# High Dimensional Discrete Integration by Hashing and Optimization

@article{Maity2018HighDD, title={High Dimensional Discrete Integration by Hashing and Optimization}, author={Raj Kumar Maity and Arya Mazumdar and Soumyabrata Pal}, journal={ArXiv}, year={2018}, volume={abs/1806.11542} }

Recently Ermon et al. (2013) pioneered an ingenuous way to practically compute approximations to large scale counting or discrete integration problems by using random hashes. The hashes are used to reduce the counting problems into many separate discrete optimization problems. The optimization problems can be solved by an NP-oracle, and if they allow some amenable structure then commercial SAT solvers or linear programming (LP) solvers can be used in lieu of the NP-oracle. In particular, Ermon…

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Multi-resolution Hashing for Fast Pairwise Summations

- Computer Science, Mathematics2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

This work provides a general framework for designing data structures through hashing that reaches far beyond what previous techniques allowed, and leads to data structures with sub-linear query time that significantly improve upon random sampling and can be used for Kernel Density, Partition Function Estimation and sampling.

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