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Bargaining Compatible Explanations

Within the framework of ensemble methods, we investigate on a compatible learning scheme, denoted as learning by gossip with the aim of assessing its feasibility when facing a rather complex target function. Compatibility is in terms of probability that the learned function could be actually at the basis of the observed training set, hence an explanation of it. Feasibility is in terms of the related MSE on test sets. We base or conclusions on both theoretical and numerical arguments that are tossed on a well known benchmark.