Today was the second day of #AstroHackWeek 2016. Josh Bloom (UCB) spoke in the morning about machine learning, with a great set of tutorials based on the Jupyter notebook and lots of experience introducing scientists to supervised machine learning. He emphasized Random Forest, of course!
In the afternoon, Matt Mechtley (ASU) and Dalya Baron (TAU) generalized my toy one-d-angle molecular imaging problem to a three-d angle problem. Mechtley also sped up and improved the generation of the fake data, and Baron also got the inference (including the stochastic gradient descent) to work end-to-end. Exciting!
Adrian Price-Whelan (Princeton) and I capitalized on the finite time span of any radial-velocity data set to make a safe period grid for inference, and then did exact sampling at each period in a mixture-of-sinusoids model. That's awesome! But we realized that if we try to go to second order—that is, put in a sine and cosine at half the period as well as at the period—there is no way to control the amplitudes such that we maintain both linearity (which is crucial to our exact sampling) and interpretability (in terms of the true orbital parameters, which is what we really want to sample in). So we decided to implement the first-order problem only today and make a judgement about whether it works for our purposes tomorrow. We got a long way, and made some awesome plots that clearly show the multimodality of the posterior for sparse data sets. I think this could still be a useful tool, even if it doesn't do everything for all customers.