All Learning, Inference and Decision Under Uncertainty

This group gathers theorems about what can be concluded or chosen when information is limited, the part of probability and statistics that overlaps with machine learning and decision theory. It covers the no free lunch theorem, which concerns the limits of learning and optimization algorithms when averaged over all possible problems, and Rabin's calibration theorem, a result about the calibration of risk aversion within expected-utility theory which shows that moderate risk aversion over small gambles implies implausibly high risk aversion over large ones. Limit theorems, inequalities, and estimation results about random variables themselves belong with the probability theory and estimation groups.