Testably Learning Polynomial Threshold Functions
Lucas Slot, Stefan Tiegel, Manuel Wiedmer

TL;DR
This paper demonstrates that polynomial threshold functions of any constant degree can be testably learned under Gaussian data with guarantees similar to the agnostic model, using a connection to distribution fooling.
Contribution
It establishes the first testable learning algorithm for polynomial threshold functions of arbitrary constant degree with near-optimal guarantees.
Findings
Testable learning of PTFs matches agnostic model guarantees.
Distributions that match Gaussian moments fool PTFs up to error ε.
Direct fooling-based approaches are necessary for PTFs, unlike halfspaces.
Abstract
Rubinfeld & Vasilyan recently introduced the framework of testable learning as an extension of the classical agnostic model. It relaxes distributional assumptions which are difficult to verify by conditions that can be checked efficiently by a tester. The tester has to accept whenever the data truly satisfies the original assumptions, and the learner has to succeed whenever the tester accepts. We focus on the setting where the tester has to accept standard Gaussian data. There, it is known that basic concept classes such as halfspaces can be learned testably with the same time complexity as in the (distribution-specific) agnostic model. In this work, we ask whether there is a price to pay for testably learning more complex concept classes. In particular, we consider polynomial threshold functions (PTFs), which naturally generalize halfspaces. We show that PTFs of arbitrary constant…
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Taxonomy
TopicsMachine Learning and Algorithms · Machine Learning and Data Classification · Neural Networks and Applications
MethodsFocus
