Summary of Testably Learning Polynomial Threshold Functions, by Lucas Slot et al.
Testably Learning Polynomial Threshold Functions
by Lucas Slot, Stefan Tiegel, Manuel Wiedmer
First submitted to arxiv on: 10 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Data Structures and Algorithms (cs.DS)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The recent introduction of the testable learning framework relaxes distributional assumptions, making it more feasible to verify conditions efficiently by a tester. The framework ensures that when data satisfies original assumptions, the tester accepts, and the learner succeeds when the tester accepts. In this study, we focus on standard Gaussian data, where basic concept classes like halfspaces can be learned testably with similar time complexity as in the agnostic model. We investigate whether there’s a price to pay for learning more complex concept classes testably, particularly polynomial threshold functions (PTFs). Our results show that PTFs of arbitrary constant degree can be testably learned up to excess error > 0 in time n^{(1/)}, matching the best known guarantees in the agnostic model. The connection between testable learning and fooling is crucial, as we demonstrate that distributions approximating at least (1/) moments of the standard Gaussian can fool constant-degree PTFs (up to error ). As a secondary result, we prove that the direct approach to show testable learning without fooling, which worked for halfspaces, cannot be applied to PTFs. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores how we can learn from data without assuming it comes from a specific distribution. Instead of trying to verify these assumptions, we use a “tester” that checks if the data satisfies certain conditions. In this study, researchers focus on learning more complex concepts using this approach. They show that it’s possible to learn about polynomial threshold functions (which are used in computer vision and other areas) without making strong assumptions about the data. This is important because it can help us develop better machine learning models that work well even when we don’t know the underlying distribution of the data. |
Keywords
* Artificial intelligence * Machine learning
