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Abstract:
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We present density estimation methods for high dimensional binary/categorical data. Our density estimation models are tree- or list- structured and can be visualized to provide an interpretable representation of the data. Our methods are high dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the density is constant, similar to the flat density within the bin of a histogram. Histograms, however, cannot easily be visualized in higher dimensions, whereas our models can. The accuracy of histograms fades as dimensions increase, whereas our models have priors that help with generalization. We present three generative models, where the first one allows the user to specify the number of desired leaves in the tree within a Bayesian prior. The second model allows the user to specify the desired number of branches within the prior. The third model allows the user to specify the desired number of rules and the length of rules within the prior and returns a list. Our results indicate that the new approach yields a better balance between sparsity and accuracy of density estimates than other methods for this task.
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