Tight Bounds for Equivalence Testing with Non-Adaptive Conditional Samples

Key points

• Specifically, we give tight bounds for equivalence testing, determining whether two unknown distributions are equal to or $\varepsilon$-far from each other in total variation distance.1
• Our algorithm and lower bound show that $\tilde Θ\left(\frac{\log n}{\varepsilon^2}\right)$ queries are necessary and sufficient for this problem.1
• These results demonstrate that the complexity of uniformity, identity, and equivalence testing with non-adaptive conditional samples are all $\tilde Θ(\log n)$.1

Sources (1)

• [1]Tight Bounds for Equivalence Testing with Non-Adaptive Conditional Samples
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 03:10 AM

  We study distribution testing with access to non-adaptive conditional samples.

  Specifically, we give tight bounds for equivalence testing, determining whether two unknown distributions are equal to or $\varepsilon$-far from each other in total variation distance.

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