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Abstract:
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We present a Bayesian nonparametric density estimation method based only on coarse histogram count data. The method uses the Karhunen-Loeve Expansion to construct a finite-dimensional Gaussian Process; with an appropriate choice of basis, the integration over the bins becomes trivial and can be pre-computed analytically. This avoids numerical approximations or complicated sampling schemes to calculate the normalizing constant, as in many other nonparametric methods. In a simulation study, we demonstrate that our method is nearly as accurate as a comparable method using the Logistic Gaussian Process prior, while having lower runtime and much faster mixing. Using this foundation, we extend the model to density regression. Our regression model trains on a set of histograms and corresponding input parameters so that for any new input parameter, the full density can be predicted. The model shows excellent predictive accuracy for the full density, which would not be possible with naive approaches that treat the histogram data as multivariate.
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