Interpreting High-Resolution Spectroscopy of Exoplanets Using Cross-Correlations and Supervised Machine Learning

We present a new method for performing atmospheric retrieval on ground-based, high-resolution data of exoplanets. Our method combines cross-correlation functions with a random forest, a supervised machine learning technique, to overcome challenges associated with high-resolution data. A series of cross-correlation functions are concatenated to give a "CCF-sequence" for each model atmosphere, which reduces the dimensionality by a factor of ~100. The random forest, trained on our grid of ~65,000 models, provides a likelihood-free method of retrieval. The pre-computed grid spans 31 values of both temperature and metallicity, and incorporates a realistic noise model. We apply our method to HARPS-N observations of the ultra-hot Jupiter KELT-9b, and obtain a metallicity consistent with solar (logM = $-0.2\pm0.2$). Our retrieved transit chord temperature (T = $6000^{+0}_{-200}$K) is unreliable as the ion cross-correlations lie outside of the training set, which we interpret as being indicative of missing physics in our atmospheric model. We compare our method to traditional nested-sampling, as well as other machine learning techniques, such as Bayesian neural networks. We demonstrate that the likelihood-free aspect of the random forest makes it more robust than nested-sampling to different error distributions, and that the Bayesian neural network we tested is unable to reproduce complex posteriors. We also address the claim in Cobb et al. (2019) that our random forest retrieval technique can be over-confident but incorrect. We show that this is an artefact of the training set, rather than the machine learning method, and that the posteriors agree with those obtained using nested-sampling.