Related papers: Gaussian Approximation for High-Dimensional Second…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…
I propose two U-statistics to test coefficients in generalized linear models. One of them is used to deal with global hypothesis and the other one to test with the nuisance parameter. Both the statistics proposed are within high-dimensional…
In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and…
Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…
In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…
This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n \to \infty$ with fixed kernel size $k$. Under some regularity conditions,…
This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…
We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD…
This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…
A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional…
Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…
Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data…