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Lecture 39

Lecture 39. CSE 331 Dec 7, 2016. Final exam piazza post. Mini project video grading. Will be done tonight. If your group is selected for presentation you ’ ll be notified by tonight. Algorithms for Data Science. What is different?. Algorithms for non-discrete inputs.

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Lecture 39

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  1. Lecture 39 CSE 331 Dec 7, 2016

  2. Final exam piazza post

  3. Mini project video grading Will be done tonight If your group is selected for presentation you’ll be notified by tonight

  4. Algorithms for Data Science What is different? Algorithms for non-discrete inputs A Representative Problem Compute Eigenvalues Further Reading http://research.microsoft.com/en-US/people/kannan/book-no-solutions-aug-21-2014.pdf

  5. Johnson Lindenstrauss Lemma http://www.scipy-lectures.org/_images/pca_3d_axis.jpg

  6. The simplest non-trivial join query S R A Intersection of R and S Assume R and S are sorted Let us concentrate on comparison based algorithms Assume |R| = |S| = N

  7. Not all inputs are created equal R S R S 1 1 2 2 3 3 4 4 5 5 6 6 Ω(N) comparisons 1 comparison!

  8. We need a faster/adaptive algorithm

  9. The MERGE algorithm works R S 1 N

  10. An assumption Output of the join is empty

  11. MERGE is (near) instance optimal Benchmark: Minimum number of comparisons (C) to “certify” output 1 Value not ruled out yet Munro Demaine Lopez-Oritz C logNcomparions (and time) Need a comparison to rule the value out Each value involved with ≤2 comparisons Once the pointer moves the value is never seen again N R S Each move takes log N comparisons

  12. Coding Theory

  13. Communicating with my 5 year old C(x) x y = C(x)+error • “Code”C • “Akash English” • C(x) is a “codeword” x Give up

  14. The setup C(x) x y = C(x)+error • Mapping C • Error-correcting code or just code • Encoding: xC(x) • Decoding: yx • C(x) is a codeword x Give up

  15. Different Channels and Codes • Internet • Checksum used in multiple layers of TCP/IP stack • Cell phones • Satellite broadcast • TV • Deep space telecommunications • Mars Rover

  16. “Unusual” Channels • Data Storage • CDs and DVDs • RAID • ECC memory • Paper bar codes • UPS (MaxiCode) Codes are all around us

  17. 1 1 1 0 0 1 0 0 0 0 1 1 Redundancy vs. Error-correction • Repetition code: Repeat every bit say 100 times • Good error correcting properties • Too much redundancy • Parity code: Add a parity bit • Minimum amount of redundancy • Bad error correcting properties • Two errors go completely undetected • Neither of these codes are satisfactory

  18. Two main challenges in coding theory • Problem with parity example • Messages mapped to codewords which do not differ in many places • Need to pick a lot of codewords that differ a lot from each other • Efficient decoding • Naive algorithm: check received word with all codewords

  19. The fundamental tradeoff • Correct as many errors as possible with as little redundancy as possible Can one achieve the “optimal” tradeoff with efficient encoding and decoding ?

  20. Interested in more? CSE 545, Spring 201?

  21. Whatever your impression of the 331 IT WAS RIDING

  22. Hopefully it was fun!

  23. Thanks! Except of course, HW 10, presentations and the final exam

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