arXiv subjects

Mengchu Li

Publications and source records attributed to Mengchu Li.

10 recordsLinked to original sources

arXiv2026

Contaminated Multi-task Learning with Heterogeneity: Fundamental Limits and Optimal Algorithms

Integrating information across related tasks can improve estimation and prediction in transfer, multi-task, and federated learning, but contamination and heterogeneity make robust borrowing challenging. We study a contaminated multi-task empirical risk minimization (ERM) framework in which an $\epsilon$ fraction of $K$ tasks, each with sample size $n$, may be arbitrarily contaminated while the remaining tasks are heterogeneous. Our goal is to estimate both the global minimizer of the average risk and the clean task-specific minimizers, thereby combining robustness and personalization. In the Gaussian mean model, we show that several common paradigms, including adaptive and robust regularization around a shared center, global matrix regularization, decomposition-based regularization, and score-based outlier-task detection, all suffer from a worst-case contamination error of order $\epsilon\sqrt{d/n}$, which is suboptimal compared to the lower bound $\epsilon/\sqrt{n}$. This identifies a dimension-dependent barrier for these approaches. We then establish minimax lower bounds for a general heterogeneous ERM setting and propose a computationally efficient filtering-based robust multi-task gradient descent method. Under local strong convexity, smoothness, and sub-Gaussian gradient assumptions, the proposed method attains high-probability upper bounds matching the minimax rates up to logarithmic factors over a broad regime. In particular, it removes the extra $\sqrt{d}$ contamination dependence of many regularization-based methods and score-based outlier detection, while achieving personalization to local tasks under strong heterogeneity. Simulations and a real-data analysis demonstrate strong robustness and personalization relative to a broad range of benchmark methods.

stat.ML↗

arXiv2026

Online change point detection under heavy-tailedness and contamination

We study an online version of the robust mean change point detection problem under a dynamic Huber contamination model with arbitrary contamination distribution and inlier distribution possessing exponentially- or polynomially-decaying tails. This robustness framework is systematically studied for the first time in the change point literature. For univariate data, we characterise the detection delay by partitioning the parameter space into four regimes, in terms of the true change location, signal size and contamination level. Efficient detection procedures are accompanied by matching lower bounds, up to poly-logarithmic factors. For the multivariate setting, we devise an efficient robust mean testing procedure and apply this to the robust online change point problem. The theoretical analysis of the robust mean testing procedure is the first in dealing with both Huber contamination and heavy-tailedness, and is thus of independent interest. Extensive numerical experiments are conducted to support our theoretical findings.

math.ST↗

arXiv2026

Segmenting Human-LLM Co-authored Text via Change Point Detection

The rise of large language models (LLMs) has created an urgent need to distinguish between human-written and LLM-generated text to ensure authenticity and societal trust. Existing detectors typically provide a binary classification for an entire passage; however, this is insufficient for human--LLM co-authored text, where the objective is to localize specific segments authored by humans or LLMs. To bridge this gap, we propose algorithms to segment text into human- and LLM-authored pieces. Our key observation is that such a segmentation task is conceptually similar to classical change point detection in time-series analysis. Leveraging this analogy, we adapt change point detection to LLM-generated text detection, develop a weighted algorithm and a generalized algorithm to accommodate heterogeneous detection score variability, and establish the minimax optimality of our procedure. Empirically, we demonstrate the strong performance of our approach against a wide range of existing baselines. The python implementation of our proposal is available at https://github.com/Mamba413/DetectLLMSegmentation.

cs.CL↗

arXiv2025

MMP for generalized foliated threefolds of rank one

We establish the minimal model program (MMP) for generalized foliated threefolds $(X, \mathcal{F}, B, \mathbf{M})$ of rank 1, extending the result of Cascini and Spicer in [CS25d]. As an application of the generalized foliated MMP, we prove a base-point-free theorem for foliated triples on threefolds. We also prove the ACC for log canonical thresholds for generalized foliated threefolds of rank 1.

math.AG↗

arXiv2024

Volume of algebraically integrable foliations and locally stable families

In this paper, we study the volume of algebraically integrable foliations and locally stable families. We show that, for any canonical algebraically integrable foliation, its volume belongs to a discrete set depending only on its rank and the volume of its general leaves. In particular, if the foliation is of general type, then its volume has a positive lower bound depending only on its rank and the volume of its general leaves. This implies some special cases of a question posed by Cascini, Hacon, and Langer. As a consequence, we show that the relative volume of a stable family with a normal generic fiber belongs to a discrete set if the dimension and the volume of its general fibers are bounded. Log versions of the aforementioned theorems are also provided and proved.

