Functional linear model is a fruitfully applied general framework for regression problems,
including those with intrinsically infinite-dimensional data. Online gradient descent methods …

Physics-informed machine learning combines the expressiveness of data-based
approaches with the interpretability of physical models. In this context, we consider a …

We consider the theory of regression on a manifold using reproducing kernel Hilbert space
methods. Manifold models arise in a wide variety of modern machine learning problems …

In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the
statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is …

Despite the curse of dimensionality, kernel ridge regression often exhibits good performance
in practical applications, even when the dimension is moderately large. However, it has …

We study linear ill-posed inverse problems with noisy data in the framework of statistical
learning. The corresponding linear operator equation is assumed to fit a given Hilbert scale …

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 …

In this chapter, 1 we consider the problem of estimating a low-rank matrix from the
observation of all or a subset of its entries in the presence of Poisson noise. When we …