Related papers: Minimax Optimal Estimation of Mean and Covariance …
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…
A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…
Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…
Inspired by the recent work [28] on the statistical robustness of empirical risks in reproducing kernel Hilbert space (RKHS) where the training data are potentially perturbed or even corrupted, we take a step further in this paper to…
In this paper, we study the problem of early stopping for iterative learning algorithms in a reproducing kernel Hilbert space (RKHS) in the nonparametric regression framework. In particular, we work with the gradient descent and (iterative)…
We study kernel least-squares estimation under a norm constraint. This form of regularisation is known as Ivanov regularisation and it provides better control of the norm of the estimator than the well-established Tikhonov regularisation.…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the "native" Hilbert space $\calh$ in which they are reproducing. Continuous kernels on compact domains have an expansion into…
In this paper, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We approach this problem…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
We derive minimax adaptive rates for a new, broad class of Tikhonov-regularized learning problems in Hilbert scales under general source conditions. Our analysis does not require the regression function to be contained in the hypothesis…
We develop regularization methods to find flat minima while training deep neural networks. These minima generalize better than sharp minima, yielding models outperforming baselines on real-world test data (which may be distributed…