  We present here a novel statistical learning approach for detection and
attribution (D&A) of climate change. Traditional optimal D&A studies try to
directly model the observations from model simulations, but practically this is
challenging due to high-dimensionality. Dimension reduction techniques reduce
the dimensionality, typically using empirical orthogonal functions, but as
these techniques are unsupervised, the reduced space considered is somewhat
arbitrary. Here, we propose a supervised approach where we predict a given
external forcing, e.g., anthropogenic forcing, directly from the spatial
pattern of climate variables, and use the predicted forcing as a test statistic
for D&A. We want the prediction to work well even under changes in the
distribution of other external forcings, e.g., solar or volcanic forcings, and
therefore formulate the optimization problem from a distributional robustness
perspective.
