of dimensionality or their reliance on the asymptotic linearity and normality of parameter estimators -- properties that may no longer hold under ultra-high dimensional settings. To address these limitations, our strategy first constructs multiple test statistics based on projected predictors from distinct projections and establishes their asymptotic properties under both the null and alternative hypotheses. This projection-based approach significantly mitigates the dimensionality problem, enabling our tests to detect local alternatives converging to the null at the rate as if the predictor were univariate. An important finding is that the resulting test statistics based on linearly independent projections are asymptotically independent under the null hypothesis. Based on this, our second step employs powerful $p$-value combination procedures, such as the minimum $p$-value and the Fisher combination of $p$-value, to form our final tests and enhance power. Theoretically, our tests only require the standard convergence rate of parameter estimators to derive their limiting distributions, thereby circumventing the need for asymptotic linearity or normality of parameter estimators. Simulations and real-data applications confirm that our approach provides robust and powerful goodness-of-fit testing in ultra-high dimensional settings.

stat.ME↗

arXiv2025

Improving Medical Visual Representation Learning with Pathological-level Cross-Modal Alignment and Correlation Exploration

Learning medical visual representations from image-report pairs through joint learning has garnered increasing research attention due to its potential to alleviate the data scarcity problem in the medical domain. The primary challenges stem from the lengthy reports that feature complex discourse relations and semantic pathologies. Previous works have predominantly focused on instance-wise or token-wise cross-modal alignment, often neglecting the importance of pathological-level consistency. This paper presents a novel framework PLACE that promotes the Pathological-Level Alignment and enriches the fine-grained details via Correlation Exploration without additional human annotations. Specifically, we propose a novel pathological-level cross-modal alignment (PCMA) approach to maximize the consistency of pathology observations from both images and reports. To facilitate this, a Visual Pathology Observation Extractor is introduced to extract visual pathological observation representations from localized tokens. The PCMA module operates independently of any external disease annotations, enhancing the generalizability and robustness of our methods. Furthermore, we design a proxy task that enforces the model to identify correlations among image patches, thereby enriching the fine-grained details crucial for various downstream tasks. Experimental results demonstrate that our proposed framework achieves new state-of-the-art performance on multiple downstream tasks, including classification, image-to-text retrieval, semantic segmentation, object detection and report generation. Code is available at https://github.com/Markin-Wang/PLACE.

cs.CV↗

arXiv2025

Weighted residual empirical processes, martingale transformations, and model specification tests for regressions with diverging number of parameters

This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical process-based tests, both with and without martingale transformations. The asymptotic properties of these tests are derived from the behavior of weighted residual empirical processes and their martingale transformations under the null and alternative hypotheses. The proposed tests without martingale transformations achieve the fastest possible rate of detecting local alternatives, specifically of order $n^{-1/2}$, which is unaffected by dimensionality. However, these tests are not asymptotically distribution-free. To address this limitation, we propose a smooth residual bootstrap approximation and establish its validity in diverging-dimension settings. In contrast, tests incorporating martingale transformations are asymptotically distribution-free but exhibit an unexpected limitation: they can only detect local alternatives converging to the null at a much slower rate of order $n^{-1/4}$, which remains independent of dimensionality. This finding reveals a theoretical advantage in the power of tests based on weighted residual empirical process without martingale transformations over their martingale-transformed counterparts, challenging the conventional wisdom of existing asymptotically distribution-free tests based on martingale transformations. To validate our approach, we conduct simulation studies and apply the proposed tests to a real-world dataset, demonstrating their practical effectiveness.

math.ST↗

arXiv2025

In-Context Learning as Nonparametric Conditional Probability Estimation: Risk Bounds and Optimality

This paper investigates the expected excess risk of in-context learning (ICL) for multiclass classification. We formalize each task as a sequence of labeled examples followed by a query input; a pretrained model then estimates the query's conditional class probabilities. The expected excess risk is defined as the average truncated Kullback-Leibler (KL) divergence between the predicted and true conditional class distributions over a specified family of tasks. We establish a new oracle inequality for this risk, based on KL divergence, in multiclass classification. This yields tight upper and lower bounds for transformer-based models, showing that the ICL estimator achieves the minimax optimal rate (up to logarithmic factors) for conditional probability estimation. From a technical standpoint, our results introduce a novel method for controlling generalization error via uniform empirical entropy. We further demonstrate that multilayer perceptrons (MLPs) can also perform ICL and attain the same optimal rate (up to logarithmic factors) under suitable assumptions, suggesting that effective ICL need not be exclusive to transformer architectures.

