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Logarithmically Concave Sampling


Logarithmically concave sampling is the problem of generating a random vector whose law approximates a specified logarithmically concave distribution. One oracle model specifies a twice continuously differentiable potential V:R^d->R with V(0)=0, del V(0)=0, and

 I_d<=del ^2V(x)<=2I_d.

The target probability density is Z_V^(-1)e^(-V(x)), with Z_V=int_(R^d)e^(-V(x))dx. An exact first-order oracle query returns V(x) and del V(x). Random real variables and unrestricted computation between queries are allowed.


See also

Logarithmically Concave Distribution, Oracle, Randomized Algorithm, Total Variation Distance

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References

Chewi, S.; de Dios Pont, J.; Li, J.; Lu, C.; and Narayanan, S. "Query Lower Bounds for Log-Concave Sampling." J. ACM 71, Article 29, 2024. https://doi.org/10.1145/3673651.

Cite this as:

Weisstein, Eric W. "Logarithmically Concave Sampling." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LogarithmicallyConcaveSampling.html

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