?at??????p???s? ??I

1
?at??????p???s? ??I
2
?at??????p???t?? ?a?????
3
?at??????p???s? µe ?a???e?
?at??????p???s? t?? e???af?? µe ß?s? ??a s?????
ap? ?a???e? t?? µ??f?? ifthen ?a???a?
(S??????) ? y ?p?? S?????? (Condition) e??a?
s??e??? s??????? sta ?????sµata y ? et???ta t??
???s?? LHS rule antecedent (p??te??) ?
condition (s??????) RHS rule consequent
(epa??????? ? ap?t???) ?a?ade??µata ?a?????
?at??????p???s?? (Blood TypeWarm) ? (Lay
EggsYes) ? Birds (Taxable Income lt 50K) ?
(RefundYes) ? CheatNo
4
?at??????p???s? µe ?a???e?
?a??de??µa
???t??? S????? ?a????? (Rule Set)

• R1 (Give Birth no) ? (Can Fly yes) ? Birds
• R2 (Give Birth no) ? (Live in Water yes) ?
  Fishes
• R3 (Give Birth yes) ? (Blood Type warm) ?
  Mammals
• R4 (Give Birth no) ? (Can Fly no) ? Reptiles
• R5 (Live in Water sometimes) ? Amphibians

5
?at??????p???s? µe ?a???e?
?fa?µ??? ?at??????p???t?? µe ?a???e?
??a? ?a???a? r ?a??pte? (covers) ??a st??µ??t?p?
(e???af?) a? ta ?????sµata t?? st??µ??t?p??
??a??p????? t? s?????? t?? ?a???a
R1 (Give Birth no) ? (Can Fly yes) ?
Birds R2 (Give Birth no) ? (Live in Water
yes) ? Fishes R3 (Give Birth yes) ? (Blood
Type warm) ? Mammals R4 (Give Birth no) ?
(Can Fly no) ? Reptiles R5 (Live in Water
sometimes) ? Amphibians
? ?a???a? R1 ?a??pte? t? hawk (? a????? t? hawk
e?e???p??e? /p???d?te? (trigger) t?? ?a???a) gt
Bird ? ?a???a? R3 ?a??pte? t? grizzly bear gt
Mammals
6
?at??????p???s? µe ?a???e?
?????? ?a???a - Coverage ?? p?s?st? t??
e???af?? p?? ??a??p????? t? LHS t?? ?a???a
????ße?a ?a???a - Accuracy ?? p?s?st? t??
e???af?? p?? ?a??pt??? ?a? t? LHS ?a? t? RHS t??
?a???a
(StatusSingle) ? No Coverage 40,
Accuracy 50
7
?at??????p???s? µe ?a???e? ?fa?µ???
R1 (Give Birth no) ? (Can Fly yes) ?
Birds R2 (Give Birth no) ? (Live in Water
yes) ? Fishes R3 (Give Birth yes) ? (Blood
Type warm) ? Mammals R4 (Give Birth no) ?
(Can Fly no) ? Reptiles R5 (Live in Water
sometimes) ? Amphibians

• Lemur R1
• Turtle R4, R5
• Godfish -

8
?at??????p???s? µe ?a???e? ?fa?µ???
?d??t?te? ?at??????p???t?? ?a?????

• ?µ??ßa?a ap???e??µe??? ?a???e? (Mutually
  exclusive rules)
• ??a? ?at??????p???t?? pe????e? aµ??ßa?a
  ap???e??µe???? ?a???e?, a? ?? ?a???e? e??a?
  a?e???t?t?? ? ??a? ap? t?? ????
• ???e e???af? ?a??pteta? ap? t? p??? ??a? ?a???a
  de? ?p?????? d?? ?a???e? p?? ?a p???d?t???ta?
  ap? t?? ?d?a e???af?
• ????e?? ?a???e? (Exhaustive rules)
• ??a? ?at??????p???t?? ??e? p???? ??????
  (coverage) a? ?a??pte? ????? t??? p??a????
  s??d?asµ??? t?µ?? ?????sµ?t?? ?p???e? ??a?
  ?a???a? ??a ???e s??d?asµ? t?µ?? ?????sµ?t??
• ???e e???af? ?a??pteta? ap? t??????st?? ??a?
  ?a???a

9
?at??????p???s? µe ?a???e? ?fa?µ???

