Robust Optimization and Inference on Manifolds
From MaRDI portal
Publication:6342708
arXiv2006.06843MaRDI QIDQ6342708
Lizhen Lin, Bayan Sarpabayeva, Drew Lazar, David B. Dunson
Publication date: 11 June 2020
Abstract: We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data science in which a statistical learning problem can be cast as an optimization problem over manifolds. Being able to incorporate the underlying geometry for inference while addressing the need for robustness and scalability presents great challenges. We address these challenges by first proving a key lemma that characterizes some crucial properties of geometric medians on manifolds. In turn, this allows us to prove robustness and tighter concentration of our proposed final estimator in a subsequent theorem. This estimator aggregates a collection of subset estimators by taking their geometric median over the manifold. We illustrate bounds on this estimator via calculations in explicit examples. The robustness and scalability of the procedure is illustrated in numerical examples on both simulated and real data sets.
Has companion code repository: https://github.com/DrewLazar/RobustManifold
This page was built for publication: Robust Optimization and Inference on Manifolds
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6342708)
