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With a single training image and using wavelet phase harmonic augmentation,we present polarized Cosmic Microwave Background (CMB) foregroundmarginalization in a high-dimensional likelihood-free (Bayesian) framework. Wedemonstrate robust foreground removal using only a single frequency ofsimulated data for a BICEP-like sky patch. Using Moment Networks we estimatethe pixel-level posterior probability for the underlying {E,B} signal andvalidate the statistical model with a quantile-type test using the estimatedmarginal posterior moments. The Moment Networks use a hierarchy of U-Netconvolutional neural networks. This work validates such an approach in the mostdifficult limiting case: pixel-level, noise-free, highly non-Gaussian dustforegrounds with a single training image at a single frequency. For a real CMBexperiment, a small number of representative sky patches would provide thetraining data required for full cosmological inference. These results enablerobust likelihood-free, simulation-based parameter and model inference forprimordial B-mode detection using observed CMB polarization data.

Single frequency CMB B-mode inference with realistic foregrounds from a single training image