Slides for this YouTube video https://www.youtube.com/watch?v=Q8l0Vip5YUw

1. Naive Bayes

2. Luis Serrano
Naive Bayes Classifier

3. Bayes Theorem
P(A B) =
P(B A)
P(B A)
P(A)
P(A)+ P(B Ac
)P(Ac
)

4. 3. Bayes Theorem

5. Spam Detector
100 e-mails

6. Spam No spam
Spam Detector
25 75

7. Spam No spam
“Buy”
Spam Detector
25 75

8. Spam No spam
“Buy”
Spam Detector
25 75

9. Spam No spam
“Buy”
Spam Detector
25 75

10. Spam No spam
“Buy”
Spam Detector

11. Spam No spam
“Buy”
Spam Detector
Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?

12. Spam No spam
“Buy”
Spam Detector
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?

13. Spam No spam
“Buy”
Spam Detector
60%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?

14. Spam No spam
“Buy”
Spam Detector
60%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?

15. Spam No spam
“Buy”
Spam Detector
60%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%

16. Spam No spam
“Buy”
Spam Detector
20
60%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%

17. Spam No spam
“Buy”
Spam Detector
20 5
60%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%

18. Spam No spam
“Buy”
Spam Detector
20 580% 20%
60%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%

19. Spam No spam
“Buy”
Spam Detector
20 580% 20%
60%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%

20. Spam No spam
“Buy”
Spam Detector
20 580% 20%
60%
Solution:
80%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%

21. Spam No spam
“Buy”
Spam Detector
20 580% 20%
60%
Solution:
80%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%

22. Spam No spam
“Buy”
Spam Detector
20 580% 20%
60%
Solution:
80%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%
80%

23. Spam No spam
“Buy”
20 580% 20%
60%
Solution:
80%
80%
40%Quiz: If an e-mail
contains the word “buy”,
what is the probability
that it is spam?
100%
80%
Bayes Theorem

24. Spam No spam
Spam Detector

25. Spam No spam
Spam Detector
“Cheap”

26. Spam No spam
Spam Detector
“Cheap”

27. Spam No spam
Spam Detector
“Cheap”

28. Spam No spam
“Cheap”
Bayes Theorem

29. Spam No spam
“Cheap”
Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
Bayes Theorem

30. Spam No spam
“Cheap”
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
Bayes Theorem

31. Spam No spam
“Cheap”
60%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
Bayes Theorem

32. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
Bayes Theorem

33. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
100%
Bayes Theorem

34. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
100%
Bayes Theorem

35. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
100%
Bayes Theorem

36. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
100%
Bayes Theorem

37. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
15
100%
Bayes Theorem

38. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
15 10
100%
Bayes Theorem

39. Spam No spam
“Cheap”
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
15 1060% 40%
100%
Bayes Theorem

40. Spam No spam
“Cheap”
60%
Solution:
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
15 1060% 40%
100%
Bayes Theorem

41. Spam No spam
“Cheap”
60%
Solution:
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
15 1060% 40%
100%
Bayes Theorem

42. Spam No spam
“Cheap”
60%
Solution:
60%
80%
40%Quiz: If an e-mail
contains the word
“cheap”, what is the
probability that it is
spam?
15 1060% 40%
100%
60%
Bayes Theorem

