Related papers: Monotonicity preservation properties of kernel reg…

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve…

Consider a nonlinear regression model : y_{i}=g(x_{i},{\theta})+e_{i}, i=1,...,n, where the x_{i} are random predictors x_{i} and {\theta} is the unknown parameter vector ranging in a set {\Theta}\subsetR^{p}. All known results on the…

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the…

The paper presents a comparative study of state-of-the-art approaches for question classification task: Logistic Regression, Convolutional Neural Networks (CNN), Long Short-Term Memory Network (LSTM) and Quasi-Recurrent Neural Networks…

The Kronecker coefficients are the decomposition multiplicities of the tensor product of two irreducible representations of the symmetric group. Unlike the Littlewood--Richardson coefficients, which are the analogues for the general linear…

Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to…

This paper presents a novel kernel-based generative classifier which is defined in a distortion subspace using polynomial series expansion, named Kernel-Distortion (KD) classifier. An iterative kernel selection algorithm is developed to…

Quantum kernel methods have been widely recognized as one of promising quantum machine learning algorithms that have potential to achieve quantum advantages. In this paper, we theoretically characterize the power of noisy quantum kernels…

The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…

We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate $n^{2/5}$ and that the limit distribution at a fixed…

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…

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…

As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been…

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Generative adversarial networks (GANs) are popular for generative tasks; however, they often require careful architecture selection, extensive empirical tuning, and are prone to mode collapse. To overcome these challenges, we propose a…

Kernel Principal Component Analysis (KPCA) is a popular dimensionality reduction technique with a wide range of applications. However, it suffers from the problem of poor scalability. Various approximation methods have been proposed in the…

We prove new monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations of bounded sets of positive kernel operators on $L^2$. To our knowledge, several proved…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

Restricted kernel machines (RKMs) represent a versatile and powerful framework within the kernel machine family, leveraging conjugate feature duality to address a wide range of machine learning tasks, including classification, regression,…