Naive Bayes Classifier | Part 4 | Bayes Theorem in Probability — Transcript

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1. 0:00Next, we're going to discuss Bayes
2. 0:01theorem.
3. 0:03I guess
4. 0:04Bayes theorem is a very, very important
5. 0:06theorem in probability. And in fact,
6. 0:08it's a very old theorem, but uh
7. 0:101700s may uh Thomas Bayes made the
8. 0:12theorem.
9. 0:13And this theorem is very applicable. In
10. 0:15fact, statistics make a whole field of
11. 0:17statistics. This is called Bayesian
12. 0:19statistics or Bayesian thinking.
13. 0:21Okay? So, it's a great theorem, to be
14. 0:23honest. And the best part is it's very
15. 0:25easy to understand. It's very simple.
16. 0:27And it's very applicable. Okay? In fact,
17. 0:29if you remember
18. 0:31Our algorithm is called Naive Bayes.
19. 0:33Naive
20. 0:34Bayes. So, to be honest
21. 0:39The Bayes theorem implementation is We
22. 0:41just take an assumption on the Bayes
23. 0:44theorem and we get our algorithm, Naive
24. 0:46Bayes.
25. 0:49Let's understand what Bayes theorem is.
26. 0:52Okay? So, if there are two events, A and
27. 0:55B
28. 0:56According to Bayes theorem
29. 0:59Probability of A given B is equal to
30. 1:03probability of B given A multiplied by
31. 1:07probability of A divided by probability
32. 1:10of
33. 1:11B.
34. 1:13Obviously, given
35. 1:16P of B
36. 1:17is not equal to zero.
37. 1:20This is what Bayes theorem is. Okay? Or
38. 1:23You have to in terms of which one is
39. 1:24that. I'll quickly write it down. This
40. 1:27is known as the posterior probability.
41. 1:32This is known as the likelihood.
42. 1:37This is known as
43. 1:39the prior.
44. 1:41And this is known as the evidence.
45. 1:45Okay? Uh In general, it's not so good to
46. 1:48be honest.
47. 1:50It's not that important to remember
48. 1:52these things.
49. 1:55Uh
50. 1:57Now, let's do one thing.
51. 1:58Uh it's about discussion.
52. 2:02But before that, let's actually prove
53. 2:05Bayes' theorem.
54. 2:09So,
55. 2:10you already know by the definition of
56. 2:12conditional probability, P of A given B
57. 2:17is actually equal to P of A intersection
58. 2:21B divided by P of
59. 2:24P. Right? This is conditional
60. 2:26probability.
61. 2:29Uh
62. 2:30you know this,
63. 2:31uh that A intersection B is equal to B
64. 2:34intersection A.
65. 2:38A B. This is A intersection B. Basic set
66. 2:41theory is going to come out of it like A
67. 2:43intersection B will be equal to B
68. 2:45intersection A.
69. 2:46So, what if
70. 2:49P of B given A?
71. 2:52This would be equal to P of
72. 2:54uh B intersection A divided by P of A.
73. 3:00Right? And this could be written as P of
74. 3:03A intersection B divided by P of A.
75. 3:08Right? Replaced that here.
76. 3:10Uh but just give me a second to
77. 3:12rearrange the formula.
78. 3:14P of A intersection B would become P of
79. 3:18B given A multiplied by P of A.
80. 3:21Rearranged that here.
81. 3:23Now, this is equation one.
82. 3:25This is equation two.
83. 3:30P of A given B would become P of B given
84. 3:35A multiplied by P of A divided by P of
85. 3:39B.
86. 3:40And this is
87. 3:42Bayes' theorem.
88. 3:44What is simple proof conditional
89. 3:45probability of the rearrangement here?
90. 3:50Now, see Bayes' theorem is super
91. 3:52important or the naive Bayes' formula is
92. 3:54here. with an example of maths and
93. 3:56probability
94. 3:58is just meaning these are just symbols.
95. 4:00But just actual problem solve let's say
96. 4:03email spam classifier
97. 4:05you will actually notice behind the
98. 4:06scenes Bayes theorem is just working. So
99. 4:09just be patient. In the next video what
100. 4:12we are going to do is we are going to
101. 4:14solve a problem using Bayes theorem. So
102. 4:17the real world problem
103. 4:18or then you will understand things a lot
104. 4:21better.
105. 4:21Okay, so thanks for watching.