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 introduce a multifidelity estimator of covariance matrices formulated asthe solution to a regression problem on the manifold of symmetric positivedefinite matrices. The estimator is positive definite by construction, and theMahalanobis distance minimized to obtain it possesses properties which enablepractical computation. We show that our manifold regression multifidelity(MRMF) covariance estimator is a maximum likelihood estimator under a certainerror model on manifold tangent space. More broadly, we show that ourRiemannian regression framework encompasses existing multifidelity covarianceestimators constructed from control variates. We demonstrate via numericalexamples that our estimator can provide significant decreases, up to one orderof magnitude, in squared estimation error relative to both single-fidelity andother multifidelity covariance estimators. Furthermore, preservation ofpositive definiteness ensures that our estimator is compatible with downstreamtasks, such as data assimilation and metric learning, in which this property isessential.

Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices