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We consider nonparametric inference of finite dimensional, potentially non-pathwise differentiable target parameters. In a nonparametric model, some examples of such parameters that are always non pathwise differentiable target parameters…
Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…
The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able…
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their…
In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows. Under the widely adopted capacity-source condition framework…
We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our…
It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), Improved Variable Window Kernel Estimates of Probability Densities, {\it Annals of Statistics}, 23, 1--10] modification of Abramson's [Abramson, I. (1982),…
We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient,…
This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…
Among dissimilarities between probability distributions, the Kernel Stein Discrepancy (KSD) has received much interest recently. We investigate the properties of its Wasserstein gradient flow to approximate a target probability distribution…
We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density $p(x)$…
In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…
Semicontinuous outcomes occur frequently in health services, insurance, and cost studies. Standard nonparametric density estimators are not well suited to such data because they do not naturally accommodate the mixed structure, the…