publication . Preprint . 2017

Fourier-Based Testing for Families of Distributions

Canonne, Clément L.; Diakonikolas, Ilias; Stewart, Alistair;
Open Access English
  • Published: 18 Jun 2017
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution $\mathbf{P}$, we want to distinguish (with high probability) between the case that $\mathbf{P} \in \mathcal{P}$ and the case that $\mathbf{P}$ is $\epsilon$-far, in total variation distance, from every distribution in $\mathcal{P}$. This is the prototypical hypothesis testing problem that has received significant attention in statistics and, more recently, in theoretical computer science. The sample complexity of this general infer...
free text keywords: Computer Science - Data Structures and Algorithms, Computer Science - Computational Complexity, Computer Science - Discrete Mathematics, Mathematics - Probability, Mathematics - Statistics Theory
Funded by
NSF| AF: Small: Learning and Testing Classes of Distributions
  • Funder: National Science Foundation (NSF)
  • Project Code: 1319788
  • Funding stream: Directorate for Computer & Information Science & Engineering | Division of Computing and Communication Foundations
RCUK| Sublinear Algorithms for Approximating Probability Distributions
  • Funder: Research Council UK (RCUK)
  • Project Code: EP/L021749/1
  • Funding stream: EPSRC
NSF| AF: Small: The Boundary of Learnability for Monotone Boolean Functions
  • Funder: National Science Foundation (NSF)
  • Project Code: 1115703
  • Funding stream: Directorate for Computer & Information Science & Engineering | Division of Computing and Communication Foundations
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