arXiv subjects

Mingshuo Liu

Publications and source records attributed to Mingshuo Liu.

10 recordsLinked to original sources

arXiv2026

Graph-Based Change-Point Detection for Partially Observed High-Dimensional Data

Partial missingness is common in high-dimensional data, but most existing change-point procedures are developed for fully observed sequences. We introduce gMiss, a graph-based framework for testing and localizing a change in the observed-data distribution of a partially observed high-dimensional sequence. The method treats the observed values together with the missingness indicators as the object of inference, so the target alternative is a change in the induced observed data law. It is designed for general distributional changes and requires neither sparsity nor Gaussianity. When the augmented observations are independent, the full permutation test controls type I error in finite samples. The procedure combines graph scans based on elementwise imputation and distance imputation. The two scans capture complementary graph patterns. Simulation results indicate that gMiss maintains accurate null calibration across the MCAR and MAR designs considered, remains competitive under Gaussian location alternatives, and exhibits strong power and localization performance in many non-Gaussian location and scale settings. We further illustrate the practical utility of the method through an application to genomic copy-number data, where gMiss identifies additional candidate boundaries that are visually plausible in the raw heatmap.

stat.ME↗

arXiv2026

Generalized Independence Test

Testing independence is a widely encountered problem in modern data analysis, especially in high-dimensional settings where complex dependency structures are common. Traditional methods often lack power in such scenarios. To address this, we propose a novel test statistic that leverages both similarity and dissimilarity information to capture intricate relationships within the data. The proposed test demonstrates strong power across a wide range of alternatives in high-dimensional settings, as shown through extensive simulation studies. Under mild conditions, we prove that the permutation null distribution of the statistic converges to the $χ^2_4$ distribution, enabling straightforward control of the type I error. Our theoretical analysis further advances the moment method to establish joint asymptotic normality for a class of double-indexed permutation statistics. Moreover, we prove the power consistency of the proposed test without imposing explicit restrictions on the data dimension, under mild conditions that allow for detecting complex dependencies. We illustrate the proposed test using gene-expression data from the Genotype-Tissue Expression project, where GIT rejects independence between the GTEx category "Breast - Mammary Tissue" and the cell-line category "Cells - EBV-transformed lymphocytes."

stat.ME↗

arXiv2026

A Goodness-of-Fit Test for Independent Component Models in High Dimensions

Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit tests for assessing their compatibility with data. We develop the first goodness-of-fit test for IC models that is supported by a theoretical validity guarantee when the data dimension and sample size diverge proportionally. This is made possible by the fact that the test does not rely on a pre-whitening step, which often limits the applicability of other goodness-of-fit tests in high dimensions. Our theoretical analysis is complemented with numerical experiments that demonstrate the test's size control and power under a range of conditions. In addition, we provide examples involving gene-expression data to illustrate that the test has potential for effective diagnostic use in practice.

math.ST↗

arXiv2026

PIIGuard: Mitigating PII Harvesting under Adversarial Sanitization

Browsing-enabled LLM assistants can fetch webpages and answer contact-seeking queries, creating a practical channel for scraping contact-style personally identifiable information (PII) from public pages. Many prior defenses are deployed at the model, service, or agent layer rather than at the webpage itself, leaving ordinary page owners with limited deployable options. We present PIIGuard, a webpage-level defense that repurposes indirect prompt injection as a protective mechanism: the page owner embeds optimized hidden HTML fragments that steer the model away from verbatim or reconstructible disclosure of contact PII. PIIGuard searches over fragment text and insertion position using rule-based leakage scoring, evolutionary mutation, and final judge-based recoverability assessment. In direct-HTML evaluation on three target models (GPT-5.4-nano, Claude-haiku-4.5, and DeepSeek-chat(latest v3.2)), PIIGuard achieves at least 97.0% defense success rate under both rule-based and judge-based leakage evaluation, often reaching 100.0%, while preserving benign same-page QA utility. We further evaluate two harder settings: public-URL browsing and attacker-side LLM sanitization of fetched webpage. These results show that page-side defensive fragments can remain effective in deployment for some model-position pairs, but robustness varies substantially across browsing interfaces and sanitizer prompts. Overall, PIIGuard demonstrates that page owners can use page-side fragments as a practical mitigation for web-grounded PII leakage.

cs.CR↗

arXiv2026

Evaluating AI Grading on Real-World Handwritten College Mathematics: A Large-Scale Study Toward a Benchmark

Grading in large undergraduate STEM courses often yields minimal feedback due to heavy instructional workloads. We present a large-scale empirical study of AI grading on real, handwritten single-variable calculus work from UC Irvine. Using OCR-conditioned large language models with structured, rubric-guided prompting, our system produces scores and formative feedback for thousands of free-response quiz submissions from nearly 800 students. In a setting with no single ground-truth label, we evaluate performance against official teaching-assistant grades, student surveys, and independent human review, finding strong alignment with TA scoring and a large majority of AI-generated feedback rated as correct or acceptable across quizzes. Beyond calculus, this setting highlights core challenges in OCR-conditioned mathematical reasoning and partial-credit assessment. We analyze key failure modes, propose practical rubric- and prompt-design principles, and introduce a multi-perspective evaluation protocol for reliable, real-course deployment. Building on the dataset and evaluation framework developed here, we outline a standardized benchmark for AI grading of handwritten mathematics to support reproducible comparison and future research.

