  Clicking data, which exists in abundance and contains objective user
preference information, is widely used to produce personalized recommendations
in web-based applications. Current popular recommendation algorithms, typically
based on matrix factorizations, often have high accuracy and achieve good
clickthrough rates. However, diversity of the recommended items, which can
greatly enhance user experiences, is often overlooked. Moreover, most
algorithms do not produce interpretable uncertainty quantifications of the
recommendations. In this work, we propose the Bayesian Mallows for Clicking
Data (BMCD) method, which augments clicking data into compatible full ranking
vectors by enforcing all the clicked items to be top-ranked. User preferences
are learned using a Mallows ranking model. Bayesian inference leads to
interpretable uncertainties of each individual recommendation, and we also
propose a method to make personalized recommendations based on such
uncertainties. With a simulation study and a real life data example, we
demonstrate that compared to state-of-the-art matrix factorization, BMCD makes
personalized recommendations with similar accuracy, while achieving much higher
level of diversity, and producing interpretable and actionable uncertainty
estimation.
