相关论文: On kernels of descent statistics

The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…

We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…

Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…

Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights.…

Motivated by recent progress in quantum information theory, this article aims at optimizing trace polynomials, i.e., polynomials in noncommuting variables and traces of their products. A novel Positivstellensatz certifying positivity of…

We develop a comparison, base-change, and descent framework for the algebraic $K$-theory of non-commutative $n$-ary $\Gamma$-semirings. Working in the Quillen-exact (and Waldhausen) setting of bi-finite, slot-sensitive $\Gamma$-modules and…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…

Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$-functions in a family at a low-lying height on the critical line (measured…

We introduce and study a class $\mathcal{M}$ of generalized positive definite kernels of the form $K\colon X\times X\to L(\mathfrak{A},L(H))$, where $\mathfrak{A}$ is a unital $C^{*}$-algebra and $H$ a Hilbert space. These kernels encode…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

We show that if a reproducing kernel Hilbert space $H_K,$ consisting of functions defined on ${\bf E},$ enjoys Double Boundary Vanishing Condition (DBVC) and Linear Independent Condition (LIC), then for any preset natural number $n,$ and…

We~identify the standard weighted Bergman kernels of spaces of nearly holomorphic functions, in~the sense of Shimura, on~bounded symmetric domains. This also yields a description of the analogous kernels for spaces of…

Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK) defined by the nonlinear feature map of a feedforward neural network. However, existing results only establish weak convergence of the empirical eigenvalue…

We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given…

Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid…

In 1916, MacMahon showed that permutations in $S_n$ with a fixed descent set $I$ are enumerated by a polynomial $d_I(n)$. Diaz-Lopez, Harris, Insko, Omar, and Sagan recently revived interest in this descent polynomial, and suggested the…

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…