相关论文: On kernels of descent statistics

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

The MinRank (MR) problem is a computational problem that arises in many cryptographic applications. In Verbel et al. (PQCrypto 2019), the authors introduced a new way to solve superdetermined instances of the MinRank problem, starting from…

Let $k$ be a field of characteristic zero, and $R=k[x_1, \ldots, x_d]$ with $d \geq 3$ be a polynomial ring in $d$ variables. Let $\m=(x_1, \ldots, x_d)$ be the homogeneous maximal ideal of $R$. Let $\mathcal{K}$ be the kernel of the…

Let $\{X_n\}_{n\in\N}$ be a Markov chain on a measurable space $\X$ with transition kernel $P$ and let $V:\X\r[1,+\infty)$. The Markov kernel $P$ is here considered as a linear bounded operator on the weighted-supremum space $\cB_V$…

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory.…

We study the kernel instrumental variable (KIV) algorithm, a kernel-based two-stage least-squares method for nonparametric instrumental variable regression. We provide a convergence analysis covering both identified and non-identified…

Neural operators are aiming at approximating operators mapping between Banach spaces of functions, achieving much success in the field of scientific computing. Compared to certain deep learning-based solvers, such as Physics-Informed Neural…

Benchmarks and datasets have important role in evaluation of machine learning algorithms and neural network implementations. Traditional dataset for images such as MNIST is applied to evaluate efficiency of different training algorithms in…

Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social…

Kernel methods provide a flexible and powerful framework for nonparametric statistical testing by embedding probability distributions into a reproducing kernel Hilbert space (RKHS). In this work, we study the kernel two-sample testing…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…

We propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The `quantization commutes with reduction' conjecture of Guillemin and…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

Energy statistics was proposed by Sz\' ekely in the 80's inspired by Newton's gravitational potential in classical mechanics and it provides a model-free hypothesis test for equality of distributions. In its original form, energy statistics…

Research of cycles through specific vertices is a central topic in graph theory. In this context, we focus on a well-studied computational problem, \textsc{$T$-Cycle}: given an undirected $n$-vertex graph $G$ and a set of $k$ vertices…

Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…

The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…

The main contribution of the paper is to show that Gaussian sketching of a kernel-Gram matrix $\boldsymbol K$ yields an operator whose counterpart in an RKHS $\mathcal H$, is a \emph{random projection} operator---in the spirit of…