Probability Overview Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

머신러닝의학습방법들 - Gradient descent based learning - Probability theory based learning - Information theory based learning - Distance similarity based learning

Probability - 이산형값 count(event X) P (X) = count(all Event) - 연속형값 P ( 1 <x<1) Z 1 1 f(x) dx =1 Source: https://goo.gl/d9vcsl Source: https://goo.gl/dvnsh2

Basic concepts of probability 0 apple P (E) apple 1 P (S) = NX i=1 P (E i ) = 1 if all E i are independent P (A \ B) P (A [ B) P (A c )=1 P (A)

Conditional probability A B P (A B) = P (A \ B) P (B) A \ B

Conditional probability P (A B) = P (A \ B) P (B) P (A) = {set of odd number} P (B) = {less than 4 in a dice} P (B A) = P (A \ B) P (A) A B A \ B

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Bayes s Theorem Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

Bayes s theorem - 경험에의한확률의업데이트 - 사전확률 (given) 에서사건발생을통해사후확률로 - 빈도주의 vs. 베이즈주의 - 객관적확률은존재하지않는다!

Queen card game

Probability updated 1 3 1 3 1 3 3 30 8 30 19 30

Probability updated 3 30 8 30 19 30

Bayes s theorem P (A B) = P (A \ B) P (B) P (B A) = P (A \ B) P (A) P (A \ B) =P (B)P (A B) =P (A)P (B A) P (A B) = P (A \ B) P (B) = P (A)P (B A) P (B)

Cookie Quiz 쿠키두그릇이있다고한다. 첫번째그릇에는바닐라쿠키 30개와초콜렛쿠키 10개가있고, 두번째그릇에는각쿠키가 20개씩있다. 임의쿠키를집었는데해당쿠키가바닐라쿠키이다. 이쿠키가그릇 1에서나왔을확률은? Source: https://goo.gl/gzopzy

Cookie Quiz 쿠키두그릇이있다고한다. 첫번째그릇에는바닐라쿠키 30 개와초콜렛쿠키 10 개가있고, 두번째그릇에는각 쿠키가 20 개씩있다. 임의쿠키를집었는데해당쿠키가바닐라쿠키이다. 이쿠키가그릇 1 에서나왔을확률은? P (Choco) P (A B) = P (A \ B) P (B) = P (A)P (B A) P (B) P (Vanilla) P (B1) P (B2) Source: https://goo.gl/gzopzy

