Active Learning Polynomial Threshold Functions
This addresses a theoretical challenge in machine learning for efficiently learning complex classifiers, though it is incremental as it builds on known lower bounds and focuses on specific settings.
The paper tackles the problem of actively learning polynomial threshold functions (PTFs), showing that basic access to derivatives enables efficient active learning for univariate PTFs with a query complexity of ̃O(d^3 log(1/εδ)), but proves this approach fails for multivariate PTFs.
We initiate the study of active learning polynomial threshold functions (PTFs). While traditional lower bounds imply that even univariate quadratics cannot be non-trivially actively learned, we show that allowing the learner basic access to the derivatives of the underlying classifier circumvents this issue and leads to a computationally efficient algorithm for active learning degree-$d$ univariate PTFs in $\tilde{O}(d^3\log(1/\varepsilonδ))$ queries. We also provide near-optimal algorithms and analyses for active learning PTFs in several average case settings. Finally, we prove that access to derivatives is insufficient for active learning multivariate PTFs, even those of just two variables.