arXiv subjects

Yixi Ding

Publications and source records attributed to Yixi Ding.

3 recordsLinked to original sources

arXiv2025

Gaussian Multiplier Bootstrap Procedure for the $k$th Largest Coordinate of High-Dimensional Statistics

We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has been studied previously for $k=1$ (i.e., maxima). However, in many applications, a general $k$ ($k\geq 1$) is of great interest. We provide the upper bounds for the errors between Gaussian approximations and Gaussian multiplier approximations. The dimension $p$ is allowed to be larger than the sample size $n$. The effectiveness of the proposed methods is demonstrated via the computer numerical results and a real-world data analysis.

math.ST↗

arXiv2024

CCSBench: Evaluating Compositional Controllability in LLMs for Scientific Document Summarization

To broaden the dissemination of scientific knowledge to diverse audiences, it is desirable for scientific document summarization systems to simultaneously control multiple attributes such as length and empirical focus. However, existing research typically focuses on controlling single attributes, leaving the compositional control of multiple attributes underexplored. To address this gap, we introduce CCSBench, the first evaluation benchmark for compositional controllable summarization in the scientific domain. Our benchmark enables fine-grained control over both explicit attributes (e.g., length), which are objective and straightforward, and implicit attributes (e.g., conceptual or empirical focus), which are more subjective and abstract. We conduct extensive experiments using various large language models (LLMs) under various settings, including in-context learning, parameter-efficient fine-tuning, and two-stage modular methods for balancing control over different attributes. Our findings reveal significant limitations in LLMs capabilities in balancing trade-offs between control attributes, especially implicit ones that require deeper understanding and abstract reasoning.

cs.CL↗

arXiv2024

Gaussian Approximations for the $k$th coordinate of sums of random vectors

We consider the problem of Gaussian approximation for the $\kappa$th coordinate of a sum of high-dimensional random vectors. Such a problem has been studied previously for $\kappa=1$ (i.e., maxima). However, in many applications, a general $\kappa\geq1$ is of great interest, which is addressed in this paper. We make four contributions: 1) we first show that the distribution of the $\kappa$th coordinate of a sum of random vectors, $\boldsymbol{X}= (X_{1},\cdots,X_{p})^{\sf T}= n^{-1/2}\sum_{i=1}^n \boldsymbol{x}_{i}$, can be approximated by that of Gaussian random vectors and derive their Kolmogorov's distributional difference bound; 2) we provide the theoretical justification for estimating the distribution of the $\kappa$th coordinate of a sum of random vectors using a Gaussian multiplier procedure, which multiplies the original vectors with i.i.d. standard Gaussian random variables; 3) we extend the Gaussian approximation result and Gaussian multiplier bootstrap procedure to a more general case where $\kappa$ diverges; 4) we further consider the Gaussian approximation for a square sum of the first $d$ largest coordinates of $\boldsymbol{X}$. All these results allow the dimension $p$ of random vectors to be as large as or much larger than the sample size $n$.

math.ST↗