Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of dependent data streams remains largely unexplored. In this talk, we present results showing that a non-convex generalization of the well-known OMF algorithm for i.i.d. data converges almost surely to the set of critical points of the expected loss function, even when the data matrices are functions of some underlying Markov chain satisfying a mild mixing condition. As the main application, by combining online non-negative matrix factorization and a recent MCMC algorithm for sampling motifs from networks, we propose a novel framework of Network Dictionary Learning that extracts `network dictionary patches' from a given network in an online manner that encodes main features of the network. We demonstrate this technique on real-world data and discuss recent extensions and variations.
Hanbake Lyu (UCLA)
Hanbaek Lyu is a Hedrick Assistant Professor in the Department of Math at UCLA. He earned his Ph.D. degree from the Ohio State University in 2018, under the guidance of Prof. David Sivakoff. His research interests lie at probability, combinatorics, complex systems, and machine learning. His main research topics include online dictionary learning for dependent signals, dictionary learning for networks, and MCMC motif sampling sparse networks.
Deanna Needell (UCLA)
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Denny Wu · Chengrun Yang · Tolga Ergen · sanae lotfi · Charles Guille-Escuret · Boris Ginsburg · Hanbake Lyu · Cong Xie · David Newton · Debraj Basu · Yewen Wang · James Lucas · MAOJIA LI · Lijun Ding · Jose Javier Gonzalez Ortiz · Reyhane Askari Hemmat · Zhiqi Bu · Neal Lawton · Kiran Thekumparampil · Jiaming Liang · Lindon Roberts · Jingyi Zhu · Dongruo Zhou
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Reinhard Heckel · Paul Hand · Alexandros Dimakis · Joan Bruna · Deanna Needell · Richard Baraniuk
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