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Joint probability mass function (PMF) estimation is a fundamental machinelearning problem. The number of free parameters scales exponentially withrespect to the number of random variables. Hence, most work on nonparametricPMF estimation is based on some structural assumptions such as cliquefactorization adopted by probabilistic graphical models, imposition of low rankon the joint probability tensor and reconstruction from 3-way or 2-waymarginals, etc. In the present work, we link random projections of data to theproblem of PMF estimation using ideas from tomography. We integrate this ideawith the idea of low-rank tensor decomposition to show that we can estimate thejoint density from just one-way marginals in a transformed space. We provide anovel algorithm for recovering factors of the tensor from one-way marginals,test it across a variety of synthetic and real-world datasets, and also performMAP inference on the estimated model for classification.

Recovery of Joint Probability Distribution from one-way marginals: Low rank Tensors and Random Projections