Properties of the Concrete distribution
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Abstract (arXiv)
We examine properties of the Concrete (or Gumbel-softmax) distribution on the simplex. Using the natural vector space structure of the simplex, the Concrete distribution can be regarded as a transformation of the uniform distribution through a reflection and a location-scale transformation. The Fisher information is computed and the corresponding information metric is hyperbolic space. We explicitly give an explicit transformation of the parameters of the distribution to Poincar'e half-space coordinates, which correspond to an orthogonal parameterization, and the Fisher-Rao geodesic distance is computed.
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5 of 34 references.
References · 5
- 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
- 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,148
- 2021A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learningcited by 82
- 2018An elementary introduction to information geometrycited by 76
- 2013Black-box optimization using geodesics in statistical manifoldscited by 4
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