Related papers: A Simple and Scalable Kernel Density Approach for …

Kernel Density Estimation (KDE) is a nonparametric method for estimating the shape of a density function, given a set of samples from the distribution. Recently, locality-sensitive hashing, originally proposed as a tool for nearest neighbor…

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…

Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal…

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…

Several disciplines, like the social sciences, epidemiology, sentiment analysis, or market research, are interested in knowing the distribution of the classes in a population rather than the individual labels of the members thereof.…

We study efficient mechanisms for differentially private kernel density estimation (DP-KDE). Prior work for the Gaussian kernel described algorithms that run in time exponential in the number of dimensions $d$. This paper breaks the…

Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…

The development of edge computing places critical demands on energy-efficient model deployment for multiple-input multiple-output (MIMO) detection tasks. Deploying deep unfolding models such as PGD-Nets and ADMM-Nets into…

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,…

We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids…

We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…

Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce and the dimensionality is high. Although GPs are known for…

This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the…

This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density…

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models…

This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate…

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…