When I learned EM algorithm, I saw many literatures use (the expectation of ) the log-likelihood. Is there any reason other than that the log-likelihood may reduce computation?
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Generally, statisticians like to take the log-likelihood because it is easier to maximize. If we find the value of $x$ that maximizes $\log(f(x))$ we've also found the value of $x$ that maximizes $f(x)$ due to the monotonicity of logarithms. This is also what is happening in the EM algorithm.
The reason it is easier to maximize is because of the nice property of logs that says $\log(f(X)g(Y)h(Z)) = \log(f(X)) + \log(g(Y)) + \log(h(Z))$. When maximizing, a common approach is to use partial derivatives, set it equal to zero, and solve for the variable we are interested in. It is much simpler and easier to take the partial derivative of a sum of functions than a product of functions. The log function takes a product, $XYZ$, and turns it into a sum $\log(X) + \log(Y) + \log(Z)$.