Learning Mixtures of Separable Dictionaries for High-Dimensional Tensor Data

Data-driven feature representations comprise one of the first and most important steps within a data analysis pipeline. Dictionary learning, which involves using training data to obtain an overcomplete matrix that sparsifies the unseen data, has emerged as one of the most powerful data-driven feature representation methods during the last decade-and-a-half. When utilized for high-dimensional tensor (aka, multiway) data, however, conventional dictionary learning suffers from high sample complexity and computational overhead. We address this challenge in the talk by proposing a new model for dictionary learning for high-dimensional tensor data that corresponds to learning a mixture of separable dictionaries. The proposed model better captures the richness of tensor data by generalizing the separable dictionary learning model to one that offers an improved tradeoff between bias and variance. In the talk, we explore two different structured optimization approaches for learning a mixture of separable dictionaries and also derive sufficient conditions for local identifiability of the underlying dictionary in each case. Moreover, we discuss computational algorithms that can be used to solve the problem of learning a mixture of separable dictionaries in both batch and online settings.

This talk is based on a joint work with Mohsen Ghassemi, Zahra Shakeri, and Anand Sarwate.

Note: This meeting will be via Zoom.  This semester, we anticipate some talks will be in person but most will be by Zoom.