No abstract

We establish a normal approximation for the limiting distribution of partial sums of random Rademacher multiplicative functions over function fields, provided the number of irreducible factors of the polynomials is small enough. This parallels work of Harper for random Rademacher multiplicative functions over the integers.

We consider the problem of multilabel classification and investigate learnability in batch and online settings. In both settings, we show that a multilabel function class is learnable if and only if each single-label restriction of the function class is learnable. As extensions, we also study multioutput regression in the batch setting and bandit feedback in the online setting. For the former, we characterize learnability w.r.t. Lp losses. For the latter, we show a similar characterization as in the full-feedback setting.