Faster Deterministic Volume Estimation in the

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Description: Faster Deterministic Volume Estimation in the Oracle Model via Thin Lattice Coverings Daniel Dadush Centrum Wiskunde Informatica Volume Estimation Problem Volume Estimation Problem Assume appropriate sandwiching guarantees. Volume

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slide1. Faster Deterministic Volume Estimation in the Oracle Model via Thin Lattice Coverings Daniel Dadush
Centrum Wiskunde & Informatica<br>
slide2. Volume Estimation Problem<br>
slide3. Volume Estimation Problem Assume appropriate sandwiching guarantees.<br>
slide4. Volume Estimation: Known Bounds<br>
slide5. Volume Estimation: Known Bounds<br>
slide6. Volume Estimation: Known Bounds<br>
slide7. Main Result<br>
slide8. asymmetric symmetric<br>
slide9. Lattices<br>
slide10. Lattices<br>
slide11. Lattices<br>
slide12. High Level Idea<br>
slide13. High Level Algorithm<br>
slide14. High Level Algorithm Treat above as optimization problem.<br>
slide15. High Level Algorithm<br>
slide16. High Level Algorithm<br>
slide17. High Level Algorithm<br>
slide18. High Level Algorithm<br>
slide19. Algorithm Recap<br>
slide20. Algorithm Recap<br>
slide21. Algorithm Recap<br>
slide24. Milman’s Ellipsoid<br>
slide25. Milman’s Ellipsoid<br>
slide26. Milman’s Ellipsoid<br>
slide27. Milman’s Ellipsoid<br>
slide37. Summary Nearly optimal deterministic algorithm for volume estimation in the oracle model.
New construction of “easy to enumerate” thin-covering lattices. Open Questions Ignoring efficiency, can we match query lower bound?
Other applications of thin-covering lattices?<br>