When reading the lecture note of 5a classification, I found it says that
"To minimize the probilily of misclassfication, we should chose the decision rule
which is called MAP criterion.”
But in the note of 5b logistic regression, it used maximum likelihood criterion and gave a probabilistic intepretation.
I wanted to link the decision rule(MAP) of optimal classification and probabilistic intepretation of logistic regression(maximum likelihood criterion) cause they both are classification, but now I was confused about the maximum likelihood criterion and MAP.
Could you please tell me what's the relationship between MAP and maximum likelihood criterion?
Thanks in advance:)
I am not sure about my answer but I'll give a try. I have found this website : https://wiseodd.github.io/techblog/2017/01/01/mle-vs-map/
And there is a demonstration of the link between MAP and MLE. The only difference between them is the prior term \(p(y)\) in the equation of MAP. I think that since in practice we do not know the underlying distribution of our data it's difficult to calculate \(p(y)\). Thus, we prefer to use the MLE where the prior is not involved
I have a question about this though: if in the lecture note above the expression is just argmaxp(y|x) why is it called the MAP and not called MLE? since we are missing the prior distribution no?
I consulted the website shared on the linked post but it doesn't explain why in the lecture notes it is also called MAP but doesn't have the same formula as MAP where we multiply by a prior
MAP and maximum likelihood criterion
Hello everyone,
When reading the lecture note of 5a classification, I found it says that
"To minimize the probilily of misclassfication, we should chose the decision rule
which is called MAP criterion.”
But in the note of 5b logistic regression, it used maximum likelihood criterion and gave a probabilistic intepretation.
I wanted to link the decision rule(MAP) of optimal classification and probabilistic intepretation of logistic regression(maximum likelihood criterion) cause they both are classification, but now I was confused about the maximum likelihood criterion and MAP.
Could you please tell me what's the relationship between MAP and maximum likelihood criterion?
Thanks in advance:)
2
Hi,
I am not sure about my answer but I'll give a try. I have found this website : https://wiseodd.github.io/techblog/2017/01/01/mle-vs-map/
And there is a demonstration of the link between MAP and MLE. The only difference between them is the prior term \(p(y)\) in the equation of MAP. I think that since in practice we do not know the underlying distribution of our data it's difficult to calculate \(p(y)\). Thus, we prefer to use the MLE where the prior is not involved
1
Thank you very much! That's clear!
I have a question about this though: if in the lecture note above the expression is just argmaxp(y|x) why is it called the MAP and not called MLE? since we are missing the prior distribution no?
In the exam 2018 question 20 it phrases the MAP differently then in the lecture notes expression seen above
Just based on the lecture notes I would have been inclined to say true but the correct answer is false :( can you please explain
3
http://oknoname.herokuapp.com/forum/topic/549/mle-vs-map/
I consulted the website shared on the linked post but it doesn't explain why in the lecture notes it is also called MAP but doesn't have the same formula as MAP where we multiply by a prior
2
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