Add to ORKGWe 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.Comment: 19 page
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1 Real-valued random variables and distributions Let µ be any probability measure over the space R e...
We develop the notion of discrete degrees of freedom of a log-concave sequence and use it to prove t...
Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability...
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It is well known that the Fisher information induces a Riemannian geometry on parametric families of...
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We consider dense random packing of disks with a power-law distribution of radii and investigate the...
We provide a new perspective on Stein's so-called density approach by introducing a new operator and...
Distribution of the mean concreteness ratings for both English (left column) and Italian (right colu...
In the first part of the work, we show a general relation between the spatially disjoint product of ...
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradie...
The Fisher information matrix induces a metric on parametric spaces of families of probability densi...
The Chernoff information between two probability measures is a statistical divergence measuring thei...
We introduce a metric for probability distributions, which is bounded, information-theoretically mot...
We introduce a novel approach to inference on parameters that take values in a Riemannian manifold e...
1 Real-valued random variables and distributions Let µ be any probability measure over the space R e...
We develop the notion of discrete degrees of freedom of a log-concave sequence and use it to prove t...
Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability...
Approximating distributions from their samples is a canonical statistical-learning problem. One of i...
It is well known that the Fisher information induces a Riemannian geometry on parametric families of...
A large part of non-parametric statistical techniques are in one way or another related to the geome...
We consider dense random packing of disks with a power-law distribution of radii and investigate the...
We provide a new perspective on Stein's so-called density approach by introducing a new operator and...
Distribution of the mean concreteness ratings for both English (left column) and Italian (right colu...
In the first part of the work, we show a general relation between the spatially disjoint product of ...