Reviews: Contrastive Learning from Pairwise Measurements

The paper considers a family of statistical models for pairwise measurements, in which we observe scores that come from triplets of the form (user, item1, item2). The problem is to estimate the underlying score function of user-item pair, which is assumed to be low-rank, and the observation to be generated by a natural exponential family. The authors address the problem from a novel angle as a semiparametric estimation problem, which avoids the need to specify the log-partition function in the natural exponential family. A penalized contrastive estimator is derived and its consistency and error bound are analyzed. Numerical simulation supports the rate established in the bound.