Pairwise comparison data arises in various domains, including recommender systems, website ranking and social choice. There has been a recent surge of interest in studying permutation-based models, such as the noisy sorting model and the strong stochastic transitivity model, for ranking from pairwise comparisons. In this talk, I will focus on statistical estimation for the noisy sorting model given structured partial observations. The optimal rate of estimation is established up to a constant (resp. a logarithmic factor) for pairwise comparisons sampled according to an Erdős–Rényi graph (resp. certain classes of fixed graphs). In addition, I will discuss efficient algorithms that generalize the classical Borda count estimator. The talk is based on the following joint works with Jonathan Weed, Philippe Rigollet, Ashwin Pananjady, Vidya Muthukumar, Martin J. Wainwright, Thomas A. Courtade: https://arxiv.org/abs/1710.10388 https://arxiv.org/abs/1707.06217 Bio: Cheng Mao is a fifth-year graduate student in the Mathematics Department at MIT, working with Professor Philippe Rigollet. His broad research interests include statistics theory, machine learning and probability. Recently, he has been working on matrix and graph estimation problems with latent permutations. Cheng received his B.S. and M.A degrees in Mathematics from UCLA.