Related papers: Tropical reproducing kernels and optimization

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…

In this paper, we discuss the convergence analysis of the conjugate gradient-based algorithm for the functional linear model in the reproducing kernel Hilbert space framework, utilizing early stopping results in regularization against…

In this paper we investigate the idea of a tropical critical point of the superpotential for the full flag variety of type A. Recall that associated to an irreducible representation of G=SLn(C) are various polytopes whose integral points…

We consider the reproducing kernel function of the theta Bargmann-Fock Hilbert space associated to given full-rank lattice and pseudo-character, and we deal with some of its analytical and arithmetical properties. Specially, the…

Toeplitz kernels can be defined by Riemann-Hilbert problems, by maximal functions, or by multipliers acting on model spaces. In this paper we study those different characterisations and their relations, highlighting, on the one hand, the…

The decomposition of polynomial spaces on unions of Grassmannians $\mathcal G_{{k_1},d}\cup\ldots\cup \mathcal G_{{k_r},d}$ into irreducible orthogonally invariant subspaces and their reproducing kernels are investigated. We also generalize…

Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.…

Let $\mathscr T=(V, \mathcal E)$ be a leafless, locally finite rooted directed tree. We associate with $\mathscr T$ a one parameter family of Dirichlet spaces $\mathscr H_q~(q \geqslant 1)$, which turn out to be Hilbert spaces of…

Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way,…

We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…

Let $(X,\mu)$ be a strictly-positive Borel measure space. We show that the modes of convergence in a reproducing kernel Hilbert (RKHS) space, pointwise, weak and strong are all equivalents. From this we describe some important consequences…

There exists a plethora of parametric models for positive definite kernels, and their use is ubiquitous in disciplines as diverse as statistics, machine learning, numerical analysis, and approximation theory. Usually, the kernel parameters…

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…

This paper presents two models of neural-networks and their training applicable to neural networks of arbitrary width, depth and topology, assuming only finite-energy neural activations; and a novel representor theory for neural networks in…

This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

We define tropical analogues of the notions of linear space and Plucker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated…

For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…

We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness…