Related papers: Inner-product Kernels are Asymptotically Equivalen…

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…

Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant…

This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…

Let $(X_1,\ldots,X_n)$ be an i.i.d. sequence of random variables in $\mathbb{R}^d$, $d\geq 1$. We show that, for any function $\varphi :\mathbb{R}^d\rightarrow\mathbb{R}$, under regularity conditions, \[n^…

We study the minimax estimation of covariance eigenfunctions and eigenvalues in functional principal component analysis when $n$ trajectories are observed at $p$ common grid points with additive noise. We consider covariance kernels with…

We present an integrated iontronic memristor circuit that reproduces biologically inspired Spike Rate-Dependent Plasticity (SRDP) and functions as a physical nonlinear frequency kernel, which we demonstrate can be used to classify natural…

We study the asymptotic behaviour of the sequence of sine products $P_n(\alpha) = \prod_{r=1}^n |2\sin \pi r \alpha|$ for real quadratic irrationals $\alpha$. In particular, we study the subsequence $Q_n(\alpha)=\prod_{r=1}^{q_n} |2\sin \pi…

We study the intermittency properties of two branching processes, one with a uniform and another with a singular splitting kernel. The asymptotic intermittency indices, as well as the leading corrections to the asymptotic linear regime are…

We provide a methodology for learning sparse statistical models that use as features all possible multiplicative interactions among an underlying atomic set of features. While the resulting optimization problems are exponentially sized, our…

We study the spectral properties of infinitely smooth multivariate kernel matrices when the nodes form a single cluster. We show that the geometry of the nodes plays an important role in the scaling of the eigenvalues of these kernel…

Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an…

Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…

Considering a determinantal point process on the real line, we establish a connection between the sine-kernel asymptotics for the correlation kernel and the CLT for mesoscopic linear statistics. This implies universality of mesoscopic…

We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are…

Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…

In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…

This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…

In this paper, we develop a new scaling method to study spectral and Bergman kernels for the k-th tensor power of a line bundle over a complex manifold under local spectral gap condition. In particular, we establish a simple proof of the…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…