Computational optimal transport: With applications to data science
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
Kernel mean embedding of distributions: A review and beyond
A Hilbert space embedding of a distribution—in short, a kernel mean embedding—has
recently emerged as a powerful tool for machine learning and statistical inference. The basic …
recently emerged as a powerful tool for machine learning and statistical inference. The basic …
Learning generative models with sinkhorn divergences
The ability to compare two degenerate probability distributions, that is two distributions
supported on low-dimensional manifolds in much higher-dimensional spaces, is a crucial …
supported on low-dimensional manifolds in much higher-dimensional spaces, is a crucial …
Estimating individual treatment effect: generalization bounds and algorithms
There is intense interest in applying machine learning to problems of causal inference in
fields such as healthcare, economics and education. In particular, individual-level causal …
fields such as healthcare, economics and education. In particular, individual-level causal …
Sample complexity of Sinkhorn divergences
Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in
machine learning to compare probability measures. We focus in this paper on Sinkhorn …
machine learning to compare probability measures. We focus in this paper on Sinkhorn …
Stochastic optimization for large-scale optimal transport
Optimal transport (OT) defines a powerful framework to compare probability distributions in a
geometrically faithful way. However, the practical impact of OT is still limited because of its …
geometrically faithful way. However, the practical impact of OT is still limited because of its …
Frameworks and results in distributionally robust optimization
The concepts of risk aversion, chance-constrained optimization, and robust optimization
have developed significantly over the last decade. The statistical learning community has …
have developed significantly over the last decade. The statistical learning community has …
A unified recipe for deriving (time-uniform) PAC-Bayes bounds
We present a unified framework for deriving PAC-Bayesian generalization bounds. Unlike
most previous literature on this topic, our bounds are anytime-valid (ie, time-uniform) …
most previous literature on this topic, our bounds are anytime-valid (ie, time-uniform) …
Equivalence of distance-based and RKHS-based statistics in hypothesis testing
We provide a unifying framework linking two classes of statistics used in two-sample and
independence testing: on the one hand, the energy distances and distance covariances …
independence testing: on the one hand, the energy distances and distance covariances …
[كتاب][B] Basics and trends in sensitivity analysis: Theory and practice in R
S Da Veiga, F Gamboa, B Iooss, C Prieur - 2021 - SIAM
In many fields, such as environmental risk assessment, agronomic system behavior,
aerospace engineering, and nuclear safety, mathematical models turned into computer code …
aerospace engineering, and nuclear safety, mathematical models turned into computer code …