Related papers: A note on boundary kernels for distribution functi…
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
We propose kernel-type smoothed Kolmogorov-Smirnov and Cram\'{e}r-von Mises tests for data on general interval, using bijective transformations. Though not as severe as in the kernel density estimation, utilizing naive kernel method…
Anomaly detection based on one-class classification algorithms is broadly used in many applied domains like image processing (e.g. detection of whether a patient is "cancerous" or "healthy" from mammography image), network intrusion…
Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis. Over the last two decades, numerous graph kernels, i.e. kernel functions…
We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.
The fragmentation equation is commonly expressed in terms of two functions, the rate of fragmentation and the mean number of fragments. In the case of binary fragmentation an alternative description is possible based on the fragmentation…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
Let $X=\{X_n: n\in \mathbb{N}\}$ be a linear process with bounded probability density function $f(x)$. Under certain conditions, we use the kernel estimator \[ \frac{2}{n(n-1)h_n} \sum_{1\le i<j\le n}K\Big(\frac{X_i-X_j}{h_n}\Big) \] to…