stat.ML↗

arXiv2025

Statistical Theory of Multi-stage Newton Iteration Algorithm for Online Continual Learning

We focus on the critical challenge of handling non-stationary data streams in online continual learning environments, where constrained storage capacity prevents complete retention of historical data, leading to catastrophic forgetting during sequential task training. To more effectively analyze and address the problem of catastrophic forgetting in continual learning, we propose a novel continual learning framework from a statistical perspective. Our approach incorporates random effects across all model parameters and allows the dimension of parameters to diverge to infinity, offering a general formulation for continual learning problems. To efficiently process streaming data, we develop a Multi-step Newton Iteration algorithm that significantly reduces computational costs in certain scenarios by alleviating the burden of matrix inversion. Theoretically, we derive the asymptotic normality of the estimator, enabling subsequent statistical inference. Comprehensive validation through synthetic data experiments and two real datasets analyses demonstrates the effectiveness of our proposed method.

stat.ME↗

arXiv2024

Score function-based tests for ultrahigh-dimensional linear models

In this paper, we investigate score function-based tests to check the significance of an ultrahigh-dimensional sub-vector of the model coefficients when the nuisance parameter vector is also ultrahigh-dimensional in linear models. We first reanalyze and extend a recently proposed score function-based test to derive, under weaker conditions, its limiting distributions under the null and local alternative hypotheses. As it may fail to work when the correlation between testing covariates and nuisance covariates is high, we propose an orthogonalized score function-based test with two merits: debiasing to make the non-degenerate error term degenerate and reducing the asymptotic variance to enhance power performance. Simulations evaluate the finite-sample performances of the proposed tests, and a real data analysis illustrates its application.

stat.ME↗

arXiv2024

Effective Positive Cauchy Combination Test

In the field of multiple hypothesis testing, combining p-values represents a fundamental statistical method. The Cauchy combination test (CCT) (Liu and Xie, 2020) excels among numerous methods for combining p-values with powerful and computationally efficient performance. However, large p-values may diminish the significance of testing, even extremely small p-values exist. We propose a novel approach named the positive Cauchy combination test (PCCT) to surmount this flaw. Building on the relationship between the PCCT and CCT methods, we obtain critical values by applying the Cauchy distribution to the PCCT statistic. We find, however, that the PCCT tends to be effective only when the significance level is substantially small or the test statistics are strongly correlated. Otherwise, it becomes challenging to control type I errors, a problem that also pertains to the CCT. Thanks to the theories of stable distributions and the generalized central limit theorem, we have demonstrated critical values under weak dependence, which effectively controls type I errors for any given significance level. For more general scenarios, we correct the test statistic using the generalized mean method, which can control the size under any dependence structure and cannot be further optimized. Our method exhibits excellent performance, as demonstrated through comprehensive simulation studies. We further validate the effectiveness of our proposed method by applying it to a genetic dataset.

stat.ME↗

arXiv2024

Consistent Order Determination of Markov Decision Process

The Markov assumption in Markov Decision Processes (MDPs) is fundamental in reinforcement learning, influencing both theoretical research and practical applications. Existing methods that rely on the Bellman equation benefit tremendously from this assumption for policy evaluation and inference. Testing the Markov assumption or selecting the appropriate order is important for further analysis. Existing tests primarily utilize sequential hypothesis testing methodology, increasing the tested order if the previously-tested one is rejected. However, This methodology cumulates type-I and type-II errors in sequential testing procedures that cause inconsistent order estimation, even with large sample sizes. To tackle this challenge, we develop a procedure that consistently distinguishes the true order from others. We first propose a novel estimator that equivalently represents any order Markov assumption. Based on this estimator, we thus construct a signal function and an associated signal statistic to achieve estimation consistency. Additionally, the curve pattern of the signal statistic facilitates easy visualization, assisting the order determination process in practice. Numerical studies validate the efficacy of our approach.