43. Spam No spam
Spam Detector
“Buy” and “Cheap”

44. Spam No spam
Spam Detector
“Buy” and “Cheap”

45. Spam No spam
Spam Detector
“Buy” and “Cheap”

46. Spam No spam
Spam Detector
“Buy” and “Cheap”

47. Spam No spam
Spam Detector
“Buy” and “Cheap”

48. Spam No spam
Spam Detector
“Buy” and “Cheap”

49. Spam No spam
Spam Detector
“Buy” and “Cheap”

50. Spam No spam
“Buy” and “Cheap”
Spam Detector

51. Spam No spam
“Buy” and “Cheap”
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
Spam Detector

52. Spam No spam
“Buy” and “Cheap”
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
Spam Detector

53. Spam No spam
“Buy” and “Cheap”
60%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
Spam Detector

54. Spam No spam
“Buy” and “Cheap”
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
Spam Detector

55. Spam No spam
“Buy” and “Cheap”
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

56. Spam No spam
“Buy” and “Cheap”
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

57. Spam No spam
“Buy” and “Cheap”
12
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

58. Spam No spam
“Buy” and “Cheap”
12
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

59. Spam No spam
“Buy” and “Cheap”
012
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

60. Spam No spam
“Buy” and “Cheap”
00%12100%
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

61. Spam No spam
“Buy” and “Cheap”
00%12100%
60%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

62. Spam No spam
“Buy” and “Cheap”
00%12100%
60%
Solution:
100%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

63. Spam No spam
“Buy” and “Cheap”
00%12100%
60%
Solution:
100%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
Spam Detector

64. Spam No spam
“Buy” and “Cheap”
00%12100%
60%
Solution:
100%
80%
40%Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
100%
100% ?
Spam Detector

65. Problem
Spam No spam
“Buy” and “Cheap”

66. Problem
Spam No spam
“Buy” and “Cheap”
12 e-mails

67. Problem
Spam No spam
“Buy” and “Cheap”
12 e-mails 0 e-mails?

68. Solution: Collect more data?

69. Solution: Collect more data?

70. Solution: Collect more data?

71. Spam Detector
Spam No spam
“Buy” and “Cheap”
12 e-mails 0 e-mails?

72. Spam Detector
Spam No spam
“Buy” and “Cheap”
12 e-mails 0 e-mails?
Guess?

73. Spam Detector

74. Spam Detector
100 e-mails

75. Spam Detector
100 e-mails
5 “Buy”

76. Spam Detector
100 e-mails
5 “Buy”

77. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”

78. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”

79. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”
5% “Buy”

80. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”
5% “Buy”
10% “Cheap”

81. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”
5% “Buy”
10% “Cheap”

82. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”
5% “Buy”
10% “Cheap”
0.5% “Buy” and “Cheap”

83. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”
5% “Buy”
10% “Cheap”
0.5% “Buy” and “Cheap”

84. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”
5% “Buy”
10% “Cheap”
0.5% “Buy” and “Cheap”
Independent

