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 \sim 100 .
The random forest , trained on our grid of \sim 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 ( \log { M } = -0.2 \pm 0.2 ) .
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 .