A Polynomial Number of Random Points Does Not Determine the Volume of a Convex Body
By Ronen Eldan. 2009
8 citations recorded by the source corpus.
We show that there is no algorithm which, provided a polynomial number of random points uniformly distributed over a convex body in ℝn, can approximate the volume of the body up to a constant factor with high probability.
Subfields: Applied Mathematics, Statistics and Probability
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In Applied Mathematics
In Statistics and Probability
Citations in the corpus
- Efficient Formal Safety Analysis of Neural Networks (2018, methodology): “Similarly, sampling-based inference techniques like blackbox Monte Carlo sampling may need an enormous amount of data to generate tight accurate bounds on the decision boundary [8].”