Embedding Hard Learning Problems Into Gaussian Space

  title={Embedding Hard Learning Problems Into Gaussian Space},
  author={Adam R. Klivans and Pravesh Kothari},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
We give the first representation-independent hardness result for agnostically learning halfspaces with respect to the Gaussian distribution. We reduce from the problem of learning sparse parities with noise with respect to the uniform distribution on the hypercube (sparse LPN), a notoriously hard problem in computer science and show that any algorithm for agnostically learning halfspaces requires n (1/ )) time, ruling out a polynomial time algorithm for the problem. As far as we are aware, this… CONTINUE READING
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