In the mixture models problem it is assumed that there are K
distributions θ1,…,θK and one gets to observe
a sample from a mixture of these distributions with unknown coefficients.
The goal is to associate instances with their generating
distributions, or to identify the parameters of the hidden distributions.
In this work we make the assumption that we have access to several
samples drawn from the same K underlying distributions, but with
different mixing weights. As with topic modeling, having multiple samples is often a reasonable
assumption. Instead of pooling the data into one sample, we prove that
it is possible to use the differences between the samples to better recover
the underlying structure. We present algorithms that
recover the underlying structure
under milder assumptions than the current state of art when either the
dimensionality or the separation is high. The methods, when applied to
topic modeling, allow generalization to words not present in the training