85. Spam Detector
100 e-mails
5 “Buy”
10 “Cheap”
5% “Buy”
10% “Cheap”
0.5% “Buy” and “Cheap”
Independent
That’s
naive!

86. Spam
Spam Detector

87. Spam
Spam Detector
25 e-mails

88. Spam
Spam Detector
25 e-mails

89. Spam
Spam Detector
25 e-mails
20 “Buy”

90. Spam
Spam Detector
25 e-mails
20 “Buy” 4/5

91. Spam
Spam Detector
25 e-mails
20 “Buy” 4/5

92. Spam
Spam Detector
25 e-mails
20 “Buy”
15 Cheap
4/5

93. Spam
Spam Detector
25 e-mails
20 “Buy”
15 Cheap
4/5
3/5

94. Spam
Spam Detector
25 e-mails
20 “Buy”
15 Cheap
4/5
3/5

95. Spam
Spam Detector
25 e-mails
20 “Buy”
15 Cheap
4/5
3/5
12/25

96. Spam
Spam Detector
25 e-mails
20 “Buy”
15 Cheap
4/5
3/5
12/25 x 25

97. Spam
Spam Detector
25 e-mails
20 “Buy”
15 Cheap
4/5
3/5
12/25 = 12 “Buy” and “Cheap”x 25

98. Spam
Spam Detector
25 e-mails
20 “Buy”
15 Cheap
4/5
3/5
12/25 = 12 “Buy” and “Cheap”x 25

99. No spam
Spam Detector

100. No spam
Spam Detector
75 e-mails

101. No spam
Spam Detector
75 e-mails
5 “Buy”

102. No spam
Spam Detector
75 e-mails
5 “Buy” 1/15

103. No spam
Spam Detector
75 e-mails
5 “Buy”
10 “Cheap”
1/15

104. No spam
Spam Detector
75 e-mails
5 “Buy”
10 “Cheap”
1/15
2/15

105. No spam
Spam Detector
75 e-mails
5 “Buy”
10 “Cheap”
1/15
2/15
2/225

106. No spam
Spam Detector
75 e-mails
5 “Buy”
10 “Cheap”
1/15
2/15
2/225 x 75

107. No spam
Spam Detector
75 e-mails
5 “Buy”
10 “Cheap”
1/15
2/15
2/225 = 2/3 “Buy” and “Cheap”x 75

108. No spam
Spam Detector
75 e-mails
5 “Buy”
10 “Cheap”
1/15
2/15
2/225 = 2/3 “Buy” and “Cheap”x 75

109. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3

110. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3

111. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12 2/312

112. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/312

113. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/31212 + 2/3
12

114. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
=
38
36
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/31212 + 2/3
12

115. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
=
38
36
= 94.737%
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/31212 + 2/3
12

116. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
=
38
36
= 94.737%
94.737%
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/31212 + 2/3
12

117. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
5.263% =
38
36
= 94.737%
94.737%
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/31212 + 2/3
12

118. Spam No spam
Spam Detector
“Buy” and “Cheap”
12 2/3
5.263% =
38
36
= 94.737%
94.737%
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/31212 + 2/3
12
94.737%

119. Spam No spam
“Buy” and “Cheap”
12 2/3
5.263% =
38
36
= 94.737%
94.737%
Quiz: If an e-mail
contains the words “buy”
and “cheap”, what is the
probability that it is
spam?
12
2/31212 + 2/3
12
Naive Bayes Classifier
94.737%

120. Naive Bayes
Spam No spam

121. Total
Buy
Cheap
Buy & Cheap
Naive Bayes
Spam No spam

122. Total
Buy
Cheap
Buy & Cheap
25
Naive Bayes
Spam No spam

123. Total
Buy
Cheap
Buy & Cheap
25 75
Naive Bayes
Spam No spam

124. Total
Buy
Cheap
Buy & Cheap
25 75
20
Naive Bayes
Spam No spam

125. Total
Buy
Cheap
Buy & Cheap
25 75
20 4/5
Naive Bayes
Spam No spam

126. Total
Buy
Cheap
Buy & Cheap
25 75
20 4/5 5
Naive Bayes
Spam No spam

127. Total
Buy
Cheap
Buy & Cheap
25 75
20 4/5 5 1/15
Naive Bayes
Spam No spam

128. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5 5 1/15
Naive Bayes
Spam No spam

129. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
5 1/15
Naive Bayes
Spam No spam

130. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
5
10
1/15
Naive Bayes
Spam No spam

131. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
5
10
1/15
2/15
Naive Bayes
Spam No spam

132. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
5
10
1/15
2/15
Naive Bayes
Spam No spam

133. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
12/25
5
10
1/15
2/15
Naive Bayes
Spam No spam

134. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
12/25
5
10
1/15
2/15
Naive Bayes
Spam No spam

135. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
12/25
5
10
1/15
2/15
Naive Bayes
Spam No spam

136. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
4/5
3/5
12/25
5
10
1/15
2/15
Naive Bayes
Spam No spam

137. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
1/15
2/15
Naive Bayes
Spam No spam

138. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
1/15
2/15
Naive Bayes
Spam No spam

139. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
1/15
2/15
Naive Bayes
Spam No spam

140. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
1/15
2/15
2/225
Naive Bayes
Spam No spam

141. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
1/15
2/15
2/225
Naive Bayes
Spam No spam

142. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
1/15
2/15
2/225
Naive Bayes
Spam No spam

143. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
1/15
2/15
2/225
Naive Bayes
Spam No spam

144. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
2/3
1/15
2/15
2/225
Naive Bayes
Spam No spam

145. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
2/3
1/15
2/15
2/225
Naive Bayes
Spam No spam

146. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
2/3
1/15
2/15
2/225
Naive Bayes
Spam No spam

147. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
2/3
1/15
2/15
2/225
Naive Bayes
Spam No spam

148. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
2/3
1/15
2/15
2/225
12 + 2/3
12
Naive Bayes
Spam No spam

149. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
2/3
1/15
2/15
2/225
=
38
36
12 + 2/3
12
Naive Bayes
Spam No spam

150. Total
Buy
Cheap
Buy & Cheap
25 75
20
15
12
4/5
3/5
12/25
5
10
2/3
1/15
2/15
2/225
=
38
36
= 94.737%
12 + 2/3
12
Naive Bayes
Spam No spam

151. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
Naive Bayes

152. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5
Naive Bayes

153. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 30
Naive Bayes

154. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30
Naive Bayes

155. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
Naive Bayes

156. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
Naive Bayes

157. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/125
Naive Bayes

158. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/125
Naive Bayes

159. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/125
Naive Bayes

160. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/125
Naive Bayes

161. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125
Naive Bayes

162. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125
Naive Bayes

163. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125
Naive Bayes

164. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 12/3375
Naive Bayes

165. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 12/3375
Naive Bayes

166. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 12/3375
Naive Bayes

167. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 12/3375
Naive Bayes

168. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 4/15 12/3375
Naive Bayes

169. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 4/15 12/3375
Naive Bayes

170. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 4/15 12/3375
Naive Bayes

171. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 12/125 4/15 12/3375
Naive Bayes

172. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
12/5 + 4/15
12/5
12/5 12/125 4/15 12/3375
Naive Bayes

173. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
=
40
36
12/5 + 4/15
12/5
12/5 12/125 4/15 12/3375
Naive Bayes

174. Total
Buy 20 4/5 5 1/15
Cheap 15 3/5 10 2/15
Work
Buy, Cheap,
& Work
Spam No Spam
25 75
5 1/5 30 6/15
=
40
36
= 90%
12/5 + 4/15
12/5
12/5 12/125 4/15 12/3375
Naive Bayes

175. 4. The math

176. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’

177. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =

178. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =

179. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25

180. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25
25
100

181. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25
25
100
20
25

182. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25
25
100
20
25
25
100

183. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25
25
100
20
25
25
100 +

184. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25
25
100
20
25
25
100
5
75+

185. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25
25
100
20
25
25
100
5
75
75
100+

186. Bayes Theorem
P(S B) =
P(B S)
P(B S)
P(S)
P(S)+P(B H)P(H)
S: Spam
H: Ham (not spam)
B: ‘Buy’
P(spam if “Buy”) =
20
25
25
100
20
25
25
100
5
75
75
100+
= 80%

187. Naive Bayes

188. P(“Buy” & “Cheap”) = P(“Buy”) P(“Cheap”)
Naive Bayes

189. P(“Buy” & “Cheap”) = P(“Buy”) P(“Cheap”)
P(B C) = P(B) P(C)
U
Naive Bayes

190. P(“Buy” & “Cheap”) = P(“Buy”) P(“Cheap”)
Naive
P(B C) = P(B) P(C)
U
Naive Bayes

191. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)

192. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =

193. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =

194. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25

195. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
15
25

196. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
15
25

197. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
15
25

198. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
15
25
15
25

199. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
25
100
15
25
15
25

200. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
25
100
+
15
25
15
25

201. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
25
100
5
75
+
15
25
15
25

202. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
25
100
5
75
+
15
25
15
25
10
75

203. Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
25
100
5
75
75
100
+
15
25
15
25
10
75

204. = 94.737%
Naive BayesS: Spam
H: Ham (not spam)
B: ‘Buy’
C: ‘Cheap’
P(S B C) =
P(S)
P(S) + P(H)
U P(B C S)
U
P(B C S)
U
P(B C H)
U
P(B S)P(C S)
P(B S)P(C S) P(B H)P(C H)
P(spam if “Buy” & “Cheap”) =
20
25
25
100
20
25
25
100
5
75
75
100
+
15
25
15
25
10
75

205. Thank you!

206. Thank you!
Subscribe, like,
share, comment
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207. Thank you!
@luis_likes_math
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share, comment
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