cs.LG↗

arXiv2026

Single Index Bandits: Generalized Linear Contextual Bandits with Unknown Reward Functions

Generalized linear bandits have been extensively studied due to their broad applicability in real-world online decision-making problems. However, these methods typically assume that the expected reward function is known to the users, an assumption that is often unrealistic in practice. Misspecification of this link function can lead to the failure of all existing algorithms. In this work, we address this critical limitation by introducing a new problem of generalized linear bandits with unknown reward functions, also known as single index bandits. We first consider the case where the unknown reward function is monotonically increasing, and propose two novel and efficient algorithms, STOR and ESTOR, that achieve decent regrets under standard assumptions. Notably, our ESTOR can obtain the nearly optimal regret bound $\tilde{O}_T(\sqrt{T})$ in terms of the time horizon $T$. We then extend our methods to the high-dimensional sparse setting and show that the same regret rate can be attained with the sparsity index. Next, we introduce GSTOR, an algorithm that is agnostic to general reward functions, and establish regret bounds under a Gaussian design assumption. Finally, we validate the efficiency and effectiveness of our algorithms through experiments on both synthetic and real-world datasets.

stat.ML↗

arXiv2025

Robust Max Statistics for High-Dimensional Inference

Although much progress has been made in the theory and application of bootstrap approximations for max statistics in high dimensions, the literature has largely been restricted to cases involving light-tailed data. To address this issue, we propose an approach to inference based on robust max statistics, and we show that their distributions can be accurately approximated via bootstrapping when the data are both high-dimensional and heavy-tailed. In particular, the data are assumed to satisfy an extended version of the well-established $L^{4}$-$L^2$ moment equivalence condition, as well as a weak variance decay condition. In this setting, we show that near-parametric rates of bootstrap approximation can be achieved in the Kolmogorov metric, independently of the data dimension. Moreover, this theoretical result is complemented by encouraging empirical results involving both Euclidean and functional data.

stat.ME↗

arXiv2025

A Trainable Centrality Framework for Modern Data

Measuring how central or typical a data point is underpins robust estimation, ranking, and outlier detection, but classical depth notions become expensive and unstable in high dimensions and are hard to extend beyond Euclidean data. We introduce Fused Unified centrality Score Estimation (FUSE), a neural centrality framework that operates on top of arbitrary representations. FUSE combines a global head, trained from pairwise distance-based comparisons to learn an anchor-free centrality score, with a local head, trained by denoising score matching to approximate a smoothed log-density potential. A single parameter between 0 and 1 interpolates between these calibrated signals, yielding depth-like centrality from different views via one forward pass. Across synthetic distributions, real images, time series, and text data, and standard outlier detection benchmarks, FUSE recovers meaningful classical ordering, reveals multi-scale geometric structures, and attains competitive performance with strong classical baselines while remaining simple and efficient.

cs.LG↗

arXiv2025

An Adaptive Tensor-Train Decomposition Approach for Efficient Deep Neural Network Compression

In the field of model compression, choosing an appropriate rank for tensor decomposition is pivotal for balancing model compression rate and efficiency. However, this selection, whether done manually or through optimization-based automatic methods, often increases computational complexity. Manual rank selection lacks efficiency and scalability, often requiring extensive trial-and-error, while optimization-based automatic methods significantly increase the computational burden. To address this, we introduce a novel, automatic, and budget-aware rank selection method for efficient model compression, which employs Layer-Wise Imprinting Quantitation (LWIQ). LWIQ quantifies each layer's significance within a neural network by integrating a proxy classifier. This classifier assesses the layer's impact on overall model performance, allowing for a more informed adjustment of tensor rank. Furthermore, our approach includes a scaling factor to cater to varying computational budget constraints. This budget awareness eliminates the need for repetitive rank recalculations for different budget scenarios. Experimental results on the CIFAR-10 dataset show that our LWIQ improved by 63.2% in rank search efficiency, and the accuracy only dropped by 0.86% with 3.2x less model size on the ResNet-56 model as compared to the state-of-the-art proxy-based automatic tensor rank selection method.

cs.LG↗

arXiv2025

WISE: A Weighted Similarity Aggregation Test for Serial Independence

We propose a nonparametric test for serial independence that aggregates pairwise similarities of observations with lag-dependent weights. The resulting statistic is powerful to general forms of temporal dependence, including nonlinear and uncorrelated alternatives, and applies to ultra-high-dimensional and non-Euclidean data. We derive asymptotic normality under both permutation and population nulls, and establish consistency in classical large-sample and high-dimension-low-sample-size (HDLSS) regimes. The test therefore provides the first theoretical power guarantees for serial independence in the HDLSS setting. Simulations demonstrate accurate size and strong power against a wide range of alternatives, showing significant power improvement over existing methods under various high-dimensional time series models. An application to spatio-temporal data illustrates the method's utility for non-Euclidean observations.

stat.ME↗