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 consider semi-supervised regression when the predictor variables are drawnfrom an unknown manifold. A simple two step approach to this problem is to: (i)estimate the manifold geodesic distance between any pair of points using boththe labeled and unlabeled instances; and (ii) apply a k nearest neighborregressor based on these distance estimates. We prove that given sufficientlymany unlabeled points, this simple method of geodesic kNN regression achievesthe optimal finite-sample minimax bound on the mean squared error, as if themanifold were known. Furthermore, we show how this approach can be efficientlyimplemented, requiring only O(k N log N) operations to estimate the regressionfunction at all N labeled and unlabeled points. We illustrate this approach ontwo datasets with a manifold structure: indoor localization using WiFifingerprints and facial pose estimation. In both cases, geodesic kNN is moreaccurate and much faster than the popular Laplacian eigenvector regressor.

Minimax-optimal semi-supervised regression on unknown manifolds