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We describe a method for unmixing mixtures of ‘freely’ independent random variables in a manner analogous to the independent component analysis (ICA) based method for unmixing independent random variables from their additive mixture. Random matrices play the role of free random variables in this context so the method we develop, which we call Free component analysis (FCA), unmixes matrices from an...
Random projection is a technique which was first used for data compression, by using a matrix with random variables to map a high dimensional vector to a lower dimensional one. The lower dimensional vector preserves certain properties of the higher dimensional vector, up to a certain degree of accuracy. However, random projections can also be used for matrix decompositions and factorizations, described...
In this work, we study the upper bound of second order statistical correlation. We provide a condition for a random variable reaching the upper-bound, and an algorithm that transform any variable to have the maximum second order statistical correlation.
Suppose we have samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to discover the number of hidden components, and to learn a statistical model over the entire collection of variables? We address this question in the setting in which the...
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