• ?? ?? ?a???e? de? e??a? p?a aµ??ßa?a
  ap???e??µe???
• ??a e???af? µp??e? ?a e?e???p???se? pa?ap??? ap?
  ??a? ?a???a
• ??s? (conflict resolution)
• ???ta?? t?? s?????? ?a????? a? µ?a e???af?
  e?e???p??e? p?????? ?a???e?, t?? a?at??eta? a?t??
  µe t? µe?a??te?? p??te?a??t?ta
• ??a d?ateta?µ??? s????? ?a????? ???eta? ?a?
  ??sta ?p?fas?? (Decision list)
• ?? ?a???e? e?et????ta? µe t? se???
• ? d??ta?? µe ß?s? ??p??? ???t????, p?. (a) µe
  t? se??? p?? pa?????ta?, (ß) ?????? ?/?a?
  a???ße?a, (?) µe t? a???µ? ???? (size ordering)
  
• d??ta?? t?? ???se?? a? µ?a e???af? e?e???p??e?
  p?????? ?a???e?, t?? a?at??eta? ? ???s? µe t?
  µe?a??te?? p??te?a??t?ta
• ????? d??ta?? t?? s?????? ?a????? ???s?
  s??µat?? ??f?f???a?, ? p?e????f??sa ???s?
  st??µ?s? ??f?? µe ß?s? t?? a???ße?a t?? ?a???a
  (misclassification cost)
• ?? ?a???e? de? e??a? e?a?t??t????
• ??a e???af? µp??e? ?a µ?? e?e???p??e? ??p????
  ?a???a
• ???s? default ???s?? µe ?de?a LHS

10
?at??????p???s? µe ?a???e? ?atas?e??
?atas?e?? ?at??????p???t?? µe ?a???e?

• ?µes? ????d??
• ??a???? ?a????? ape??e?a? ap? ta ded?µ??a
• ?.?. RIPPER, CN2, Holtes 1R
• ?µµes? ????d??
• ??a???? ?a????? ap? ???a µ??t??a
  ?at??????p???t?? (p? ap? d??t?a ap?fas??)
• ?.?. C4.5 ?a???e?

11
?at??????p???s? µe ?a???e? ?atas?e??
?µes?? ????d?? ?atas?e?? ?at??????p???t?? µe
?a???e?
Se???a?? ?????? (sequential covering)

• ?e???a µe ??a ?de?? ?a???a
• G?a ???e ?at?????a ?e????st?
• Repeat
• Grow a rule using the Learn-One-Rule function
• Remove training records covered by the rule
• Add rule to the set
• until stopping condition

12
?at??????p???s? µe ?a???e? ?atas?e??
Se???a?? ?????? ?a??de??µa

• ???ta?? t?? ???se??
• ?p? ta pe??ss?te?a de??µata

13
?at??????p???s? µe ?a???e? ?atas?e??
Se???a?? ?????? Rule-Growing Strategy
Ge???? se e?d??? ?e???a ap? t?? ?a???a R ?
y ??ad????? p??s?ese ??e? s??e??e?? ??a ?a
ße?t???e? ? p???t?ta t?? ?a???a
??d??? se ?e???? ?p??e?e ??a ap? ta de??µata
t??a?a Ge???e?se afa????ta? s??e??e??
14
?at??????p???s? µe ?a???e? ?atas?e??
Se???a?? ?????? Remove Training Records

• G?at? sß????µe ta ?et??? de??µata?
• ?ste ? ep?µe??? ?a???a? ?a e??a? d?af??et????
• Sß????µe ? ??? ?a? ta a???t??? de??µata?

?????? ? R1 µe a???ße?a 12/15 80, R2 7/10 20,
R3 8/12 70 ?p????? R1, sß????µe ta ?et???
de??µata (?a??pt??ta?) ta a???t???? St? s????e?a
t?? R2 ? t?? R3?
15
?at??????p???s? µe ?a???e? ?atas?e??
Se???a?? ??????

