1. CS 9633 Machine Learning Computational Learning Theory Adapted from notes by Tom Mitchell http://www-2.cs.cmu.edu/~tom/mlbook-chapter-slides.html

13. M No Yes No No 10 B Yes No No No 9 M Yes No Yes Yes 8 M No Yes Yes Yes 7 F No No No Yes 6 B Yes No No Yes 5 M Yes Yes No No 4 F No Yes Yes No 3 B No No No Yes 2 B Yes No No Yes 1 Class a 4 a 3 a 2 a 1 Instance

15. Error of h with respect to c Instance space X + + + c h - - - -

21. Block Diagram of PAC Learning Model Learning algorithm L Training sample Control Parameters  ,  Hypothesis h

28. Exhausting the version space VS H,D error = 0.1 r=0.2 error = 0.3 r=0.2 error = 0.2 r=0 error = 0.1 r=0 error = 0.3 r=0.4 error = 0.2 r=0.3 Hypothesis Space H

32. Number of Training Examples (Eq. 7.2)

49. Shattered Instance Space

51. Shattering the real number line -1.2 3.4 6.7 What is VC(H)? What is |H|? -1.2 3.4

53. Shattering the x-y plane 2 instances 3 instances VC(H) = ? |H| = ?

59. Comparing the Bounds