Maximum-likelihood learning

We have defined likelihood as a filtering term in the Bayes formula. In general, it has the form of:

Here the first term expresses the actual likelihood of a hypothesis, given a dataset X. As you can imagine, in this formula there are no more Apriori probabilities, so, maximizing it doesn't imply accepting a theoretical preferential hypothesis, nor considering unlikely ones. A very common approach, known as expectation-maximization and used in many algorithms (we're going to see an example in logistic regression), is split into two main parts:

  • Determining a log-likelihood expression based on model parameters (they ...

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