• ???t???? te?µat?sµ??
• ?e ß?s? t? ???d??
• ?? µ???? a????se t? ???d??
• ???deµa ?a????? (?p?? ?a? sta d??t?a ap?fas??)
• G?a pa??de??µa
• Sß?se µ?a ap? t?? s??e??e??
• S??????e t? ???µ? sf??µat?? µe ta ded?µ??a
  e??????
• ?? ße?t???eta?, sß??eta?

16
?at??????p???s? µe ?a???e? ?atas?e??
?µµes? ????d?? ?p? ???t?a ?p?fas?? se ?a???e?
??a? ?a???a? ??a ???e µ???p?t? ap? t? ???a se
f???? ???e ?e????? ?????sµa-t?µ? st? µ???p?t?
ap?te?e? ??a ??? st? s??e??? ?a? t? f???? af???
t?? ???s? (RHS)

• ?a???e? aµ??ßa?a ap???e??µe??? ?a? e?a?t??t????
• ?? s????? ?a????? pe????e? ?s? p????f???a
  pe????e? ?a? t? d??t??

17
?at??????p???s? µe ?a???e? ?atas?e??
?µµes? ????d?? ?p? ???t?a ?p?fas?? se ?a???e?
P
No
Yes
Rule Set
Q
R
-
r1 (PNo,QNo) gt
No
No
Yes
Yes
r2 (PNo,QYes) gt
-


Q
r3 (PYes,RNo) gt
r4 (PYes,RYes,QNo) gt -
No
Yes
r5 (PYes,RYes,QYes) gt
-

18
?at??????p???s? µe ?a???e? ?atas?e??
?? ?a???e? µp??e? ?a ap??p??????? (apa???f?
??p???? ???? st? LHS a? de? a????e? p??? t? ?????)
??????? ?a???a? (RefundNo) ?
(StatusMarried) ? No ?p??p???µ???? ?a???a?
(StatusMarried) ? No
19
?at??????p???s? µe ?a???e? ?atas?e??

• ?? ???e? ap??p???s? (???deµa)
• ?? ?a???e? de? e??a? p?a aµ??ßa?a ap???e??µe???
• ?? ?a???e? de? e??a? p?a e?a?t??t????

20
?at??????p???t?? ???t???te??? Ge?t??a
21
?at??????p???t?? ßas?sµ???? se St??µ??t?pa
????? st??µ?? ?at??????p???s? ßas?sµ??? se d??
ß?µata ??µa 1 Induction Step ?atas?e??
???t???? ??µa 2 Deduction Step ?fa?µ??? t??
µ??t???? ??a ??e??? pa?ade??µ?t??
Eager Learners vs Lazy Learners p? Instance Based
Classifiers (?at??????p???t?? ßas?sµ???? se
st??µ??t?pa) ??? ?atas?e??se?? µ??t??? a? de
??e?aste?
22
?at??????p???t?? ßas?sµ???? se St??µ??t?pa

• ?p????e?se t?? e???af?? t?? s?????? e?pa?de?s??
• ???s?µ?p???se t?? ap????e?µ??e? e???af?? ??a t??
  e?t?µ?s? t?? ???s?? t?? ???? pe??pt?se??

23
?at??????p???t?? ßas?sµ???? se St??µ??t?pa

• ?a?ade??µata
• Rote-learner
• ??at? (Memorizes) ??? t? s????? t?? ded?µ????
  e?pa?de?s?? ?a? ta????µe? µ?a e???af? a?
  ta?????e? p????? µe ??p??? ap? ta ded?µ??a
  e?pa?de?s??
• Nearest neighbor ???t???te??? Ge?t??a?
• ???s? t?? k ???t???te??? closest s?µe???
  (nearest neighbors) ??a t?? ?at??????p???s?

