Communication Efficient Parallel Algorithms for Optimization on Manifolds

By Bayan Saparbayeva, Michael Minyi Zhang, Lizhen Lin. 2018

5 citations recorded by the source corpus.

The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical inference. However, the existing literature on parallel inference almost exclusively focuses on Euclidean data and parameters. While this assumption is valid for many applications, it is increasingly more common to encounter problems where the data or the parameters lie on a non-Euclidean space, like a manifold for example. Our work aims to fill a critical gap in the literature by generalizing parallel inference algorithms to optimization on manifolds. We show that our proposed algorithm is both communication efficient and carries theoretical convergence guarantees. In addition, we demonstrate the performance of our algorithm to the estimation of Fr\'echet means on simulated spherical data and the low-rank matrix completion problem over Grassmann manifolds applied to the Netflix prize data set.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Vision and Pattern Recognition

In Statistics and Probability

Citations in the corpus

DoubleSqueeze: Parallel Stochastic Gradient Descent with Double-Pass Error-Compensated Compression (2019, background): “, 2018), optimization on manifolds (Saparbayeva et al., 2018), compressed PCA (Garber et al.”