<latexit sha1_base64="sud+tka9qbtmtepj5vavo7nckmu=">aaacchicbzbps8mwgmbt+w/of1wpxojdwc+jfue9cen32lgcdyotjdrlt7a0lukqjg5xl34vlx5uvporvpltzlyedpobwc/p+74k7xmkjepl299gywv1bx2jufna2t7z3tp3d+5lnapmpbyzwlqcjamjnhikkkzaisaochhpbsobab35qiskmb9to4t4eepzglkmlla6jnqrjxhdglewewqem3213ep93lammuvwpguw7ao9e1wgj4cyyov2za9ol8zprljcdenzduxe+rksimjgjqvokkmc8bd1svsjrxgrfjbbzajptnodysz04qro3n8tgyqkhewb7oyqgsjf2tt8r9zovxjhz5qnqsiczx8kuwzvdkexwb4vbcs20ocwopqvea+qtktp8eo6bgdx5wxwtquxvef2rfy7ztmoginwdcraaeegbhrabr7a4be8g1fwzjwzl8a78tfvlrj5zch4i+pzb4jfl0q=</latexit> <latexit sha1_base64="sud+tka9qbtmtepj5vavo7nckmu=">aaacchicbzbps8mwgmbt+w/of1wpxojdwc+jfue9cen32lgcdyotjdrlt7a0lukqjg5xl34vlx5uvporvpltzlyedpobwc/p+74k7xmkjepl299gywv1bx2jufna2t7z3tp3d+5lnapmpbyzwlqcjamjnhikkkzaisaochhpbsobab35qiskmb9to4t4eepzglkmlla6jnqrjxhdglewewqem3213ep93lammuvwpguw7ao9e1wgj4cyyov2za9ol8zprljcdenzduxe+rksimjgjqvokkmc8bd1svsjrxgrfjbbzajptnodysz04qro3n8tgyqkhewb7oyqgsjf2tt8r9zovxjhz5qnqsiczx8kuwzvdkexwb4vbcs20ocwopqvea+qtktp8eo6bgdx5wxwtquxvef2rfy7ztmoginwdcraaeegbhrabr7a4be8g1fwzjwzl8a78tfvlrj5zch4i+pzb4jfl0q=</latexit> <latexit sha1_base64="sud+tka9qbtmtepj5vavo7nckmu=">aaacchicbzbps8mwgmbt+w/of1wpxojdwc+jfue9cen32lgcdyotjdrlt7a0lukqjg5xl34vlx5uvporvpltzlyedpobwc/p+74k7xmkjepl299gywv1bx2jufna2t7z3tp3d+5lnapmpbyzwlqcjamjnhikkkzaisaochhpbsobab35qiskmb9to4t4eepzglkmlla6jnqrjxhdglewewqem3213ep93lammuvwpguw7ao9e1wgj4cyyov2za9ol8zprljcdenzduxe+rksimjgjqvokkmc8bd1svsjrxgrfjbbzajptnodysz04qro3n8tgyqkhewb7oyqgsjf2tt8r9zovxjhz5qnqsiczx8kuwzvdkexwb4vbcs20ocwopqvea+qtktp8eo6bgdx5wxwtquxvef2rfy7ztmoginwdcraaeegbhrabr7a4be8g1fwzjwzl8a78tfvlrj5zch4i+pzb4jfl0q=</latexit> <latexit sha1_base64="sud+tka9qbtmtepj5vavo7nckmu=">aaacchicbzbps8mwgmbt+w/of1wpxojdwc+jfue9cen32lgcdyotjdrlt7a0lukqjg5xl34vlx5uvporvpltzlyedpobwc/p+74k7xmkjepl299gywv1bx2jufna2t7z3tp3d+5lnapmpbyzwlqcjamjnhikkkzaisaochhpbsobab35qiskmb9to4t4eepzglkmlla6jnqrjxhdglewewqem3213ep93lammuvwpguw7ao9e1wgj4cyyov2za9ol8zprljcdenzduxe+rksimjgjqvokkmc8bd1svsjrxgrfjbbzajptnodysz04qro3n8tgyqkhewb7oyqgsjf2tt8r9zovxjhz5qnqsiczx8kuwzvdkexwb4vbcs20ocwopqvea+qtktp8eo6bgdx5wxwtquxvef2rfy7ztmoginwdcraaeegbhrabr7a4be8g1fwzjwzl8a78tfvlrj5zch4i+pzb4jfl0q=</latexit> Bayes s theorem H is Class 사전확률우도사후확률 P (H)P (D H) P (H D) = P (D) D is Data 데이터가발생할확률 (Evidence)

Bayes s theorem P (H D) = P (C)P (D H) P (D) P (A 1 \ B)+P (A 2 \ B)+P (A 3 \ B) P (B) =P (A 1 )P (B \ A 1 )+P (A 2 )P (B \ A 2 )+P (A 3 )P (B \ A 3 ) P (A \ B) =P (B)P (A B) =P (A)P (B A)

Example 공 1 무작위로 1 개나오는다음과같은완구가있다. 나온공이 큰공 일때, 검은색일확률은? Source: https://goo.gl/gzopzy

Example P (H D) = P (C)P (D H) P (D) P (B) =P (A 1 )P (B \ A 1 )+P (A 2 )P (B \ A 2 )+P (A 3 )P (B \ A 3 ) Source: https://goo.gl/gzopzy

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Simple Bayes Classifier Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

Viagra 스팸필터기 - Viagra 라는단어의유무를통해스팸여부확인 - Viagra 단어가들어가면무조건스팸? - 어느정도확률로스팸이라고해야할까?

