Lost Relatives of the Gumbel Trick

    Abstract

    The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of related methods, of which the Gumbel trick is one member, and show that the new methods have superior properties in several settings with minimal additional computational cost. In particular, for the Gumbel trick to yield computational benefits for discrete graphical models, Gumbel perturbations on all configurations are typically replaced with socalled low-rank perturbations. We show how a subfamily of our new methods adapts to this setting, proving new upper and lower bounds on the log partition function and deriving a family of sequential samplers for the Gibbs distribution. Finally, we balance the discussion by showing how the simpler analytical form of the Gumbel trick enables additional theoretical results.

    Authors

    Matej Balog, Nilesh Tripuraneni, Zoubin Ghahramani, Adrian Weller

    Conference

    ICML 2017

    Full Paper

    ‘Lost Relatives of the Gumbel Trick’ (PDF)

    Uber AI

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    Zoubin Ghahramani
    Zoubin Ghahramani is Chief Scientist of Uber and a world leader in the field of machine learning, significantly advancing the state-of-the-art in algorithms that can learn from data. He is known in particular for fundamental contributions to probabilistic modeling and Bayesian approaches to machine learning systems and AI. Zoubin also maintains his roles as Professor of Information Engineering at the University of Cambridge and Deputy Director of the Leverhulme Centre for the Future of Intelligence. He was one of the founding directors of the Alan Turing Institute (the UK's national institute for Data Science and AI), and is a Fellow of St John's College Cambridge and of the Royal Society.