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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 derive estimators of the density of the event times of current status data. The estimators are derived for the situations where the distribution of the observation times is known and where this distribution is unknown. The density…
Nonparametric curve estimation by kernel methods has attracted widespread interest in theoretical and applied statistics. One area of conflict between theory and application relates to the evaluation of the performance of the estimators.…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We give large-time asymptotic estimates, both in uniform and $L^1$ norms, for solutions of the Dirichlet heat equation in the complement of a bounded open set of $\mathbb{R}^d$ satisfying certain technical assumptions. We always assume that…
High dynamic range (HDR) imaging is of fundamental importance in modern digital photography pipelines and used to produce a high-quality photograph with well exposed regions despite varying illumination across the image. This is typically…
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…
Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency…
Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…
We derive the asymptotic distribution of the supremum distance of the deconvolution kernel density estimator to its expectation for certain supersmooth deconvolution problems. It turns out that the asymptotics are essentially different from…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…
This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density $f$. Points on the filament are considered as local extrema of the density when traversing the support of $f$ along…