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Publications [#338622] of Jian-Guo Liu

Papers Published

  1. Feng, Y; Li, L; Liu, JG, Semigroups of stochastic gradient descent and online principal component analysis: Properties and diffusion approximations, Communications in Mathematical Sciences, vol. 16 no. 3 (January, 2018), pp. 777-789 [doi]
    (last updated on 2019/06/16)

    © 2018 International Press. We study the Markov semigroups for two important algorithms from machine learning: stochastic gradient descent (SGD) and online principal component analysis (PCA). We investigate the effects of small jumps on the properties of the semigroups. Properties including regularity preserving, L ∞ contraction are discussed. These semigroups are the dual of the semigroups for evolution of probability, while the latter are L 1 contracting and positivity preserving. Using these properties, we show that stochastic differential equations (SDEs) in Rd (on the sphere Sd -1 ) can be used to approximate SGD (online PCA) weakly. These SDEs may be used to provide some insights of the behaviors of these algorithms.
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