Finding Correlations in Subquadratic Time, with Applications to Learning Parities and the Closest Pair Problem

@article{Valiant2015FindingCI,
  title={Finding Correlations in Subquadratic Time, with Applications to Learning Parities and the Closest Pair Problem},
  author={Gregory Valiant},
  journal={J. ACM},
  year={2015},
  volume={62},
  pages={13:1-13:45}
}
Given a set of <i>n</i> <i>d</i>-dimensional Boolean vectors with the promise that the vectors are chosen uniformly at random with the exception of two vectors that have Pearson correlation coefficient ρ (Hamming distance <i>d</i>ċ 1−ρ&frac;2), how quickly can one find the two correlated vectors? We present an algorithm which, for any constant &eps;>0, and… CONTINUE READING