1. Fast Fourier Sparsity Testing over the Boolean Hypercube Grigory Yaroslavtsev http://grigory.us Joint with Andrew Arnold (Waterloo), Arturs Backurs (MIT), Eric Blais (Waterloo) and Krzysztof Onak (IBM).

2. Fourier Analysis

4. PAC-style learning

5. Fourier Analysis and Learning

6. k- sparse NO Property Tester Don’t care Tolerant Property Tester Don’t care NO k- sparse

7. Previous work under Hamming

8. Pairwise Independent Hashing

9. Pairwise Fourier Hashing [FGKP’09]

10. Testing k-sparsity [GOSSW’11] #

11. Our Algorithm

12. Analysis Two main challenges – Top-k coefficients may collide – Noise from non top-k coefficients

13. Analysis: Large coefficients

14. Analysis: Small coefficients

15. Analysis: Putting it together

16. Other results + Open Problems