Foilsクラスを適当に使ってみた例。 題材は機械学習とかそのあたりのもの。

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