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

A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…

As a generalization of the work in [Lee et al., 2017], this note briefly discusses when the prior of a neural network output follows a Gaussian process, and how a neural-network-induced Gaussian process is formulated. The posterior mean…

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…

We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…

The Neural Tangent Kernel (NTK) has discovered connections between deep neural networks and kernel methods with insights of optimization and generalization. Motivated by this, recent works report that NTK can achieve better performances…

In this note we extend kernel function approximation results for neural networks with Gaussian-distributed weights to single-layer networks initialized using Haar-distributed random orthogonal matrices (with possible rescaling). This is…

Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian…

We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of…

The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…

Kernel methods are used extensively in classical machine learning, especially in the field of pattern analysis. In this paper, we propose a kernel-based quantum machine learning algorithm that can be implemented on a near-term, intermediate…

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…

In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

The averages of ratios of characteristic polynomials det(lambda - X) of N x N random matrices X, are investigated in the large N limit for the GUE, GOE and GSE ensemble. The density of states and the two-point correlation function are…

Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Neural tangent kernels (NTKs) have been proposed to study the behavior of trained neural networks from the perspective of Gaussian processes. An important result in this body of work is the theorem of equivalence between a trained neural…

In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…