Property testing of joint distributions using conditional samples

Rishiraj Bhattacharyya, Sourav Chakraborty

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this article, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, sample complexity of testing properties of joint distributions are exponential in the dimension, resulting in inefficient algorithms for practical use. While recent results achieve efficient algorithms for product distributions with significantly smaller sample complexity, no efficient algorithm is expected when the marginals are not independent. In this article, we initialize the study of conditional sampling in the multidimensional setting. We propose a subcube conditional sampling model where the tester can condition on a (adaptively) chosen subcube of the domain. Due to its simplicity, this model is potentially implementable in many practical applications, particularly when the distribution is a joint distribution over Σn for some set Σ. We present algorithms for various fundamental properties of distributions in the subcube-conditioning model and prove that the sample complexity is polynomial in the dimension n (and not exponential as in the traditional model). We present an algorithm for testing identity to a known distribution using Õ(n2)subcube-conditional samples, an algorithm for testing identity between two unknown distributions using Õ(n5)-subcube-conditional samples and an algorithm for testing identity to a product distribution using Õ(n5)-subcube-conditional samples. The central concept of our technique involves an elegant chain rule, which can be proved using basic techniques of probability theory, yet it is powerful enough to avoid the curse of dimensionality.

Original languageEnglish
Article number16
JournalACM Transactions on Computation Theory
Issue number4
Publication statusPublished - Aug 2018

Bibliographical note

Publisher Copyright:
© 2018 ACM


  • Conditional sampling
  • Distribution testing
  • Subcube conditioning

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


Dive into the research topics of 'Property testing of joint distributions using conditional samples'. Together they form a unique fingerprint.

Cite this