相关论文: Empirical bounds for functions with weak interacti…

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0…

We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the…

We study estimation of a multivariate function $f:{\bf R}^d \to {\bf R}$ when the observations are available from function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are studied.…

We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…

In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…

This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…

Some exact formulae of the expectation values and probability densities in a weak measurement for an operator ${\bf A}$ which satisfies the property ${\bf A}^{2}=1$ are derived. These formulae include all-order effects of the unitary…

The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically…

We devise a general result on the consistency of model-based bootstrap methods for U- and V-statistics under easily verifiable conditions. For that purpose, we derive the limit distributions of degree-2 degenerate U- and V-statistics for…

Scientific and business practices are increasingly resulting in large collections of randomized experiments. Analyzed together, these collections can tell us things that individual experiments in the collection cannot. We study how to learn…

We study the stationary phi^6 model given by the equation -phi''(x) + 2 phi(x) - 8 phi(x)^3 + 6 phi(x)^5 = 0 for x in R, and establish sharp quantitative stability estimates for configurations close to two weakly interacting kinks. More…

We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We demonstrate that existing estimators and confidence intervals (CIs) can be heavily biased and…

We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…

It has been observed that certain loss functions can render deep-learning pipelines robust against flaws in the data. In this paper, we support these empirical findings with statistical theory. We especially show that empirical-risk…

We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining…

We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…

This paper investigates weak convergence of U-statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U-statistic exists is relaxed to having 4/3 moments only (modulo a…

We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the…

Linear mixed-effects models are widely used in analyzing repeated measures data, including clustered and longitudinal data, where inferences of both fixed effects and variance components are of importance. Unlike the fixed effect inference…