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Learning Decision Trees using the Fourier Spectrum

Learning Decision Trees using the Fourier Spectrum. By Eyal Kushilevitz Yishay Mansour. What is Learning. What are we Learning?. Term (and of literals (. DNF (or of terms). DT , : See latter. Does always. All inputs. We Want:. Randomized Algorithm. Do we always succeed ?.

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Learning Decision Trees using the Fourier Spectrum

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  1. Learning Decision Treesusing the Fourier Spectrum By Eyal Kushilevitz Yishay Mansour Haim Kermany

  2. What is Learning

  3. What are we Learning? • Term (and of literals( • DNF (or of terms) • DT , : See latter

  4. Does always All inputs We Want: Randomized Algorithm Do we always succeed ?

  5. What we want

  6. (1+ 1)mod 2=0 Fourier Transform

  7. t-phase function – a function that has at most t Fourier coefficient t-phase function Only big coefficients Very small

  8. Tree What we need

  9. Finding only big coefficients

  10. Analyzing coef()

  11. Changing coef()

  12. Approximating chernoff

  13. Proof:

  14. Approximating MQ

  15. Changing coef() Save Side

  16. chernoff Finding

  17. Coef() output

  18. There will be coefficients Running time is Coaf() time

  19. Finding chernoff

  20. Conclusion

  21. How to find h(x)

  22. Can be exp(n) Best algorithm ever

  23. +1 -1 -1 -1 -1 -1 +1 +1 +1 +1 +1 Decision Tree (DT)

  24. Decision Tree (DT) Proof:

  25. choose: Exacting

  26. Final Result

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