Continuous Maximum Entropy Distributions

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Shows that continuous maximum-entropy ensembles on a manifold reduce to a finite-dimensional convex dual that the ellipsoid method can approximate given a strong integration oracle and mild assumptions: the reference measure is balanced and the target point stays away from the convex-hull boundary (complexity worsens as the smallest eigenvalue → 0). For unitary conjugation orbits HCIZ formulas give explicit integrals, yielding efficient algorithms (ε-approximation of the objective in polylog(1/ε)). Applications: quantum von Neumann entropy, entropic barrier, Grassmannian sampling; sampling remains a separate challenge.

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" chapters (9)

1. 0:00Intro
2. 0:42A First Question
3. 4:03Computing Discrete Max-Entropy Distributions
4. 7:56An Aside: Polynomial Capacity
5. 10:35Back to Maximum Entropy Distributions
6. 19:01Motivating Example: Quantum Entropy
7. 23:26Motivating Example: Interior Point Methods
8. 30:56Integration Oracles via Symmetry
9. 44:58Conclusion This talk