24
?at??????p???t?? ???t???te??? Ge?t??a
k-???t???te??? ?e?t??e? µ?a? e???af?? x e??a?
ta s?µe?a p?? ????? t?? k-?st? µ????te?? ap?stas?
ap? t? x
25
?at??????p???t?? ???t???te??? Ge?t??a

• Basic idea If it walks like a duck, quacks like
  a duck, then its probably a duck

26
?at??????p???t?? ???t???te??? Ge?t??a

• G?a ?a ?at??????p????e? µ?a ????st? e???af?
• ?p?????sµ?? t?? ap?stas?? ap? t?? e???af?? t??
  s??????
• ???es? t?? k ???t???te??? ?e?t????
• ???s? t?? ???se?? t?? ???t???te??? ?e?t???? ??a
  t?? ?a????sµ? t?? ???s?? t?? ????st?? e???af?? -
  p.?., µe ß?s? t?? p?e????f?a (majority vote)

27
?at??????p???t?? ???t???te??? Ge?t??a

• ??e???eta?
• ?? s????? t?? ap????e?µ???? e???af??
• Distance Metric ?et???? ap?stas?? ??a ?a
  ?p?????s??µe t?? ap?stas? µeta?? e???af??
• ??? t?µ? t?? k, d??ad? t?? a???µ? t??
  ???t???te??? ?e?t???? p?? p??pe? ?a a?a???????

28
?at??????p???t?? ???t???te??? Ge?t??a

• ?p?stas? µeta?? e???af??
• ?? e???e?de?a ap?stas?
• ?a????sµ?? t????
• ?p?? t? p?e????f??? ???s?
• ????? se ???e ??f? µe ß?s? t?? ap?stas?
• weight factor, w 1/d2

29
?at??????p???t?? ???t???te??? Ge?t??a

• ?p????? t?? t?µ?? t?? k
• k p??? µ????, e?a?s??s?a sta s?µe?a ????ß??
• k p??? µe????, ? ?e?t???? µp??e? ?a pe????e?
  s?µe?a ap? ???e? ???se??
• s???? k sqr(n), ?p?? n t? µ??e??? t?? s??????
  e?pa?de?s??, se eµp????? s?st?µata, s????,
  default, k10

30
?at??????p???t?? ???t???te??? Ge?t??a

• T?µata ???µ???s??
• ?a ?????sµata ?s?? p??pe? ?a ???µa?????? ?ste ??
  ap?st?se?? ?a µ?? ????a??????? ap? ??p???
  ?????sµa
• ?a??de??µa
• ???? µp??e? ?a d?af??e? ap? 1.5m se 1.8m
• t? ß???? µp??e? ?a d?af??e? ap? 90lb se 300lb
• t? e?s?d?µa µp??e? ?a d?af??e? ap? 10Kse 1M

• ?e? ?atas?e???eta? µ??t???, µe???? ??st?? ??a
  t?? efa?µ??? t?? ?at??????p???s??
• ?????? d?ast?se?? (?at??a t?? d?ast?se??)
• T???ß? (e??tt?s? µ?s? k-?e?t????)

31
?at??????p???t?? ???t???te??? Ge?t??a

• e?et????? ?a? µ? ??aµµ???? pe??????
• t? ap?t??esµa de? ???eta? ?µesa ?ata???t?
  (st????eta? µ??? st?? a??? t?? t?p???t?ta?)

32
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a

• ??a d?µ? ??a e??t?µata d?ast?µat?? st? R2

• ???????µ??
• ?p??e?e ? t? x ? t? y s??teta?µ??? (e?a????)
• ?p??e?e t? d??µes? (a?t? ????e? µ?a ??????t?a ?
  ???et? ??aµµ?)
• ??ad??µ??? ???s?

33
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a
34
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a
35
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a
36
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a
37
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a
38
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a
39
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a
?e????? t?? u st? ?p?d??t?? µe ???a t? u ??a ta
µa??a s?µe?a
40
?at??????p???t?? ???t???te??? Ge?t??a
2-d??stata kd-d??t?a

• ??a d?µ? ??a e??t?µata d?ast?µat?? st? R2

• ?a?????µe ??a d?ad??? d??t??
• ???e??? O(n)
• ????? O(logn)
• ?????? ?atas?e??? O(nlogn)

?p??tas? ??a pa?ap??? ap? 2 d?ast?se??

