Related papers: Minimax rates for learning kernels in operators

We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…

State estimation is a key ingredient in most robotic systems. Often, state estimation is performed using some form of least squares minimization. Basically, all error minimization procedures that work on real-world data use robust kernels…

Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…

One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…

Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both the number of inputs and features. Traditional approaches often rely on the eigenvalue spectrum of…

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…

A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations…

We consider a nonparametric regression setup, where the covariate is a random element in a complete separable metric space, and the parameter of interest associated with the conditional distribution of the response lies in a separable…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…