At lunchtime I had a great conversation with Iain Murray (Edinburgh) about two things today. One was new ideas in probabilistic machine learning, and the other was this exoplanet transit spectroscopy challenge. On the former, he got me excited about normalizing flows, that use machine learning methods (like deep learning) and a good likelihood function to build probabilistic generative models for high dimensional data. These could be useful for astronomical applications; we discussed. On the latter, we discussed how transits work and how sunspots cause trouble for them. And how the effects might be low dimensional. And thus how a good machine-learning method should be able to deal with it or capture it.
In the afternoon I spent a short session with Rodrigo Luger (Flatiron) talking about the information about a stellar surface or about an exoplanet surface encoded in a photometric light curve. The information can come from rotation, or from transits, or both, and it is different (there is more information), oddly, if there is limb darkening! We talked about the main points such a paper should make, and some details of information theory. The problem is nice in part because if you transform the stellar surface map to spherical harmonics, a bunch of the calculations lead to beautiful trigonometric forms, and the degeneracy or eigenvector structure of the information tensor becomes very clear.
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