Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

In recent years neural networks have achieved impressive results on many technological
and scientific tasks. Yet, the mechanism through which these models automatically select …

Optimal transport (OT) methods seek a transformation map (or plan) between two probability
measures, such that the transformation has the minimum transportation cost. Such a …

Kriging is a powerful surrogate modeling method for the analysis and optimization of
computationally expensive problems. However, the efficient construction of high-precision …

Optimal transport has been one of the most exciting subjects in mathematics, starting from
the eighteenth century. As a powerful tool to transport between two probability measures …

Caused by Yersinia pestis, plague ravaged the world through three known pandemics: the
First or the Justinianic (6th–8th century); the Second (beginning with the Black Death during …

We propose and study a class of simple, nonparametric, yet interpretable measures of
conditional dependence, which we call kernel partial correlation (KPC) coefficient, between …

The goal of supervised representation learning is to construct effective data representations
for prediction. Among all the characteristics of an ideal nonparametric representation of high …

Surrogate models have been widely used in the uncertainty propagation and global
sensitivity analysis of complex evaluation-expensive engineering problems. However, the …

It has long been emphasized that standard PLS regression algorithms like NIPALS and
SIMPLS are not suitable for regressions in which there is a nonlinear relationship between …