• ?a??de??µa Binary Space Partitioning

41
?at??????p???t?? Bayes
42
?at??????p???t?? Bayes
X, Y t??a?e? µetaß??t?? ?esµe?µ??? p??a??t?ta
(Conditional probability) Pr(Yy Xx)
?? ?e???µa t?? Bayes
?p? ?????? p??a??t?ta Pr(Xx,Yy) S??s? µeta??
ap? ?????? (joint) ?a? desµe?µ???? (conditional)
p??a??t?ta?
43
?at??????p???t?? Bayes
?? ?e???µa t?? Bayes ?a??de??µa 1

• ?????t?? ?t?
• ?? ??p???? ??e? pe??se? t? µ???µa
  "?????aµµat?sµ?? se C", pe???e? t? µ???µa "??µ??
  ?ed?µ????" µe p??a??t?ta 4/5.
• ? e? t?? p??t???? p??a??t?ta ??p???? ?a pe??se?
  t? µ???µa "?????aµµat?sµ?? se C" e??a? 1/3
• ? e? t?? p??t???? p??a??t?ta ??p???? ?a pe??se?
  t? µ???µa "??µ?? ?ed?µ????" e??a? 2/3

• ??s?? pe????? ?a? ta d?? µa??µata
• ?? ?????µe ?t? ??a? f??t?t?? ??e? pe??se? t?
  µ???µa "??µ?? ?ed?µ????" p??a e??a? ? p??a??t?ta
  ?a ??e? pe??se? t? µ???µa "?????aµµat?sµ?? se C"

44
?at??????p???t?? Bayes
?? ?e???µa t?? Bayes ?a??de??µa 2

• ?st? 2 ?µ?de?, ? ?µ?da 0 ?a? ? ?µ?da 1
• ? ?µ?da 0 ???? st? 65 t?? µeta?? t??? a?????
• ?p? ta pa????d?a sta ?p??a ????se ? ?µ?da 0, µ???
  t? 30 ????a? st?? ?d?a t?? ?µ?da? 1
• 75 t?? ????? t?? ?µ?da? 1 ?????ta? st?? ?d?a t??

• ?? ? ?µ?da 1 a?aµ??eta? ?a f????e??se? t?? ?µ?da
  0 st?? ep?µe?? a???a, p??a ?µ?da eµfa???eta? ??
  p??a??te?? ????t??a

45
?at??????p???t?? Bayes
??? µp????µe ?a ???s?µ?p???s??µe a?t? t? ?e???µa
??a t? p??ß??µa t?? ?at??????p???s??
46
?at??????p???t?? Bayes
X s????? t?? ?????sµ?t?? Y ? µetaß??t? t??
???s?? (?at?????a?) Y e?a?t?ta? ap? t? X µe µ?
?tete?µ???st??? t??p? (non-determininstic)
P(YX) Posterior probability (e? t??
?st????) P(Y) Prior probability (e? t??
p??t????)
X(Home OwnerNo, Marital StatusMarried,
AnnualIncome120K)
?p?????se Pr(YesX), Pr(NoX) ep??e?e No ?
Yes, a?????a µe p??? ??e? t? µe?a??te?? p??a??t?ta
??? ?a ?p?????s??µe a?t?? t?? p??a??t?te?
47
?at??????p???t?? Bayes
F?s? ??pa?de?s?? ??µ???s? t?? e? t?? ?st????
p??a??t?t?? Pr(YX) ??a ???e s??d?asµ? t?? X ?a?
Y ßas?sµ??? sta ded?µ??a e?pa?de?s?? F?s?
?fa?µ???? G?a ???e e???af? e?????? X, ?p?????se
t?? ???s? Y p?? µe??st?p??e? t?? e? t?? ?st????
p??a??t?ta Pr(YX) d??ad?, t?? p?? p??a??
???s? µe ß?s? ta ded?µ??a e??????
P(X) e??a? sta?e?? ?a? µp????µe ?a t?? a????s??µe
(µa?t???a - evidence) P(Y) e?t?µ?te e????a ap?
ta ded?µ??a e?s?d??, e??a? t? p?s?st? t??
ded?µ???? e?pa?de?s?? p?? a?????? st?? ???s? Y
(e? t?? p??t???? p??a??t?ta) Pr(XY)?
48
?at??????p???t?? Bayes
?p?????sµ?? t?? e?a?t?µe??? ap? t? ?at?????a
p??a??t?ta? Pr(XY)

• ?p?????? d?? ßas???? µ???d??
• ?p??????
• ???t?? pep????s??