Viagra 스팸필터기 number viagra spam number viagra spam 1 1 1 11 1 0 2 0 0 12 0 0 3 0 0 13 0 0 4 0 0 14 1 0 5 0 0 15 0 0 6 0 0 16 0 0 7 0 1 17 0 0 8 0 0 18 0 1 9 1 1 19 0 1 10 1 0 20 1 1

Viagra 스팸필터기

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NB Classifier Overview Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

제대로된스팸필터기를만들어보자 - Viagra 단어외에영향을주는단어들은? - 오히려스팸을제외해주는단어는어떻게찾지? - 한번에여러단어들을고려하는필터기를만들자

Feature 의확장 P (spam viagra) P (spam viagra, hello, lucky, marketing...) 변수가많을때, 조건부확률의변화

Multivariate multiplication rule P (Y X 1,X 2 )= P (Y \ X 1 \ X 2 ) P (X 1 \ X 2 ) P (Y \ X 1 \ X 2 )=P (Y X 1,X 2 )P (X 1 \ X 2 ) P (X 1,X 2,X 3,...X n ) = P (X 1 )P (X 2 X 1 )P (X 3 X 1,X 2 )...P(X n X 1...X x 1 )

Problems - 계산이어려워짐 - Feature 의차원이증가하면 Sparse Vector 가생성 à 확률이 0 이되는값이늘어남

Naïve Bayes Classifier - 복잡하게하지말고단순 (naïve) 하게해결하자 - 각변수의관계가독립임을가정 - 계산이용이해지고, 성능이생각보다좋음

Joint Probability P (A \ B) =P (A)P (B) if A and B are independent P (Y X 1 \ X 2 )= P (Y )P (X 1 \ X 2 Y ) P (X 1 \ X 2 ) P (Y )P (X 1 Y )P (X 2 Y ) P (X 1 )P (X 2 )

Naïve Bayes Classifier P (Y X 1 \ X 2 )= P (Y )P (X 1 \ X 2 Y ) P (X 1 \ X 2 ) = P (Y )P (X 1 Y )P (X 2 Y ) P (X 1 )P (X 2 ) P (Y c X 1,...,X n )= P (Y c ) n Q i=1 nq i=1 P (X i Y c ) P (X i ) Y c is a label

Issues - 너무많은확률값 à 0 에수렴하게되는문제 - 곱하지말고더하자 à log ny log{p (Y c ) P (X i Y c )} = log P (Y c )+ i=1 nx i=1 log P (X i Y c ) P (Y c X 1,...,X n )= P (Y c ) n Q i=1 nq i=1 P (X i Y c ) P (X i ) Y c is a label

Issues - 확률이 0 인변수들이존재함 à 전체값 0 - 작게나마확률이나올수있도록변경 à 스무딩 P (X Y )= count(x \ Y )+k count(y )+(k number of class ) log{p (Y c ) ny i=1 P (X i Y c )} = log P (Y c )+ nx log P (X i Y c ) i=1

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NB Classifier Implementation Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

Dataset German Credit - 대출사기인가? 아닌가를예측하는문제 - 데이터를 NB 에맞도록간단하게변환 - Binary 데이터들로이루어진대출사기데이터

Preprocessing One-Hot Encoding

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Modelling Y 의 Index P(X $ Y ' )

Classifier P(Y=1 X) 의확률과 P(Y=0 X) 의확률비교

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Multinomial NB Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

Multinomial Naïve Bayes - X 값이 Binary 가아니라 1 이상의값을가지는문제 - 일반적으로 Text 문제를분류할때많이쓰임 - 단어의존재유무가아닌단어의출현횟수 Feature 로

Text 의 Feature 표현? 문자 è Feature

문자를 Vector 로 One-hot Encoding 하나의단어를 Vector 의 Index 로인식, 단어존재시 1 없으면 0

Bag of words 단어별로인덱스를부여해서 한문장 ( 또는문서 ) 의단어의개수를 Vector 로표현

다시돌아가서..

