So, I need to compute the KL Divergence between two two dimensional normal distributions.. So, say one is mean=mp, std=stdp, the other is mean=mq, std=stdq and I guess I want to compute
$\displaystyle{\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }P(x,y) (\log (P(x,y))-\log (Q(x,y)))dy\ dx}$
Where
$P(x,y) = \displaystyle{\frac{e^{-\frac{(x-\text{mp})^2}{2 \text{stdp}^2}-\frac{(y-\text{mp})^2}{2 \text{stdp}^2}}}{2 \pi \text{stdp}^2}}$
and $Q(x,y) = \displaystyle{\frac{e^{-\frac{(x-\text{mq})^2}{2 \text{stdq}^2}-\frac{(y-\text{mq})^2}{2 \text{stdq}^2}}}{2 \pi \text{stdq}^2}}$
Can someone please tell me how/if there's a way to compute this without numeric integration?
Thanks!