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This paper introduces a PAC learning framework for learning conditional averages, where the goal is to predict the average label within an instance-specific neighborhood rather than the label itself. The work provides a complete characterization of learnability in this setting, demonstrating that it depends on the joint finiteness of two novel combinatorial parameters related to the independence number of the neighborhood graph. The authors derive sample complexity bounds that are tight up to logarithmic factors, offering insights into the learnability of conditional averages.
Learning to predict averages within neighborhoods, rather than individual labels, offers a new PAC learning framework with applications in explainability, fairness, and recommendation systems.
We introduce the problem of learning conditional averages in the PAC framework. The learner receives a sample labeled by an unknown target concept from a known concept class, as in standard PAC learning. However, instead of learning the target concept itself, the goal is to predict, for each instance, the average label over its neighborhood -- an arbitrary subset of points that contains the instance. In the degenerate case where all neighborhoods are singletons, the problem reduces exactly to classic PAC learning. More generally, it extends PAC learning to a setting that captures learning tasks arising in several domains, including explainability, fairness, and recommendation systems. Our main contribution is a complete characterization of when conditional averages are learnable, together with sample complexity bounds that are tight up to logarithmic factors. The characterization hinges on the joint finiteness of two novel combinatorial parameters, which depend on both the concept class and the neighborhood system, and are closely related to the independence number of the associated neighborhood graph.
Google Research