English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a distributionally robust optimization formulation (i.e., a min-maxgame) for two representative problems in Bayesian nonparametric estimation:Gaussian process regression and, more generally, linear inverse problems. Ourformulation seeks the best mean-squared error predictor, in aninfinite-dimensional space, against an adversary who chooses the worst-casemodel in a Wasserstein ball around a nominal infinite-dimensional Bayesianmodel. The transport cost is chosen to control features such as the degree ofroughness of the sample paths that the adversary is allowed to inject. We showthat the game has a well-defined value (i.e., strong duality holds in the sensethat max-min equals min-max) and that there exists a unique Nash equilibriumwhich can be computed by a sequence of finite-dimensional approximations.Crucially, the worst-case distribution is itself Gaussian. We exploreproperties of the Nash equilibrium and the effects of hyperparameters through aset of numerical experiments, demonstrating the versatility of our modelingframework.

Distributionally Robust Gaussian Process Regression and Bayesian Inverse Problems