Ta d??µe t?? p??t? µ???d?
49
?at??????p???t?? Bayes
?a??de??µa 1 ?????sµa (µetaß??t?) µe ?at????????
t?µ??
?? ??p???? e??a? ??aµ??, e??a? a???ast?? ? ????
50
?at??????p???t?? Bayes ??pa?de?s?
Categorical attribute Xi Pr(Xi xiYy) p?s?st?
t?? ded?µ???? e?pa?de?s?? t?? ???s?? y p?? ?????
t?µ? xi st? i-?st? ?????sµa
P(homeOwner yesNo) 3/7 P(MaritalStatus
Single Yes) 2/3

1. ?? ???eta? ?ta? ????µe pa?ap??? ap? ??a
   ?????sµata
2. ?? ???eta? ?ta? ta ?????sµata pa?????? s??e???
   t?µ??

51
?at??????p???t?? Bayes ??pa?de?s?
?a??de??µa
?? ??p???? e??a? ??aµ?? ?a? 35 ??????, e??a?
a???ast?? ? ????
?e ß?s? ta P(??aµ??, 35 ?a?) ?(??aµ??, 35 ???)
52
?at??????p???t?? Bayes
?e??ss?te?a ap? ??a ?????sµata (µetaß??t??)
S????? X X1,,Xd ap? d ?????sµata Conditional
independence (?p? s?????? a?e?a?t?s?a) X e??a?
?p? s?????? a?e???t?t? t?? Y, d????t?? t?? Z a?
P(XY,Z) P(XZ) P(X,YZ) P(XZ) P(YZ)
53
?at??????p???t?? Bayes
S????? X X1,,Xd ap? d ?????sµata
54
?at??????p???t?? Bayes ??pa?de?s?
?e??ss?te?a ap? ??a ?????sµata (µetaß??t??)
?a??de??µa
?? ??p???? e??a? ??aµ?? ?a? 35 ??????, e??a?
a???ast?? ? ????
55
?at??????p???t?? Bayes
56
?at??????p???t?? Bayes
?a??de??µa
A ?????sµata M mammals N non-mammals
P(AM)P(M) gt P(AN)P(N) gt Mammals
57
?at??????p???t?? Bayes
??t?µ?s? t?? ?p? S?????? ???a??t?t?? ??a S??e??
G????sµata

• ??a???t?p???s? (discretization)
• ???????µe se d?ast?µata ?a? ? e?t?µ?s? ???eta? µe
  ß?s? t?? a?a????a t?? e???af?? e?pa?de?s?? st?
  a?t?st???? d??st?µa
• p???? d?ast?µata -gt ???e? e???af?? e?pa?de?s??
• ???a d?ast?µata -gt p??a??? ?a s??a????????
  e???af?? p?? a?????? se d?af??et???? ?at?????e?

