| Paper ID | MLSP-7.5 |
| Paper Title |
Fiber-Sampled Stochastic Mirror Descent For Tensor Decomposition with beta-Divergence |
| Authors |
Wenqiang Pu, The Chinese University of Hong Kong, Shenzhen, China; Shahana Ibrahim, Xiao Fu, Oregon State University, United States; Mingyi Hong, University of Minnesota, United States |
| Session | MLSP-7: Tensor Signal Processing |
| Location | Gather.Town |
| Session Time: | Tuesday, 08 June, 14:00 - 14:45 |
| Presentation Time: | Tuesday, 08 June, 14:00 - 14:45 |
| Presentation |
Poster
|
| Topic |
Machine Learning for Signal Processing: [MLR-LMM] Learning from multimodal data |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| Abstract |
Canonical polyadic decomposition (CPD) has been a workhorse for multimodal data analytics. This work puts forth a stochastic algorithmic framework for CPD under $\beta$-divergence, which is well-motivated in statistical learning---where the Euclidean distance is typically not preferred. Despite the existence of a series of prior works addressing this topic, pressing computational and theoretical challenges, e.g., scalability and convergence issues, still remain. In this paper, a unified stochastic mirror descent framework is developed for large-scale $\beta$-divergence CPD. Our key contribution is the integrated design of a tensor fiber sampling strategy and a flexible stochastic Bregman divergence-based mirror descent iterative procedure, which significantly reduces the computation and memory cost per iteration for various $\beta$. Leveraging the fiber sampling scheme and the multilinear algebraic structure of low-rank tensors, the proposed lightweight algorithm also ensures global convergence to a stationary point under mild conditions. Numerical results on synthetic and real data show that our framework attains significant computational saving compared with state-of-the-art methods. |
