Extreme value statistics provides accurate estimates for the small occurrence probabilities of
rare events. While theory and statistical tools for univariate extremes are well developed …

The classical development of neural networks has primarily focused on learning map**s
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

We develop a general framework for data-driven approximation of input-output maps
between infinitedimensional spaces. The proposed approach is motivated by the recent …

Carbon capture and storage (CCS) plays an essential role in global decarbonization.
Scaling up CCS deployment requires accurate and high-resolution modeling of the storage …

The privacy leakage of the model about the training data can be bounded in the differential
privacy mechanism. However, for meaningful privacy parameters, a differentially private …

A kernel embedding of probability distributions into reproducing kernel Hilbert spaces
(RKHS) has recently been proposed, which allows the comparison of two probability …

A large number of learning algorithms, for example, spectral clustering, kernel Principal
Components Analysis and many manifold methods are based on estimating eigenvalues …

An lp theory of PCA and spectral clustering Page 1 The Annals of Statistics 2022, Vol. 50, No.
4, 2359–2385 https://doi.org/10.1214/22-AOS2196 © Institute of Mathematical Statistics, 2022 …

We introduce a kernel-based method for change-point analysis within a sequence of
temporal observations. Change-point analysis of an (unlabelled) sample of observations …

We prove the first finite-sample convergence rates for any incremental PCA algorithm using
sub-quadratic time and memory per iteration. The algorithm analyzed is Oja's learning rule …