Out-of-distribution (OOD) detection and lossless compression constitute two problems that can be solved by the training of probabilistic models on a first dataset with subsequent likelihood evaluation on a second dataset, where data distributions differ. By defining the generalization of probabilistic models in terms of likelihood we show that, in the case of image models, the OOD generalization ability is dominated by local features.

In this section, in order to help readers understand the metric in the paper, we first revisit the definition of the Shapley value [14], which is widely considered as an unbiased estimation of the numerical importance w.r.t. each input variable. In game theory, the complex system is usually represented as a game, where each input variable is taken as a player, and the output of this system is regarded as the total reward of all players. Given a game with multiple players (input variables) N = {1,2,,n}, some players cooperate to pursue a high reward. Thus, the task is to divide the total reward, and fairly assign the divided elementary reward to each individual player. In this way, the elementary reward can be considered as the numerical importance of the corresponding variable to the complex system. Let 2N def= {S|S N}indicate all potential subsets of N. The game v: 2N R is a function, which estimates the overall reward v(S) earned by each specific subset of players S N. In this way, the Shapley value, denoted by φ(i), represents the numerical importance of the player ito the game v. φ(i) = X Using Shapley values to explain DNNs.