This work proposes a new computational framework for learning an explicit generative model for real-world datasets. More specifically, we propose to learn a closed-loop transcription between a multi-class multi-dimensional data distribution and a linear discriminative representation (LDR) in the feature space that consists of multiple independent linear subspaces. We argue that the optimal encoding and decoding mappings sought can be formulated as the equilibrium point of a two-player minimax game between the encoder and decoder. A natural utility function for this game is the so-called rate reduction, a simple information-theoretic measure for distances between mixtures of subspace-like Gaussians in the feature space. Our formulation draws inspiration from closed-loop error feedback from control systems and avoids expensive evaluating and minimizing approximated distances between arbitrary distributions in either the data space or the feature space. To a large extent, this new formulation unifies the concepts and benefits of Auto-Encoding and GAN and naturally extends them to the settings of learning a both discriminative and generative representation for multi-class and multi-dimensional real-world data. Our extensive experiments on many benchmark imagery datasets demonstrate tremendous potential of this new closed-loop formulation: we notice that the so learned features of different classes are explicitly mapped onto approximately independent principal subspaces in the feature space; and diverse visual attributes within each class are modeled by the independent principal components within each subspace. This work opens many deep mathematical problems regarding learning submanifolds in high-dimensional spaces as well as suggests potential computational mechanisms about how memory can be formed through a purely internal close-loop process.

This is joint work with Xili Dai, Shengbang Tong, Mingyang Li, Ziyang Wu, Kwan Ho Ryan Chan, Pengyuan Zhai, Yaodong Yu, Michael Psenka, Xiaojun Yuan, Heung-Yeung Shum.

Brief Bio of the Speaker: Yi Ma is a Professor at the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. His research interests include computer vision, high-dimensional data analysis, and intelligent systems. Yi received his Bachelor’s degrees in Automation and Applied Mathematics from Tsinghua University in 1995, two Masters degrees in EECS and Mathematics in 1997, and a PhD degree in EECS from UC Berkeley in 2000. He has been on the faculty of UIUC ECE from 2000 to 2011, the principal researcher and manager of the Visual Computing group of Microsoft Research Asia from 2009 to 2014, and the Executive Dean of the School of Information Science and Technology of ShanghaiTech University from 2014 to 2017. He then joined the faculty of UC Berkeley EECS in 2018. He has published about 60 journal papers, 120 conference papers, and three textbooks in computer vision, generalized principal component analysis, and high-dimensional data analysis. He received the NSF Career award in 2004 and the ONR Young Investigator award in 2005. He also received the David Marr prize in computer vision from ICCV 1999 and best paper awards from ECCV 2004 and ACCV 2009. He has served as the Program Chair for ICCV 2013 and the General Chair for ICCV 2015. He is a Fellow of IEEE, ACM, and SIAM.

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