Equation 5.84 - Githubissues

probml / pml-book

"Probabilistic Machine Learning" - a book series by Kevin Murphy

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Equation 5.84 #639

Closed danjenson closed 3 months ago

danjenson commented 6 months ago

Currently, the book states that we can estimate the generalization gap with Equation 5.84:

\mathbb{E}_{p^*}[R(f^*_N)-R(f^*)]\approx\mathbb{E}_{p_\text{tr}}[\ell(\mathbf{y}, f^*_N(\mathbf{x})]-\mathbb{E}_{p_\text{te}}[\ell(\mathbf{y},f^*_N(\mathbf{x}))]

However, I would expect the test loss to be higher than the training loss, which would make the RHS negative. Should the terms on the RHS be swapped?

murphyk commented 3 months ago

You are right. In fact there is a more serious issue in how I defined the generalization gap. This is now fixed - see below.