# Near-Optimal Statistical Query Hardness of Learning Halfspaces with Massart Noise

@inproceedings{Diakonikolas2020NearOptimalSQ, title={Near-Optimal Statistical Query Hardness of Learning Halfspaces with Massart Noise}, author={Ilias Diakonikolas and Daniel M. Kane}, year={2020} }

We study the problem of PAC learning halfspaces with Massart noise. Given labeled samples (x, y) from a distribution D on Rd×{±1} such that the marginalDx on the examples is arbitrary and the label y of example x is generated from the target halfspace corrupted by a Massart adversary with flipping probability η(x) ≤ η ≤ 1/2, the goal is to compute a hypothesis with small misclassification error. The best known poly(d, 1/ǫ)-time algorithms for this problem achieve error of η + ǫ, which can be…

## 3 Citations

Optimal SQ Lower Bounds for Learning Halfspaces with Massart Noise

- Computer ScienceArXiv
- 2022

Tight statistical query lower bounds for learnining halfspaces in the presence of Massart noise are given and it is shown that for arbitrary ∈ [0, 1/2] every SQ algorithm achieving misclassification error better than requires queries of super polynomial accuracy or at least a superpolynomial number of queries.

Efficient PAC Learning from the Crowd with Pairwise Comparison

- Computer Science
- 2020

A label-efficient algorithm that interleaves learning and annotation, which leads to a constant overhead of the algorithm (a notion that characterizes the query complexity) in contrast, a natural approach of annotation followed by learning leads to an overhead growing with the sample size.

Non-Gaussian Component Analysis via Lattice Basis Reduction

- Computer ScienceArXiv
- 2021

A sample and computationally efficient algorithm for NGCA in the regime that A is discrete or nearly discrete, in a well-defined technical sense is obtained.

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