ProbabilityTheoryMachineLearningStatistics
A maximum likelihood estimator (MLE) is any solution to which for i.i.d. corresponds to maximizing the sum of the log-likelihoods In M-Estimation, the contrast function giving rise to the MLE is the negative log-likelihood:
The MLE is also given by the distribution the minimizes the KL divergence to the empirical measure among all distributions in some set