C3_W1 Naive Bayes Model

Course Q&A Math for Machine Learning Probability & Statistics for Machine Learning &...
1

Hi in video about naive Bayes model
I am lost. What is advantage of assumption of independence?
How is computing P(C & V given Q) mathematically harder if we did not assume independent?

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image
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It lets you do this → image

You know how the lecture does it with the independence assumption, but how would you do it if you can’t use this → image ? It is possible to do it, but I want to hear it from you so that I know we are on the same page.

Cheers,
Raymond

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perhaps P(LUW|SP)=P(L|SP)U P(W|SP)

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Hello @Hassan_Mohamed6,

Not really.

I am not a mentor for this course, but I took the liberty to quickly go through the table of content for this course, and I think you might want to review some part of the course in the following sequence to finally come up with an answer yourself for your original question

  1. Week 2 Lesson 2 videos Joint Distribution (Discrete) - Part 1 & Joint Distribution (Discrete) - Part 2.
    They will walk through an example of how to calculate P( A ∩ B ) when there is indepedence assumption and when there is no such assumption.

  2. After that, you will know how to do it in the discrete case, and start to think that “hey, I don’t think it is much harder, still just counting work”.

  3. Then, please go through the same lesson’s videos Joint Distribution (Continuous) and Multivariate Gaussian Distribution.
    You will see how the maths there are simplified by the independence assumption.

  4. Try to come up with an answer for your own question!

Even though my step 1 wouldn’t necessarily convince you that the independence assumption makes life a lot easier, I still mention that part because the discrete case is used in the lecture that you questioned. So, for continuity, in step 1, you find out first how to compute the lecture’s discrete “P(C & V given Q)” without the independence assumption and judge whether it makes thing easier, then in step 3, you find out the difference in the continuous case. Finally, with the fact that the Navie Bayes Model can work with both discrete and continuous cases, try step 4 which is the most important step for every learner :wink:

Cheers,
Raymond