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Statistically Near-Optimal Hypothesis Selection
We derive an optimal $2$-approximation learning strategy for the Hypothesis Selection problem, outputting $q$ such that $\mathsf{TV}(p, q) \leq2 \cdot opt + \eps$, with a (nearly) optimal sample complexity of~$\tilde O(\log n/\epsilon^2)$.
Non-parametric Binary regression in metric spaces with KL loss
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.
Fast and Bayes-consistent nearest neighbors
Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects -- either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity search.
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