Gen-Oja: Simple & Efficient Algorithm for Streaming Generalized Eigenvector Computation

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Kush Bhatia, Aldo Pacchiano, Nicolas Flammarion, Peter L. Bartlett, Michael I. Jordan


In this paper, we study the problems of principle Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm for these problems. We prove the global convergence of our algorithm, borrowing ideas from the theory of fast-mixing Markov chains and two-Time-Scale Stochastic Approximation, showing that it achieves the optimal rate of convergence. In the process, we develop tools for understanding stochastic processes with Markovian noise which might be of independent interest.