Related papers: Dirichlet kernel density estimation for strongly m…
Deep neural networks lack interpretability and tend to be overconfident, which poses a serious problem in safety-critical applications like autonomous driving, medical imaging, or machine vision tasks with high demands on reliability.…
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…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
The prevailing statistical approach to analyzing persistence diagrams is concerned with filtering out topological noise. In this paper, we adopt a different viewpoint and aim at estimating the actual distribution of a random persistence…
In microbiome studies, it is often of great interest to identify clusters or partitions of microbiome profiles within a study population and to characterize the distinctive attributes of each resulting microbial community. While raw counts…
A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean…
We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…
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,…
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…
In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
Pre-trained language models have achieved noticeable performance on the intent detection task. However, due to assigning an identical weight to each sample, they suffer from the overfitting of simple samples and the failure to learn complex…
This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method…
This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the…