On the power of conditional samples in distribution testing

Authors:
Sourav Chakraborty;Eldar Fischer;Yonatan Goldhirsh;Arie Matsliah
Affiliations:
Chennai Mathematical Institute (CMI), Siruseri, India;Technion -- Israel Institute of Technology, Haifa, Israel;Technion -- Israel Institute of Technology, Haifa, Israel;Technion -- Israel Institute of Technology, Haifa, Israel
Venue:
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Year:
2013

Citing 9
Cited 0

Property testing and its connection to learning and approximation

Journal of the ACM (JACM)
Testing that distributions are close

FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Testing Random Variables for Independence and Identity

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Sublinear algorithms for testing monotone and unimodal distributions

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Complexity of Approximating the Entropy

SIAM Journal on Computing
Sublinear estimation of entropy and information distances

ACM Transactions on Algorithms (TALG)
Strong Lower Bounds for Approximating Distribution Support Size and the Distinct Elements Problem

SIAM Journal on Computing
On testing expansion in bounded-degree graphs

Studies in complexity and cryptography
Testing Symmetric Properties of Distributions

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we define and examine the power of the conditional sampling oracle in the context of distribution-property testing. The conditional sampling oracle for a discrete distribution μ takes as input a subset S ⊂ [n] of the domain, and outputs a random sample i ∈ S drawn according to μ, conditioned on S (and independently of all prior samples). The conditional-sampling oracle is a natural generalization of the ordinary sampling oracle in which S always equals [n]. We show that with the conditional-sampling oracle, testing uniformity, testing identity to a known distribution, and testing any label-invariant property of distributions is easier than with the ordinary sampling oracle. On the other hand, we also show that for some distribution properties the sample complexity remains near-maximal even with conditional sampling.