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\begin{document}


\lyxnewslide{adfa}

{\par\centering On Discriminative vs. Generative Classifiers: A Comparison of
Logistic Regression and Naive Bayes\par}

{\par\centering Andrew Ng and Michael Jordan\par}


\lyxnewslide{afa}

Generative: build a model, then extract classifier from model.

Discriminitave: build a classifier directly.


\lyxinvisible{}

Prevailing wisdom: discriminative classifiers are better.

Paper says: not always


\lyxnewoverlay{da}

Generative: build a model, then extract classifier from model.

Discriminitave: build a classifier directly.

Prevailing wisdom: discriminative classifiers are better.


\lyxinvisible{}

Paper says: not always


\lyxnewoverlay{da}

Generative: build a model, then extract classifier from model.

Discriminitave: build a classifier directly.

Prevailing wisdom: discriminative classifiers are better.

Paper says: not always


\lyxnewslide{afa}

Generative = naive bayes = \( h_{gen}(x)=\sum _{i=1}^{n}\ln \frac{\hat{p}(x_{i}|y=1)}{\hat{p}(x_{i}|y=0)}+\ln \frac{\hat{p}(y=1)}{\hat{p}(y=0)} \)

Discriminative = logistic regression = \( h_{dis}(x)=\sum _{i=1}^{n}\theta _{i}x_{i}+\theta _{0} \)


\lyxnewslide{ada}

Observation: asymptoticallly \( e(h_{dis,\infty })\leq e(h_{gen,\infty }) \)

VC says: 
\[
e(h_{dis,m})\leq e(h_{dis,\infty })+O(\sqrt{\frac{n}{m}\log \frac{m}{n}})\]
\[
e(h_{gen,m})\leq e(h_{gen,\infty })+O(\sqrt{\frac{\log n}{m}})\]


\end{document}
