Abstract: In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. Our semiparametric approach targets the best decreasing approximation of the derivative of the log-density of the noise distribution. At the population level, this fitting process is a nonparametric extension of score matching, corresponding to a log-concave projection of the noise distribution with respect to the Fisher divergence.…

Abstract: As ML models become increasingly powerful, it is an attractive proposition to use them in important decision making pipelines, in collaboration with human decision makers. But how should a human being and a machine learning model collaborate to reach decisions that are better than either of them could achieve on their own? If the human and the ML model were perfect Bayesians, operating in a setting with a commonly known and correctly specified prior, Aumann's classical agreement theorem would give us…

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