Good afternoon ,
Assume we have a dataset modeled by multinomial data of K cluster.
To apply EM algorithm parameters are :
$${\theta }^{\left(0\right)}=({p}_{k}^{\left(0\right)},k=1,\mathrm{\dots },K)$$
E-Step :
$$\hbox{ Pr }\left({z}_{i,k}=1\mid {X}_{i},{\theta }^{\left(t\right)}\right)=\frac{{P(X_{i}/C_{k}).}{p}_{k}^{\left(t\right)}}{{\sum }_{k=1}^{K}P(X_{i}/C_{k}).{p}_{k}^{\left(t\right)}},\forall $$
Where : ${z}_{i,k} = 1 $ if $ {X}_{i}\in C_{k} $
M-step :
$${n}_{k}^{(t+1)}={\displaystyle \sum _{i=1}^{N}}{z}_{i,k}^{(t+1)},\forall k$$
$${p}_{k}^{(t+1)}=\frac{{n}_{k}^{(t+1)}}{N},\forall k.$$
My question is how to estimate $ P(X_{i}/C_{k}) $ at E-step