58
?at??????p???t?? Bayes
??t?µ?s? t?? ?p? S?????? ???a??t?t?? ??a S??e??
G????sµata
???s? ??p??a? ?ata??µ?? ?p???t??µe µ?a
s???e???µ??? µ??f? ?ata??µ?? p??a??t?t?? S??????
Gauss (?a??????) ?ata??µ? ?a?a?t????eta? ap? d??
pa?aµ?t???? µ?s? (µ) d?a??µa?s? (s2)
59
?at??????p???t?? Bayes
??t?µ?s? t?? ?p? S?????? ???a??t?t?? ??a S??e??
G????sµata
To µij e??a? t? µ?s? ??a ??a ta ded?µ??a
e?pa?de?s?? t?? ?at?????a? (???s??) yi ?µ??a
e?t?µ?ta? ?a? ? d?a??µa?s?
60
?at??????p???t?? Bayes
?a?????? ?ata??µ? (Income, ClassNo) sample
mean 110 sample variance 2975
61
?at??????p???t?? Bayes
???s? ?a??????? ?ata??µ??
t? e ?a??????p??e?ta? ?p?te µp????µe ?a
???s?µ?p???s??µe t?? p??????µe?? e??s?s?
62
?at??????p???t?? Bayes
???s? ?a??????? ?ata??µ??
63
?at??????p???t?? Bayes
X (HomeOwner No, MaritalStatus Married,
Income120K) ???pe? ?a ?p?????ste? Pr(YX),
d??ad? Pr(Y)xPr(XY) But P(XY) is Y
No P(HONoNo) x P(MSMarriedNo) x
P(Inc120KNo) 4/7 x 4/7 x 0.0072
0.0024 YYes P(HONoYes) x P(MSMarriedYes) x
P(Inc120KYes) 1 x 0 x 1.2x10-9 0
64
?at??????p???t?? Bayes
X (HomeOwner No, MaritalStatus Married,
Income120K) Pr(XY Yes) e??a? 0! ?pe?d? ta
de??µata e?pa?de?s?? µp??e? ?a µ?? ?a??pt??? ??e?
t?? ?at?????e? -gt ??ad??as?a ??????s??
nc ? a???µ?? t?? e???af?? e?pa?de?s?? t?? ???s??
yj p?? pa?????? t?? t?µ? xi n s???????? a???µ??
e???af?? t?? ???s?? yj m µ?a pa??µet??? p??
?a?e?ta? ?s?d??aµ? µ??e??? de??µat?? (equivalent
sample size) (?s????pe? t?? e? t?? ?st???? (nc/n)
?a? t?? e? t?? p??t???? (p) p??a??t?ta? p
µ?a pa??µet??? p?? ?a?????e? ? ???st?? (? e? t??
p??t???? p??a??t?ta eµf???s?? t?? t?µ?? xi ??a t?
?????sµa Xi µeta?? t?? e???af?? t?? ???s?? yi)
65
?at??????p???t?? Bayes

• ????? se µ? s?et??? ?????sµata - ?? t? Xi de?
  e??a? s?et??? (irrelevant), P(XiY) e??a? s?ed??
  uniform
• ???ß??µa ?ta? ?p?????? e?a?t?se?? µeta?? t??
  ?????sµ?t?? (µetaß??t??) (correlated attributes)
• ?a?? ???µ???s? se µe???? ???? ded?µ????, µ?a
  ap?? a?????s? t?? ded?µ???? e?pa?de?s??
• ?a?? a???? st? ????ß?, ??at? ta s?µe?a ????ß??
  e??µa?????ta?
• ?e? ep??e????ta? ap? t?µ?? p?? ?e?p??? ??at?
  a?t?? µp????µe ?a t?? a????s??µe

66
???a??? ??a??sµ?t?? ?p?st?????? (Support Vector
Machines)
67
?at??????p???t?? SVM

• ??e? ??a ??aµµ??? ?pe?-ep?ped? (???? ap?fas??)
  p?? ?a d?a?????e? ta ded?µ??a

68
?at??????p???t?? SVM

• ??a p??a?? ??s?

69
?at??????p???t?? SVM

• ??a a??µa p??a?? ??s?

70
?at??????p???t?? SVM

• ???e? p??a??? ??se??

71
?at??????p???t?? SVM

• ???a e??a? ?a??te?? ? B1 ? ? B2?
• ??? ????eta? t? ?a??te?? ?e p??? ???t????

72
?at??????p???t?? SVM

• ?? ?pe?-ep?ped? p?? µe??st?p??e? t? pe???????
  (margin) gt t? B1 e??a? ?a??te?? ap? t? B2
  (????t???t?ta)

73
G?aµµ??? SVM
?at??????p???t?? SVM
1 ???s? ?????? -1 ???s? tet??????
74
?at??????p???t?? SVM

• T????µe ?a µe??st?p???s??µe
• ?? ?p??? e??a? ?s?d??aµ? µe t? ?a
  e?a??st?p???s??µe
• ?e ß?s? t??? pa?a??t? pe?????sµ??? (constraints)
• ??a p??ß??µa ße?t?st?p???s?? pe?????sµ??
  (constrained optimization problem)
• ????µ?t???? µ???d?? ??a t?? ep???s? t??

75
?at??????p???t?? SVM

• ?? s?µßa??e? a? t? p??ß??µa de? e??a? ??aµµ????
  d?a????s?µ?

76
?at??????p???t?? SVM

• ??sa???? ?a?a??? µetaß??t?? (slack variables)
• ??a??st?p???s?
• ?e t??? pe?????sµ???

77
?at??????p???t?? SVM