A number of applications require twosample testing on ranked preference data. For instance, in crowdsourcing, there is a longstanding question of whether pairwise comparison data provided by people is distributed similar to ratingsconvertedtocomparisons. Other examples include sports data analysis and peer grading. In this paper, we design twosample tests for pairwise comparison data and ranking data. For our twosample test for pairwise comparison data, we establish an upper bound on the sample complexity required to correctly distinguish between the distributions of the two sets of samples. Our test requires essentially no assumptions on the distributions. We then prove complementary lower bounds showing that our results are tight (in the minimax sense) up to constant factors. We investigate the role of modeling assumptions by proving lower bounds for a range of pairwise comparison models (WST, MST, SST, parameterbased such as BTL and Thurstone). We also provide testing algorithms and associated sample complexity bounds for the problem of twosample testing with partial (or total) ranking data. Furthermore, we empirically evaluate our results via extensive simulations as well as two realworld datasets consisting of pairwise comparisons. By applying our twosample test on realworld pairwise comparison data, we conclude that ratings and rankings providedmore »
Testing Shape Restrictions of Discrete Distributions
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution D over [n] and a property P, the goal is to distinguish between D ∈ P and ℓ1(D, P) > ε. We develop a general algorithm for this question, which applies to a large range of “shapeconstrained” properties, including monotone, logconcave, tmodal, piecewisepolynomial, and Poisson Binomial distributions. Moreover, for all cases considered, our algorithm has nearoptimal sample complexity with regard to the domain size and is computationally efficient. For most of these classes, we provide the first nontrivial tester in the literature. In addition, we also describe a generic method to prove lower bounds for this problem, and use it to show our upper bounds are nearly tight. Finally, we extend some of our techniques to tolerant testing, deriving nearly–tight upper and lower bounds for the corresponding questions.
 Award ID(s):
 1650733
 Publication Date:
 NSFPAR ID:
 10078631
 Journal Name:
 Theory of computing systems
 Volume:
 62
 Issue:
 1
 Page Range or eLocationID:
 462
 ISSN:
 14330490
 Sponsoring Org:
 National Science Foundation
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