# 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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