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It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same…
This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…
Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…
Recent results from high-resolution solar granulation observations indicate the existence of a population of small granular cells that are smaller than 600 km in diameter. These small convective cells strongly contribute to the total area…
Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and…
A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike…
Accurately quantifying and removing submerged underwater waste plays a crucial role in safeguarding marine life and preserving the environment. While detecting floating and surface debris is relatively straightforward, quantifying submerged…
Objective: The main objective of this paper is to construct a distributed clustering algorithm based upon spatial data correlation among sensor nodes and perform data accuracy for each distributed cluster at their respective cluster head…
Wave breaking is an important process for energy dissipation in the open ocean and coastal seas. It drives beach morphodynamics, controls air-sea interactions, determines when ship and offshore structure operations can occur safely, and…
Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would…
In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are unsuitable for mode estimation. We propose…
We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density…
A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found…
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…
Modeling and estimation for spatial data are ubiquitous in real life, frequently appearing in weather forecasting, pollution detection, and agriculture. Spatial data analysis often involves processing datasets of enormous scale. In this…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…
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…
The quantification of positively buoyant marine plastic debris is critical to understanding how plastic litter accumulates across the world's oceans and is also crucial to identifying hotspots for targeted cleanup efforts. Currently, the…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…