We have learned that MSEs and MLEs are two different approaches to fit the regression model. But in our tutorial, we have only calculated MSEs till now. My question is: What will be the situations where theoretically choosing MLE will be wiser?

If I have a hypothesis about the distribution of the population, I would use MLE to find the parameters of this distribution. For example, if a population is known to follow a normal distribution but the mean and the variance are unknown, MLE can be used to estimate them using a limited sample size of the population, by finding particular values of the mean and variance so that the observation is the most likely result to have occurred.

For more see also this post: https://neurostars.org/t/w1d3-when-to-use-mse-or-mle/14055

Hi, thanks for the reply, still I have little doubt.

In MSE, we donâ€™t know the parameters, and we fit the model to get the parameter values. Isnâ€™t MLE supposed to give the opposite? Where for given parameter values, we calculate the likelihood of a particular dataset (calculating joint probability)?

The link you referred to is private, and I cannot access it.

In MLE you also fit the model to get the parameters, but now your model is defined by the log-likelihood which is the same kind of thing as the â€ścost functionâ€ť of MSE. It is common to think of MSE as MLE with a Gaussian distribution, because the squared error function is the log of the Gaussian distribution.

Okay, MSE will not then be an appropriate one to model other distributions.