Elements of information theory

A machine learning problem can also be analyzed in terms of information transfer or exchange. Our dataset is composed of n features, which are considered independent (for simplicity, even if it's often a realistic assumption) drawn from n different statistical distributions. Therefore, there are n probability density functions pi(x) which must be approximated through other n qi(x) functions. In any machine learning task, it's very important to understand how two corresponding distributions diverge and what is the amount of information we lose when approximating the original dataset.

The most useful measure is called entropy:


This value is proportional to the uncertainty of X and it's measured in bits (if the ...

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