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In this paper, we study the problems of principal Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm, Gen-Oja, 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.
Neuromorphic networks based on nanodevices, such as metal oxide memristors, phase change memories, and flash memory cells, have generated considerable interest for their increased energy efficiency and density in comparison to graphics processing uni
The fundamental learning theory behind neural networks remains largely open. What classes of functions can neural networks actually learn? Why doesnt the trained network overfit when it is overparameterized? In this work, we prove that overparamete
Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural networks with
Submodular maximization problems belong to the family of combinatorial optimization problems and enjoy wide applications. In this paper, we focus on the problem of maximizing a monotone submodular function subject to a $d$-knapsack constraint, for wh
In the class of streaming anomaly detection algorithms for univariate time series, the size of the sliding window over which various statistics are calculated is an important parameter. To address the anomalous variation in the scale of the pseudo-pe