our method risk extrapolation or rex is heavily inspired by invariant risk minimization or irm by arjhovsky and all from about a year ago so both of these methods are do causal discovery using deep learning and what that means is that we have a prediction task where we don't know which of the inputs are causes of the target and which are not and so both rex and irm are able to uncover which inputs are in fact causes and learn to make a prediction based only on the causes that means if you encounter a new domain where x has been intervened on but the mechanism for y that is the way in which parts of x cause y has been preserved the prediction rule you learned will still apply and will still make good predictions so this is different than typical approaches to out of domain generalization where you frequently assume that p of y given x is preserved as opposed to here we're assuming that the mechanism for y is what's being preserved so we also show that rex has some advantage over irm in that it cares about uh covariate shift and and tries to be robust to changes in the distribution of the causes of y on the other hand that can also be a disadvantage when different inputs are easier or harder to predict