Towards a theory of out-of-distribution learning. (arXiv:2109.14501v4 [stat.ML] UPDATED)

What is learning? 20$^{st}$ century formalizations of learning theory --
which precipitated revolutions in artificial intelligence -- focus primarily on
$\mathit{in-distribution}$ learning, that is, learning under the assumption
that the training data are sampled from the same distribution as the evaluation
distribution. This assumption renders these theories inadequate for
characterizing 21$^{st}$ century real world data problems, which are typically
characterized by evaluation distributions that differ from the training data
distributions (referred to as out-of-distribution learning). We therefore make
a small …

arxiv distribution learning ml theory