相关论文: High-Dimension, Low Sample Size Asymptotics of Can…

We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…

Disorder has long been a difficult subject in condensed matter systems and the The replica method is a well-known tool in this field. Implementing the replica method the AdS/CFT correspondence has been proposed and discussed in literatures.…

Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards…

Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the…

Multi-view learning (MVL) is a strategy for fusing data from different sources or subsets. Canonical correlation analysis (CCA) is very important in MVL, whose main idea is to map data from different views onto a common space with maximum…

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…

Language models (LMs) often struggle to pay enough attention to the input context, and generate texts that are unfaithful or contain hallucinations. To mitigate this issue, we present context-aware decoding (CAD), which follows a…

We consider the hyperuniform model of d-dimensional integer lattice perturbed by independent random variables and we investigate the large scale asymptotic fluctuations of smoothed versions of the usual counting statistics, specifically of…

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and massive…

Recent studies have demonstrated that In-Context Learning (ICL), through the use of specific demonstrations, can align Large Language Models (LLMs) with human preferences known as In-Context Alignment (ICA), indicating that models can…

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…

The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…

The infinite set of coupled integral nonlinear equations for correlation functions in the case of classical canonical ensemble is considered. Some kind of graph expansions of correlation functions in the density parameter are constructed.…

The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…

Although many studies collect biomedical time series signals from multiple subjects, there is a dearth of models and methods for assessing the association between frequency domain properties of time series and other study outcomes. This…

The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom…

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…

Two dimensional large-N chiral models on the square and honeycomb lattices are investigated by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the…