1. Learning and Fourier Analysis Grigory Yaroslavtsev http://grigory.us CIS 625: Computational Learning Theory

2. Fourier Analysis and Learning

3. Boolean Functions

4. Fourier Expansion

5. Orthonormal Basis: Proof

6. Functions = Vectors, Inner Product

7. Fourier Coefficients

8. Parsevel’s Theorem

9. Plancharel’s Theorem

10. Basic Fourier Analysis

11. Convolution

12. Convolution: Proof of Property 3

13. Approximate Linearity

14. Property Testing [Goldreich, Goldwasser, Ron; Rubinfeld, Sudan] NO YES Randomized Algorithm YES NO Property Tester Don’t care

15. Linearity Testing Linear Non- linear Linearity Tester Don’t care

16. Linearity Testing [Blum, Luby, Rubinfeld]

17. Linearity Testing: Analysis

18. Linearity Testing: Analysis Continued

19. Local Correction

20. Thanks!