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The notion of Nonlocal Mean Curvature (NMC) appears recently in the mathematics literature. It is an extrinsic geometric quantity that is invariant under global reparameterization of a surface and provide a natural extension of the…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to…
For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…
Measuring a nonlocal observable on a space-like separated quantum system is a resource-hungry and experimentally challenging task. Several theoretical measurement schemes have already been proposed to increase its feasibility, using a…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We consider the classical Neymann-Pearson hypothesis testing problem of signal detection, where under the null hypothesis ($\calH_0$), the received signal is white Gaussian noise, and under the alternative hypothesis ($\calH_1$), the…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
High precision measurements of the renormalized zero-momentum 4-point coupling g_R and of the Luscher-Weisz-Wolff running coupling gbar(L) = L*m(L) performed with two different lattice actions in the non-perturbative region confirm the…
Gaussian process regression (GPR) model is a popular nonparametric regression model. In GPR, features of the regression function such as varying degrees of smoothness and periodicities are modeled through combining various covarinace…
We present a general diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. The general treatment of correlations beyond BCS theory requires a new theoretical…
This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…
We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…
Identifying the number of lags to include in an autoregressive model remains an open research problem due to the computational burden of treating it as a hyperparameter, especially in complex models. This study explores model-agnostic…
In this paper, we unify popular non-rigid registration methods for point sets and surfaces under our general framework, GiNGR. GiNGR builds upon Gaussian Process Morphable Models (GPMM) and hence separates modeling the deformation prior…
This paper investigates the statistical properties of non-linear transformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression…
In this review, we outline the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and…
We introduce new models that incorporate layer corrugation and interface roughness into standard approaches for measuring interface stress in nanomultilayers (NMLs). Applied to Cu/W NMLs, these models show that ignoring such features can…