Related papers: Local-likelihood transformation kernel density est…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…
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…
A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
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 consider the problem of estimation of a bivariate density function with support $\Re\times[0,\infty)$, where a classical bivariate kernel estimator causes boundary bias due to the non-negative variable. To overcome this problem, we…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
In recent years, the learned local descriptors have outperformed handcrafted ones by a large margin, due to the powerful deep convolutional neural network architectures such as L2-Net [1] and triplet based metric learning [2]. However,…
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…
This paper develops detailed mathematical statistical theory of a new class of cross-validation techniques of local linear kernel hazards and their multiplicative bias corrections. The new class of cross-validation combines principles of…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
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…
We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel…
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some…
Compared to nonparametric estimators in the multivariate setting, kernel estimators for functional data models have a larger order of bias. This is problematic for constructing confidence regions or statistical tests since the bias might…
Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…
Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…