Non-parametric Binary regression in metric spaces with KL loss
This work addresses computational and statistical issues in non-parametric binary regression for machine learning applications, presenting incremental improvements in optimization and generalization techniques.
The paper tackles binary regression in metric spaces using a non-parametric Lipschitz-regularized hypothesis with logarithmic loss, proposing an efficient parameter-free optimization algorithm and addressing statistical challenges via adaptive truncation with a lower bound.
We propose a non-parametric variant of binary regression, where the hypothesis is regularized to be a Lipschitz function taking a metric space to [0,1] and the loss is logarithmic. This setting presents novel computational and statistical challenges. On the computational front, we derive a novel efficient optimization algorithm based on interior point methods; an attractive feature is that it is parameter-free (i.e., does not require tuning an update step size). On the statistical front, the unbounded loss function presents a problem for classic generalization bounds, based on covering-number and Rademacher techniques. We get around this challenge via an adaptive truncation approach, and also present a lower bound indicating that the truncation is, in some sense, necessary.