Related papers: A Quasi-Monte Carlo Data Structure for Smooth Kern…
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…
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,…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
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…
In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The…
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…
Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at $M$ evaluation points given $N$ input sample points requires a quadratic…
Advancements in tools like Shapely 2.0 and Triton can significantly improve the efficiency of spatial similarity computations by enabling faster and more scalable geometric operations. However, for extremely large datasets, these…
In this paper, we apply quasi-Monte Carlo (QMC) methods with an initial preintegration step to estimate cumulative distribution functions and probability density functions in uncertainty quantification (UQ). The distribution and density…
Imbalanced data occurs in a wide range of scenarios. The skewed distribution of the target variable elicits bias in machine learning algorithms. One of the popular methods to combat imbalanced data is to artificially balance the data…
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…
When solving partial differential equations with random fields as coefficients the efficient sampling of random field realisations can be challenging. In this paper we focus on the fast sampling of Gaussian fields using quasi-random points…
Finding the mode of a high dimensional probability distribution $D$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $D$ is…
The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier…
In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
Given points $p_1, \dots, p_n$ in $\mathbb{R}^d$, how do we find a point $x$ which maximizes $\frac{1}{n} \sum_{i=1}^n e^{-\|p_i - x\|^2}$? In other words, how do we find the maximizing point, or mode of a Gaussian kernel density estimation…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Kernel Density Estimation (KDE) is a cornerstone of nonparametric statistics, yet it remains sensitive to bandwidth choice, boundary bias, and computational inefficiency. This study revisits KDE through a principled convolutional framework,…