math.AG↗

arXiv2024

Federated Transfer Learning with Differential Privacy

Federated learning has emerged as a powerful framework for analysing distributed data, yet two challenges remain pivotal: heterogeneity across sites and privacy of local data. In this paper, we address both challenges within a federated transfer learning framework, aiming to enhance learning on a target data set by leveraging information from multiple heterogeneous source data sets while adhering to privacy constraints. We rigorously formulate the notion of federated differential privacy, which offers privacy guarantees for each data set without assuming a trusted central server. Under this privacy model, we study four statistical problems: univariate mean estimation, low-dimensional linear regression, high-dimensional linear regression, and M-estimation. By investigating the minimax rates and quantifying the cost of privacy, we show that federated differential privacy is an intermediate privacy model between the well-established local and central models of differential privacy. Our analyses account for data heterogeneity and privacy, highlighting the fundamental costs associated with each factor and the benefits of knowledge transfer in federated learning.

cs.LG↗

arXiv2023

Robust mean change point testing in high-dimensional data with heavy tails

We study mean change point testing problems for high-dimensional data, with exponentially- or polynomially-decaying tails. In each case, depending on the $\ell_0$-norm of the mean change vector, we separately consider dense and sparse regimes. We characterise the boundary between the dense and sparse regimes under the above two tail conditions for the first time in the change point literature and propose novel testing procedures that attain optimal rates in each of the four regimes up to a poly-iterated logarithmic factor. By comparing with previous results under Gaussian assumptions, our results quantify the costs of heavy-tailedness on the fundamental difficulty of change point testing problems for high-dimensional data. To be specific, when the error distributions possess exponentially-decaying tails, a CUSUM-type statistic is shown to achieve a minimax testing rate up to $\sqrt{\log\log(8n)}$. As for polynomially-decaying tails, admitting bounded $\alpha$-th moments for some $\alpha \geq 4$, we introduce a median-of-means-type test statistic that achieves a near-optimal testing rate in both dense and sparse regimes. In the sparse regime, we further propose a computationally-efficient test to achieve optimality. Our investigation in the even more challenging case of $2 \leq \alpha < 4$, unveils a new phenomenon that the minimax testing rate has no sparse regime, i.e.\ testing sparse changes is information-theoretically as hard as testing dense changes. Finally, we consider various extensions where we also obtain near-optimal performances, including testing against multiple change points, allowing temporal dependence as well as fewer than two finite moments in the data generating mechanisms. We also show how sub-Gaussian rates can be achieved when an additional minimal spacing condition is imposed under the alternative hypothesis.

math.ST↗

arXiv2022

Network change point localisation under local differential privacy

Network data are ubiquitous in our daily life, containing rich but often sensitive information. In this paper, we expand the current static analysis of privatised networks to a dynamic framework by considering a sequence of networks with potential change points. We investigate the fundamental limits in consistently localising change points under both node and edge privacy constraints, demonstrating interesting phase transition in terms of the signal-to-noise ratio condition, accompanied by polynomial-time algorithms. The private signal-to-noise ratio conditions quantify the costs of the privacy for change point localisation problems and exhibit a different scaling in the sparsity parameter compared to the non-private counterparts. Our algorithms are shown to be optimal under the edge LDP constraint up to log factors. Under node LDP constraint, a gap exists between our upper bound and lower bound and we leave it as an interesting open problem.

math.ST↗

arXiv2022

On robustness and local differential privacy

It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners' privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber's contamination model and the local differential privacy (LDP) constraints. In this paper, we start with a general minimax lower bound result, which disentangles the costs of being robust against Huber's contamination and preserving LDP. We further study four concrete examples: a two-point testing problem, a potentially-diverging mean estimation problem, a nonparametric density estimation problem and a univariate median estimation problem. For each problem, we demonstrate procedures that are optimal in the presence of both contamination and LDP constraints, comment on the connections with the state-of-the-art methods that are only studied under either contamination or privacy constraints, and unveil the connections between robustness and LDP via partially answering whether LDP procedures are robust and whether robust procedures can be efficiently privatised. Overall, our work showcases a promising prospect of joint study for robustness and local differential privacy.

math.ST↗

arXiv2021

Adversarially robust change point detection

Change point detection is becoming increasingly popular in many application areas. On one hand, most of the theoretically-justified methods are investigated in an ideal setting without model violations, or merely robust against identical heavy-tailed noise distribution across time and/or against isolate outliers; on the other hand, we are aware that there have been exponentially growing attacks from adversaries, who may pose systematic contamination on data to purposely create spurious change points or disguise true change points. In light of the timely need for a change point detection method that is robust against adversaries, we start with, arguably, the simplest univariate mean change point detection problem. The adversarial attacks are formulated through the Huber $\varepsilon$-contamination framework, which in particular allows the contamination distributions to be different at each time point. In this paper, we demonstrate a phase transition phenomenon in change point detection. This detection boundary is a function of the contamination proportion $\varepsilon$ and is the first time shown in the literature. In addition, we derive the minimax-rate optimal localisation error rate, quantifying the cost of accuracy in terms of the contamination proportion. We propose a computationally feasible method, matching the minimax lower bound under certain conditions, saving for logarithmic factors. Extensive numerical experiments are conducted with comparisons to robust change point detection methods in the existing literature.

stat.ME↗