Hadamard Extensions and the Identification of Mixtures of Product Distributions
This work addresses a theoretical problem in machine learning for researchers dealing with mixture models, but it appears incremental as it builds on existing identification frameworks.
The paper tackles the problem of identifying mixtures of product distributions on binary random variables by analyzing when the Hadamard Extension of a matrix has full column rank, which is necessary for identification algorithms, and provides several theoretical results on this condition.
The Hadamard Extension of a matrix is the matrix consisting of all Hadamard products of subsets of its rows. This construction arises in the context of identifying a mixture of product distributions on binary random variables: full column rank of such extensions is a necessary ingredient of identification algorithms. We provide several results concerning when a Hadamard Extension has full column rank.