Today I sat down with Fiona McCarthy (Flatiron) to look at data-driven methods for separating cosmic microwave background data into different components. We implemented a simple polynomial regression to fit foregrounds, using (observed) difference maps as inputs (features) that are designed to contain foregrounds only. We obtained some preliminary results that looked exciting but we’ve only just started. Part of the motivation is that CNNs are hard to train, but linear combinations of image monomials are easy! I realized in all this that there are connections to the group-equivariant stuff I’ve done with Villar’s group, because we use invariants, and also to the causal inference things that Schölkopf’s group does, because we’re trying to impose some causal structure on our functions.
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