Parametric Density Estimation with Uncertainty using Deep Ensembles

Abel Peirson, Taylor Howell, Marius Aurel Tirlea

Keywords: Deep ensembles, deep learning, computer vision, density estimation, uncertainty

Abstract:

In parametric density estimation, the parameters of a known probability density are typically recovered from measurements by maximizing the log-likelihood. Prior knowledge of measurement uncertainties is not included in this method -- potentially producing degraded or even biased parameter estimates.
We propose an efficient two-step, general-purpose approach for parametric density estimation using deep ensembles.
Feature predictions and their uncertainties are returned by a deep ensemble and then combined in an importance weighted maximum likelihood estimation to recover parameters representing a known density along with their respective errors. To compare the bias-variance tradeoff of different approaches, we define an appropriate figure of merit.
We illustrate a number of use cases for our method in the physical sciences and demonstrate state-of-the-art results for X-ray polarimetry that outperform current classical and deep learning methods.

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One-sentence Summary: Deep ensemble predictive uncertainties can inform parametric density estimation in a number of applications.

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