Combining GMM's in different dimensions

by jbuchel   Last Updated October 16, 2018 22:19 PM

I have input $X$, which follows a distribution $P(X)$, which is best modeled using a mixture of Gaussians. I also have another random variable $T$, which is also best modeled by a mixture of Gaussians. The problem is that $X \in R^{500}$, but $T \in R^{10}$. These dimensions are just examples. But in general the dimension of $X$ is way higher than the one of $T$.

My question: How can I compute $P(X |T)$? Do I need to reduce the space of $X$ somehow or is there a method of sampling and approximating the conditional?



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