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Machine learning algorithms build a model of the training data. The term "machine learning" is vaguely defined; it includes what is also called statistical learning, reinforcement learning, unsupervised learning, etc. ALWAYS ADD A MORE SPECIFIC TAG.
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Why do we have to be concerned about the problem of overfitting on the training set?
Let's first be clear on the notation. Let's say the empirical risk minimization algorithm (ERM) picks a hypothesis $f\in H$. It's obvious that $f$ depends on the training data, $D_{train}$ (that's why …
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In statistical learning theory, isn't there a problem of overfitting on a test set?
Among those two inequalities, I think the later is wrong. In brief, what's wrong here is the identity $g=h_1$ given that $g$ is a function of the test data while $h_1$ is a model that is independent o …