1. Coresets, Sparse Greedy Approximation, and the Frank-Wolfe Algorithm


    Ken Clarkson

  2. The problem

  3. The approximation algorithm

    Compute a sequence `x_{:(0):}, x_{:(1):}, x_{:(2):},...` as follows
  4. What the algorithm is doing

  5. Example: Minimum Enclosing Ball


  6. Algorithm, as applied to MEB

  7. Algorithm, as applied to MEB, cont.

  8. Why is this algorithm interesting?

  9. Application areas

  10. Hard margin SVM


  11. Simplicity

  12. "Good enough approximation"

  13. Why is this algorithm interesting?

  14. Aside: history

  15. Approximation properties

  16. The Wolfe Dual

  17. Example dual: MEB

  18. One step improvement

  19. One step improvement, cont.

  20. What is `C_f`?

  21. Example `C_f`: MEB and SVM

  22. Variations

  23. Primal/dual and coresets

  24. Coresets

  25. Why are coresets interesting?

  26. Coreset variants

  27. Probabilistic coreset existence

  28. Concluding remarks

  29. Bonus Animation: MEB Approximation