Foilsを使ってみた。
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This document discusses various machine learning topics including supervised learning techniques like support vector machines, decision trees, and neural networks. It also discusses unsupervised learning techniques like clustering algorithms. It provides short code examples for algorithms like quicksort in Haskell and OCaml. Finally, it introduces other concepts like probably approximately correct learning and boosting.
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• Haskell 1.0 Haskell 98 Haskell 2010
•
qsort [] = []
qsort (p:xs) = qsort lt ++ [p] ++ qsort gteq
where
lt = [x | x <- xs, x < p]
gteq = [x | x <- xs, x >= p]
4](https://image.slidesharecdn.com/online-100813072552-phpapp02/85/Foils-4-320.jpg)
![• quicksort 4
• 2
qs [] = []
qs (p:xs) = qs [x|x<-xs,x<p]++[p]++qs[x|x<-xs,x>=p]
www
5](https://image.slidesharecdn.com/online-100813072552-phpapp02/85/Foils-5-320.jpg)
![let rec qsort= function
| [] -> []
| pivot :: rest ->
let il x = x < pivot in
let left, right = List.partition il rest in
qsort left @ [pivot] @ qsort right
(
8](https://image.slidesharecdn.com/online-100813072552-phpapp02/85/Foils-8-320.jpg)
Foilsを使ってみた。
- 1. Recently Keyword Keyword • (Artificial Intelligence) • (Pattern Recognition) • (Machine Learning) • (Mathematics) • (Ocaml, Haskell, ...) • etc. 1
- 2. 2
- 3. Haskell • OCaml 1 • • 3
- 4. • • Haskell 1.0 Haskell 98 Haskell 2010 • qsort [] = [] qsort (p:xs) = qsort lt ++ [p] ++ qsort gteq where lt = [x | x <- xs, x < p] gteq = [x | x <- xs, x >= p] 4
- 5. • quicksort 4 • 2 qs [] = [] qs (p:xs) = qs [x|x<-xs,x<p]++[p]++qs[x|x<-xs,x>=p] www 5
- 6. • • Haskell ( ) Haskell 6
- 7. OCaml • Haskell • Haskell Haskell • for while Haskell for while Microsoft F# 7
- 8. let rec qsort= function | [] -> [] | pivot :: rest -> let il x = x < pivot in let left, right = List.partition il rest in qsort left @ [pivot] @ qsort right ( 8
- 9. ML • • 9
- 10. 10
- 11. 11
- 12. Introduction to Machine Learning • ML=Machine Learning • • • wikipedia 12
- 13. Introduction to Machine Learning • • 2 – — Supervised learning – — Unsupervised Learning 13
- 14. Introduction to Machine Learning — Supervised learning • ( • – SVM — Support Vector Machine – — Regression – — Back Propagation – — Decision tree 14
- 15. Introduction to Machine Learning — Unsupervised learning • ( • – — Clustering – — Frequent Pattern Analysis 15
- 16. Introduction to Machine Learning • — statistical machine learning – – • — computational learning – – 16
- 17. Introduction to Machine Learning • – – – & • – – (?) 17
- 18. Introduction to Machine Learning (1) • – • – = • – / 18
- 19. Introduction to Machine Learning (2) • – – – • – ? – 19
- 20. Introduction to Machine Learning (3) • – ? — – — – – • 20
- 21. Introduction to Machine Learning • – symbol • (?) – – 21
- 22. Introduction to Machine Learning PRML 22
- 23. @ 23
- 24. SVM SVM — Support Vector Machine • 2 (+1, -1) • ( ) 24
- 25. SVM • • yk (w · x − θ) ≥ 1 • Maximize Margin ≡ Minimize |w|2 • Lagurange αk L ∑ ∑∑ xk · xl L= αk − αk αl yk yl 2 k k l 25
- 26. SVM • L minimize • • ? – x x → ψ(x) – 26
- 27. clustering — Clustering • & • ( 27
- 28. clustering • = • ( ) 28
- 29. clustering • = – ||x − y||2 – ∑ n 1 dk (x, y) = ( |xi − yi | ) k k i=1 – – 29
- 30. 30
- 31. • – — Black, Blonde, Brown, Red, ... – — Safe, Normal, Danger • • 31
- 32. decision tree — decision tree • • • Height Color Eatable small colorful can’t middle colorful can’t 32
- 33. decision tree • • • ? • — • ? — NP 33
- 34. decision tree • • ? 34
- 35. decision tree • ( ) • • ? • ? • 35
- 36. frequent pattern • • —A B • (1/0 — / ) 36
- 37. frequent pattern • • =1/ =0 , A B C D E F 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 37
- 38. frequent pattern • – ( ) • – A C – A,C,D • Algorithm – Apriori – FP-growth, ZDD-growth 38
- 39. frequent pattern • I = {i1, i2, · · · , in} – I = {A, B, C , D, E , F } • X ∈ 2I • σ • supp(X ) – supp(X) X – supp(X)≥ σ 39
- 40. frequent pattern • A → α, Aispattern, X ∈ I – A, B → C – A B C ( • conf supp(A∪{α}) • conf(A )≡ supp(A) • conf θ – 100 10 40
- 41. frequent pattern • – Apriori – FP tree and FP-growth – ZBDD and ZBDD-growth • – 41
- 42. add-up • • • – etc. • – — Data Mining – (?) 42
- 43. add-up • – – – • (?) – ( ) – NN – 43
- 44. 44
- 45. COLT • — • — • • DM ? 45
- 46. COLT • • – – – – ( ) • – keyword, 46
- 47. COLT • – – • • ( ) • 47
- 48. automaton and language • automaton • grammer • • automaton grammer – 0 TM( ) – 2 ( ) PDA( ) – 3 ( ) FA( ) 48
- 49. learning in the limit • • A = {(aa)n |n ≥ 0} = { , aa, aaaa, · · ·} – A Σ = {a} • M( – ( – – M 49
- 50. learning in the limit • (DFA) D = (Q, Σ, δ, s0, F ) • γ • γ L(γ) • ( ) A = {(aa)n |n ≥ 0} = { , aa, aaaa, · · ·} • A E (w , l), w ∈ Σ∗, l ∈ {1, 0} • E=(w , l) w A l = 1( ) 50
- 51. learning in the limit • A ( ) σ – σ = (w 1, l1) (w 2, l2) (w 3, l3) (w 4, l4) · · · – ∀i, wi ∈ Σ∗ – if wi ∈ A then li = 1 • – A = {(aa)n |n ≥ 0} = { , aa, aaaa, · · ·} – σ = ( , 1) (a01) (aa, 1) (aaa, 0) (aaaa, 1) · · · 51
- 52. learning in the limit • ( )L ∈ C, C (Σ ) • R, R γ • M R L M L σ g1, g2, · · · (gi γ ) {gi } L(g ) = L g 52
- 53. learning in the limit • – • – σ – – (class P? NP complete? NP hard?) • – 53
- 54. Probably Approximately Correct Learning PAC — probably approximately correct • δ • • f g d(f , g ) • PAC ∀ ,δ Pr (d(f , g ) ≤ ) ≥ 1 − δ g f PAC 54
- 55. appendix • (?) – – – – – – – etc 55
- 56. Weak Probably Approximately Correct Learning PAC — Weak PAC learning • ∀ ,δ • PAC 0 , δ0 Pr (d(f , g ) ≤ ≥ 1 − δ0 0) g f PAC • – ? – ,δ 56
- 57. boosting Boosting • • M0 • M0 Mw • Mw • ( PAC) (PAC) 57
- 58. boosting • – Boosting – – • ? • Boosting AdaBoost (?) 58