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I am new to machine learning. In an online course that I am taking the instructor claims the following: in linear regression, MLE framework gives us the squared loss cost function which overfits. In order to overcome that we use MAP estimate of the weights. I would like to get a theoretical reason behind why MLE overfits(if it indeed does so) and why using MAP we are able to overcome that(if we can indeed do so).

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    $\begingroup$ Why do you think that either of your statements - the one about MLE overfitting and MAP not overfitting in linear regression - is true? Note that if you use uniform / diffuse priors, the two will coincide... $\endgroup$ – jbowman Mar 27 '18 at 19:26
  • $\begingroup$ I do not if they are true or not. I saw it here : youtube.com/… $\endgroup$ – Abhay Gupta Mar 28 '18 at 16:36
  • $\begingroup$ @AbhayGupta neither MLE does overfit in general, nor MAP solves any problem with overfitting... $\endgroup$ – Tim Mar 28 '18 at 20:30
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Overfitting is usually related to the number of degrees of freedom of the model vs. the data.
It is not related to the method to estimate / calculate the parameters related to those degrees of freedom.

Hence either MAP or MLE doesn't create Overfitting in case the model is correctly chosen.

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