  We present a method for enhancing the sensitivity of X-ray telescopic
observations with imaging polarimeters, with a focus on the gas pixel detectors
(GPDs) to be flown on the Imaging X-ray Polarimetry Explorer (IXPE). Our
analysis determines photoelectron directions, X-ray absorption points and X-ray
energies for 1-9 keV event tracks, with estimates for both the statistical and
model (reconstruction) uncertainties. We use a weighted maximum likelihood
combination of predictions from a deep ensemble of ResNet convolutional neural
networks, trained on Monte Carlo event simulations. We define a figure of merit
to compare the polarization bias-variance trade-off in track reconstruction
algorithms. For power-law source spectra, our method improves on the current
planned IXPE analysis (and previous deep learning approaches), providing ~45%
increase in effective exposure times. For individual energies, our method
produces 20-30% absolute improvements in modulation factor for simulated 100%
polarized events, while keeping residual systematic modulation within 1 sigma
of the finite sample minimum. Absorption point location and photon energy
estimates are also significantly improved. We have validated our method with
sample data from real GPD detectors.
