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    The Bayesian Learning Rule

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    Type
    Preprint
    Authors
    Khan, Mohammad Emtiyaz
    Rue, Haavard cc
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Statistics Program
    Date
    2021-07-09
    Permanent link to this record
    http://hdl.handle.net/10754/670192
    
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    Abstract
    We show that many machine-learning algorithms are specific instances of a single algorithm called the Bayesian learning rule. The rule, derived from Bayesian principles, yields a wide-range of algorithms from fields such as optimization, deep learning, and graphical models. This includes classical algorithms such as ridge regression, Newton's method, and Kalman filter, as well as modern deep-learning algorithms such as stochastic-gradient descent, RMSprop, and Dropout. The key idea in deriving such algorithms is to approximate the posterior using candidate distributions estimated by using natural gradients. Different candidate distributions result in different algorithms and further approximations to natural gradients give rise to variants of those algorithms. Our work not only unifies, generalizes, and improves existing algorithms, but also helps us design new ones.
    Publisher
    arXiv
    arXiv
    2107.04562
    Additional Links
    https://arxiv.org/pdf/2107.04562.pdf
    Collections
    Preprints; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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