Sampling From A Manifold
By Persi Diaconis, Susan P. Holmes, Mehrdad Shahshahani. 2012
125 citations recorded by the source corpus.
We develop algorithms for sampling from a probability distribution on a submanifold embedded in R n . Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of t tests in exponential families and to Neyman's smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b0c4bd11cb7106ab0324e1e6b1f3488379199c78
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In Applied Mathematics
In Computational Theory and Mathematics
- Amos J. Storkey
- Peter Bubenik
- Wonyeol Lee
- Hongseok Yang
- Matthew M. Graham
- Hangyeol Yu
- Larry A. Wasserman
- Matthew J. Parkinson
In Mathematical Physics
Citations in the corpus
- Statistical topological data analysis using persistence landscapes (2012, methodology): “Here we combine persistence landscapes and statistical inference to discriminate between iid samples of 1000 points from a torus and a sphere in R(3) with the same surface area, using the uniform surface area measure as described by Diaconis et al. (2012) (see Figure 8).”
- Asymptotically exact inference in differentiable generative models (2016, background): “The result (10) is given in a slightly different form in [9].”
- Reparameterization Gradient for Non-differentiable Models (2018, methodology): “In general, to approximate a surface integral well, we need a parameterization of the surface, and a scheme for generating samples from it [2]; this general methodology and a known theorem related to our case are reviewed in the supplementary material.”