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).
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.