For simplicity I will only discuss binary classification. If $p_k(x) = P(X \mid Y = k)$ for $k = 0,1$, then Bayes classifier $h$ minimizes the risk $P(h(x) \neq Y)$. It is well known that $$h(x) = 1\{ \frac{p_1(x)}{p_0(x)} > \frac{1 - \pi_1}{\pi_1} \},$$ where $\pi_1 = p_0(x)$. Bayes classifier seems to naturally fit the generative approach where we directly model $p_k(x)$ and $\pi_k$. Where does the discriminant analysis approach fall in this framework? Is the discriminant analysis approach completely independent of Bayes' classifier? What exactly is the connection between these three topics?

  • $\begingroup$ Can anyone please help? This is a fairly basic question about terminology... $\endgroup$
    – user369210
    Apr 24 '17 at 3:08

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