How to Order Sushi A Nonparametric Approach to Modeling Rank Data

Rank data is often encountered in our daily lives (e.g. sports team rankings, horse races, voting). The data is deceptively simple, yet learning from the data is far from straightforward. Traditional random utility models (RUMs), such as the Plackett-Luce RUM and Normal RUM, seek to capture the structure of rank data via distributional assumptions on latent utilities. This can make infer-ence tractable, but leaves the models inexpressive and unable to fully capture features of data. I propose a new class of nonparametric random utility models (NPRUMs) for rank data, and present an estimation algorithm based on variational Monte Carlo expectation-maximization and kernel density methods. I show that NPRUMs provide better insights into random utilities in different settings, such as elections and sushi preferences. In particular, the model outperforms existing models in terms of out-of-sample likelihood, rank smoothing, and rank completion. iii Acknowledgments Firstly, I would like to thank my thesis advisor David Parkes for his encouragement, support, and time during my work on this thesis. Your advice, instruction, and high expectations have bee