I am going thorugh a Naive Bayes Classifier, and faced the following:
$p(y|a,b,c) = \frac{p(a|y,b)*p(y|c)}{p(a|b,c)}$
When I am trying to derive the above, these are my steps:
$p(y|a,b,c)=\frac{p(y,a,b,c)}{p(a,b,c)}=\frac{p(a|y,b,c)*p(y|b,c)*p(b|c)*p(c)}{p(a|b,c)*p(b|c)*p(c)}$
Which leads to: $\frac{p(a|y,b,c)*p(y|b,c)}{p(a|b,c)}$
My question is how to prove the above derivation. Where $y$ is category and it is described by Dirichlet parameters of $\theta$, and $a$ is another category is described by dirichlet parameter vector $c$.