Rapid and deterministic estimation of probability densities using scale-free field theories

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Publication date: 23 December 2013

Abstract: The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory. Here I describe new results that allow this field-theoretic approach to be rapidly and deterministically computed in low dimensions, making it practical for use in day-to-day data analysis. Importantly, this approach does not impose a privileged length scale for smoothness of the inferred probability density, but rather learns a natural length scale from the data due to the tradeoff between goodness-of-fit and an Occam factor. Open source software implementing this method in one and two dimensions is provided.

Has companion code repository: https://github.com/jbkinney/13_deft

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