Related papers: Computing nullity and kernel vectors using NF-pack…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
We explain, on the example of Wigner's quasiprobability distribution, how negative probabilities may be used in the foundations of probability.
In many remote sensing applications one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms such as…
We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall's inequality involving the power fractional…
Nuclear segmentation is important and frequently demanded for pathology image analysis, yet is also challenging due to nuclear crowdedness and possible occlusion. In this paper, we present a novel bottom-up method for nuclear segmentation.…
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
We consider the design of an image representation that embeds and aggregates a set of local descriptors into a single vector. Popular representations of this kind include the bag-of-visual-words, the Fisher vector and the VLAD. When two…
In this paper we investigate the linear and nonlinear models of optical quantum computation and discuss their scalability and efficiency. We show how there are significantly different scaling properties in single photon computation when…
We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show…
Decision forests induce supervised similarities through the partition structure of their trees. Yet forest proximity computation is still often treated as a quadratic operation in the number of samples, which limits scalability and…
We study Hilbert-Kunz multiplicity of non-singular curves in positive characteristic. We analyse the relationship between the Frobenius semistability of the kernel sheaf associated with the curve and its ample line bundle, and the HK…
A Support Vector Machine (SVM) has become a very popular machine learning method for text classification. One reason for this relates to the range of existing kernels which allow for classifying data that is not linearly separable. The…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Test equating using covariates may be applied to provide comparable scores from multiple test forms when no anchor items are available. However, its performance may be compromised if some of the covariates themselves are measured using…
We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…
We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain…
We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…
The present work has as a first goal to extend the previous results in \cite{CFL20} to weighted uncertainty principles with nontrivial radially symmetric weights applied to curl-free vector fields. Part of these new inequalities generalize…
In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…