Multinomial Naïve Bayes P (Y c X 1,...,X n )= P (Y c ) n Q i=1 nq i=1 P (X i Y c ) P (X i ) 기본식!! Y c is a label

Multinomial Naïve Bayes P (Y c X 1,...,X n )= P (Y c ) n Q i=1 nq i=1 P (X i Y c ) P (X i ) Y c is a label Likelihood 만바뀜

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sha1_base64="vhpckempjfbbycnxptzebx4flfk=">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</latexit> <latexit sha1_base64="vhpckempjfbbycnxptzebx4flfk=">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</latexit> <latexit sha1_base64="vhpckempjfbbycnxptzebx4flfk=">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</latexit> Multinomial Naïve Bayes - 식계산하는방식이다름 ny P (X i Y c ) P (X i Y c )= i=1 P tf(xi,d2 Y c )+ P Nd2Yc + V x_i: A word from the feature vector x of a particular sample. tf(xi,d y_c): The sum of raw term frequencies of word x_i from all documents in the training sample that belong to class y_c. Nd y_c: The sum of all term frequencies in the training dataset for class y_c. α: An additive smoothing parameter (α=1α=1 for Laplace smoothing). V: The size of the vocabulary (number of different words in the training set). http://sebastianraschka.com/articles/2014_naive_bayes_1.html

<latexit sha1_base64="vhpckempjfbbycnxptzebx4flfk=">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</latexit> <latexit sha1_base64="vhpckempjfbbycnxptzebx4flfk=">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</latexit> <latexit sha1_base64="vhpckempjfbbycnxptzebx4flfk=">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</latexit> <latexit sha1_base64="vhpckempjfbbycnxptzebx4flfk=">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</latexit> Multinomial Naïve Bayes P (X i Y c )= P tf(xi,d2 Y c )+ P Nd2Yc + V P (Y c X 1,...,X n )= P (Y c ) n Q i=1 nq i=1 P (X i Y c ) P (X i ) http://slideplayer.com/slide/10998986/

Multinomial Naïve Bayes P (Y c X 1,...,X n )= P (Y c ) n Q i=1 P (X i Y c ) nq P (X i ) i=1 http://slideplayer.com/slide/10998986/

Human knowledge belongs to the world.

Gaussian NB Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

Gaussian Naïve Bayes - Category 데이터가아닌경우에 NB 의적용 - Continuous 데이터의적용을위해 y의분포를정규분포 (gaussian) 으로가정함 - 확률밀도함수상의해당값 x 가나올확률로 NB를구현함

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sha1_base64="lwamupo1efsfsmwyisfcbrsynwi=">aaab8xicbvbns8naen3ur1q/qh69lbbbg5rebpvw9okxgrgfjjtndtmu3c2g3ylqqn+gfw8qxv033vw3btsctpxbwoo9gwbmxzngblz326msrk6tb1q3a1vbo7t79f2dr6nytzlplvc6gxpdbe+zdxwe62aaerkl1olht1o/88s04sp9ghhgikkgku84jwclijt5gq4nh0jsqzfcpjsdxizesrqorltx/wr7iuaspuafmsbw3ayigmjgvlbjlcwnywgdkqelle2jzcyqzidp8ilv+jhr2lykekb+niiingysy9spcqznojcv//ochjkrqobplgnl6xxrkgsmck//x32ugquxtorqze2tma6jjhrssjubgrf48jlxz5vxte/+otg6kdoooin0je6rhy5rc92hnvirrqo9o1f05odz4rw7h/pwilpohki/cd5/acjuklm=</latexit> Gaussian Naïve Bayes P (x i Y c )= 1 q2 exp 2 Yc (xi µ Yc ) 2 2 2 Y c, Y c X i - 특정에대한의평균, 표준편차를에대입 µ,

Human knowledge belongs to the world.

Naïve Bayes with Sklearn Naive Bayes Classifier Director of TEAMLAB Sungchul Choi

CountVectorizer in Scikit-learn - 문서에서 Bag of Words Vector 를뽑아주는 class http://scikitlearn.org/stable/modules/generated/sklearn.feature_extr action.text.countvectorizer.html

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Multinomial Naïve Bayes

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