stat.ME↗

arXiv2024

Distributed quasi-Newton robust estimation under differential privacy

For distributed computing with Byzantine machines under Privacy Protection (PP) constraints, this paper develops a robust PP distributed quasi-Newton estimation, which only requires the node machines to transmit five vectors to the central processor with high asymptotic relative efficiency. Compared with the gradient descent strategy which requires more rounds of transmission and the Newton iteration strategy which requires the entire Hessian matrix to be transmitted, the novel quasi-Newton iteration has advantages in reducing privacy budgeting and transmission cost. Moreover, our PP algorithm does not depend on the boundedness of gradients and second-order derivatives. When gradients and second-order derivatives follow sub-exponential distributions, we offer a mechanism that can ensure PP with a sufficiently high probability. Furthermore, this novel estimator can achieve the optimal convergence rate and the asymptotic normality. The numerical studies on synthetic and real data sets evaluate the performance of the proposed algorithm.

stat.ML↗

arXiv2024

An exhaustive selection of sufficient adjustment sets for causal inference

A subvector of predictor that satisfies the ignorability assumption, whose index set is called a sufficient adjustment set, is crucial for conducting reliable causal inference based on observational data. In this paper, we propose a general family of methods to detect all such sets for the first time in the literature, with no parametric assumptions on the outcome models and with flexible parametric and semiparametric assumptions on the predictor within the treatment groups; the latter induces desired sample-level accuracy. We show that the collection of sufficient adjustment sets can uniquely facilitate multiple types of studies in causal inference, including sharpening the estimation of average causal effect and recovering fundamental connections between the outcome and the treatment hidden in the dependence structure of the predictor. These findings are illustrated by simulation studies and a real data example at the end.

stat.ME↗

arXiv2024

OpenToM: A Comprehensive Benchmark for Evaluating Theory-of-Mind Reasoning Capabilities of Large Language Models

Neural Theory-of-Mind (N-ToM), machine's ability to understand and keep track of the mental states of others, is pivotal in developing socially intelligent agents. However, prevalent N-ToM benchmarks have several shortcomings, including the presence of ambiguous and artificial narratives, absence of personality traits and preferences, a lack of questions addressing characters' psychological mental states, and limited diversity in the questions posed. In response to these issues, we construct OpenToM, a new benchmark for assessing N-ToM with (1) longer and clearer narrative stories, (2) characters with explicit personality traits, (3) actions that are triggered by character intentions, and (4) questions designed to challenge LLMs' capabilities of modeling characters' mental states of both the physical and psychological world. Using OpenToM, we reveal that state-of-the-art LLMs thrive at modeling certain aspects of mental states in the physical world but fall short when tracking characters' mental states in the psychological world.

cs.AI↗

arXiv2024

Scene Graph Aided Radiology Report Generation

Radiology report generation (RRG) methods often lack sufficient medical knowledge to produce clinically accurate reports. The scene graph contains rich information to describe the objects in an image. We explore enriching the medical knowledge for RRG via a scene graph, which has not been done in the current RRG literature. To this end, we propose the Scene Graph aided RRG (SGRRG) network, a framework that generates region-level visual features, predicts anatomical attributes, and leverages an automatically generated scene graph, thus achieving medical knowledge distillation in an end-to-end manner. SGRRG is composed of a dedicated scene graph encoder responsible for translating the scene graph, and a scene graph-aided decoder that takes advantage of both patch-level and region-level visual information. A fine-grained, sentence-level attention method is designed to better dis-till the scene graph information. Extensive experiments demonstrate that SGRRG outperforms previous state-of-the-art methods in report generation and can better capture abnormal findings.

cs.CV↗

arXiv2023

Testing semiparametric model-equivalence hypotheses based on the characteristic function

We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving weighted--type distances between characteristic functions and are convenient from the computational point of view if the weight function is properly chosen. The asymptotic behavior of the tests under the null hypothesis is investigated, and numerical studies are conducted in order to examine the performance of the criteria in finite samples.

stat.ME↗

arXiv2023

Are NLP Models Good at Tracing Thoughts: An Overview of Narrative Understanding

Narrative understanding involves capturing the author's cognitive processes, providing insights into their knowledge, intentions, beliefs, and desires. Although large language models (LLMs) excel in generating grammatically coherent text, their ability to comprehend the author's thoughts remains uncertain. This limitation hinders the practical applications of narrative understanding. In this paper, we conduct a comprehensive survey of narrative understanding tasks, thoroughly examining their key features, definitions, taxonomy, associated datasets, training objectives, evaluation metrics, and limitations. Furthermore, we explore the potential of expanding the capabilities of modularized LLMs to address novel narrative understanding tasks. By framing narrative understanding as the retrieval of the author's imaginative cues that outline the narrative structure, our study introduces a fresh perspective on enhancing narrative comprehension.

cs.CL↗