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Kernel smoothing is a highly flexible and popular approach for estimation of probability density and intensity functions of continuous spatial data. In this role it also forms an integral part of estimation of functionals such as the…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…
For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…
Multi-objective probabilistic model checking provides a way to verify several, possibly conflicting, quantitative properties of a stochastic system. It has useful applications in controller synthesis and compositional probabilistic…
While spherical data arises in many contexts, including in directional statistics, the current tools for density estimation and population comparison on spheres are quite limited. Popular approaches for comparing populations (on Euclidean…
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…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…
Non-parametric maximum likelihood estimation encompasses a group of classic methods to estimate distribution-associated functions from potentially censored and truncated data, with extensive applications in survival analysis. These methods,…
Modern variable selection procedures make use of penalization methods to execute simultaneous model selection and estimation. A popular method is the LASSO (least absolute shrinkage and selection operator), the use of which requires…
Performance optimization of deep learning models is conducted either manually or through automatic architecture search, or a combination of both. On the other hand, their performance strongly depends on the target hardware and how…
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…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk…
Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although…
In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…