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We propose a non-parametric variant of binary regression, where thehypothesis is regularized to be a Lipschitz function taking a metric space to[0,1] and the loss is logarithmic. This setting presents novel computationaland statistical challenges. On the computational front, we derive a novelefficient optimization algorithm based on interior point methods; an attractivefeature is that it is parameter-free (i.e., does not require tuning an updatestep size). On the statistical front, the unbounded loss function presents aproblem for classic generalization bounds, based on covering-number andRademacher techniques. We get around this challenge via an adaptive truncationapproach, and also present a lower bound indicating that the truncation is, insome sense, necessary.

Non-parametric Binary regression in metric spaces with KL loss