Related papers: Dynamic Maintenance of Kernel Density Estimation D…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regularization (KBR), a localized multidimensional kernel regression…
We present a dynamic self-balancing octree data structure that enables efficient neighborhood maintenance in evolving metric spaces, a key challenge in modern machine learning systems. Many learning and generative models operate as…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to investigate statistical properties of nuclear spectra. The deviation to regular or chaotic dynamics, is exhibited by closer distances to Poisson…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
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…
Kernelization studies polynomial-time preprocessing algorithms. Over the last 20 years, the most celebrated positive results of the field have been linear kernels for classical NP-hard graph problems on sparse graph classes. In this paper,…
Comparing differently sized data sets is one main task in model assessment and calibration. This is due to field data being generally sparse compared to simulated model results. We tackled this task by the application of a new…
We study statistical/computational tradeoffs for the following density estimation problem: given $k$ distributions $v_1, \ldots, v_k$ over a discrete domain of size $n$, and sampling access to a distribution $p$, identify $v_i$ that is…
Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…
The exponential growth of available data has increased the need for interactive exploratory analysis. Dataset can no longer be understood through manual crawling and simple statistics. In Geographical Information Systems (GIS), the dataset…
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…
Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…
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…
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…
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…