Ways to deal with the intractable sum
• Set up a Markov Chain that samples from the existing
– The samples can then be used to get a noisy
estimate of the last term in the derivative
– The chain may need to run for a long time before the
fantasies it produces have the correct distribution.
• For uni-gauss experts we can set up a Markov chain by
sampling the hidden state of each expert.
– The hidden state is whether it used the Gaussian or
the uniform.
– The experts’ hidden states can be sampled in parallel
• This is a big advantage of products of experts.