I am working in a mixture model with expectation propagation. When I am trying to compute the normalizing constant, z_i, I have an integral that is not closed form.
My integral looks as follows:
Integral to solve
B_j is a continuous value that is usually << 1. The mean, and variance are known values. The EDCM distribution is a bounded Dirichlet-multinomial distribution. This will result in a discrete discrete distribution since EDCM is discrete.
- Can Laplace approximation be used since the distributions to be approximated are not completely continuous?
- Can I use BBVI? Posterior p(B|x) propto p(x,B) with an approximation q(B) that is gaussian. The approximation will be continuous, so can I use only the normalization factor of the approximate distribution to approximate p(x) (ie 1/(2pi)^(V/2)|sigma|^1/2). Will this value be considered a proper discrete distribution?
- Any other suggestions? Maybe just sample (replace the integral with a summation). I have to iterate many times this approximation.