Today was day 2 of the 2019 Math+X Symposium on Inverse Problems and Deep Learning in Space Exploration at Rice University in Houston. Again I saw and learned way too much to write in a blog post. Here are some random things:
In a talk about provably or conjectorally effective tricks for optimization, Stan Osher (UCLA) showed some really strange results, like that an operator that (pretty much arbitrarily) smooths the derivatives improves optimization. And the smoothing is in a space where there is no metric or sense of adjacency, so the result is super-weird. But the main takeaway from his talk for me was that we should be doing what he calls “Nesterov” when we do gradient descent. It is like adding in some inertia or momentum to the descent. That wasn't his point! But it was very useful for me.
There was a great talk by Soledad Villar (NYU), who showed some really nice uses of deep generative models (in the form of a GAN, but it could be anything) to de-noise data. This, for a mathematician, is like inference for an astronomer: The GAN (or equivalent) trained on data becomes a prior over new data. This connects strongly to things I have been trying to get started with Gaia data and weak-lensing data! I resolved to find Villar back in NYC in February. She also showed some nice results on constructing continuous deep-learning methods, which don't need to work in a discrete data space. I feel like this might connect to non-parametrics.
In the side action at the meeting, I had some valuable discussions. One of the most interesting was with Katherine de Kleer (Caltech), who has lots of interesting data on Io. She has mapped the surface using occultation, but also just has lots of near-infrared adaptive-optics imaging. She needs to find the volcanoes, and currently does so using human input. We discussed what it would take to replace the humans with a physically motivated generative model. By the way (I learned from de Kleer): The volcanoes are powered by tidal heating, and that heating comes from Io's eccentricity, which is 0.004. Seriously you can tidally heat a moon to continuous volcanism with an eccentricity of 0.004. Crazy Solar System we live in!
In the afternoon, Rob Fergus (NYU) talked about the work we have done on exoplanet direct detection with generative models. And he has done the same (more-or-less repeated our results but with Muandet and Schölkopf) with discriminative models too. That's interesting, because discriminative models are rarely used (or rarely power-used) in astronomy.