Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization

Understand

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or heterogeneous signals that are unexplainable by the low-rank part.

• The framework is flexible covering both linear and non-linear models, and can easily handle continuous or categorical variables.
• We propose a fast algorithm by integrating the Riemannian gradient descent and a novel gradient pruning procedure.
• Under suitable conditions, the algorithm converges linearly and can simultaneously estimate both the low-rank and sparse tensors.