相关论文: The k-Point Random Matrix Kernels Obtained from On…

We analyze the correlation between randomly chosen edge weights on neighboring edges in a directed graph. This shared-endpoint correlation controls the expected organization of randomly drawn edge flows when the flow on each edge is…

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

Hypernetworks are neural networks that generate weights for another neural network. We formulate the hypernetwork training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry…

We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…

Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…

Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can…

In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a…

We investigate random matrices whose entries are obtained by applying a nonlinear kernel function to pairwise inner products between $n$ independent data vectors, drawn uniformly from the unit sphere in $\mathbb{R}^d$. This study is…

A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance…

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…

In this short letter we present the construction of a bi-stochastic kernel p for an arbitrary data set X that is derived from an asymmetric affinity function {\alpha}. The affinity function {\alpha} measures the similarity between points in…

Kernel ridge regression (KRR) and Gaussian processes (GPs) are fundamental tools in statistics and machine learning, with recent applications to highly over-parameterized deep neural networks. The ability of these tools to learn a target…

A simple, flexible approach to creating expressive priors in Gaussian process (GP) models makes new kernels from a combination of basic kernels, e.g. summing a periodic and linear kernel can capture seasonal variation with a long term…

Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…

For the unitary ensembles of $N\times N$ Hermitian matrices associated with a weight function $w$ there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For…

We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and…