What does maximizing mutual information do?

In information theory, there is something called the maximum entropy principle. Are other information measures, such as mutual information, also commonly maximized? If mutual information describes the reduction in uncertainty of characterizing one random variable (r.v. 1) based on full knowledge of a second random variable (r.v. 2), then would maximizing mutual information mean knowing everything about r.v. 2 will allow us to also have full knowledge of r.v. 1?

Just to give one example in machine learning context, for unsupervised learning, maximizing $$I(X, Y)$$ can build good representations $$Y$$ of input $$X$$, see here and here
• Being able to pick up nonlinear correlation is nice, isn't it? However, maximum of MI is hard to obtain due to the joint probability term, so the linked papers are maximizing its lower bound instead in practice. So practically, it is hard to fully recover $X$ from $Y$. Aug 4 '20 at 10:04