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The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient…
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…
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…
Consistency of the kernel density estimator requires that the kernel bandwidth tends to zero as the sample size grows. In this paper we investigate the question of whether consistency is possible when the bandwidth is fixed, if we consider…
Kernel smooth is the most fundamental technique for data density and regression estimation. However, time-consuming is the biggest obstacle for the application that the direct evaluation of kernel smooth for $N$ samples needs ${O}\left(…
We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding…
This paper presents an intuitive application of multivariate kernel density estimation (KDE) for data correction. The method utilizes the expected value of the conditional probability density function (PDF) and a credible interval to…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
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…
In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared…
We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We…
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…
Multivariate kernel density estimations have received much spate of interest. In addition to conventional methods of (non-)classical associated-kernels for (un)bounded densities and bandwidth selections, the multiple extended-beta kernel…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these 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…
The Fast Fourier Transform (FFT) is a fundamental tool for signal analysis, widely used across various fields. However, traditional FFT methods encounter challenges in adjusting the frequency bin interval, which may impede accurate spectral…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
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…
We propose a generalization of our previous KDE (kernel density estimation) method for estimating luminosity functions (LFs). This new upgrade further extend the application scope of our KDE method, making it a very flexible approach which…
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…