Many recommendation systems produce result sets with large numbers of highly similar items. Diversifying these results is often accomplished with heuristics, which are impoverished models of users' desire for diversity. However, integrating more complex statistical models of diversity into large-scale, mature systems is challenging. Without a good match between the model's definition of diversity and users' perception of diversity, the model can easily degrade users' perception of the recommendations. In this work we present a statistical model of diversity based on determinantal point processes (DPPs). We train this model from examples of user preferences with a simple procedure that can be integrated into large and complex production systems relatively easily. We use an approximate inference algorithm to serve the model at scale, and empirical results on live YouTube homepage traffic show that this model, coupled with a re-ranking algorithm, yields substantial short- and long-term increases in user engagement.

Abstract. We prove properties of a process calculus that is designed for analysing security protocols. Our long-term goal is to develop a form of protocol analysis, consistent with standard cryptographic assumptions, that provides a language for expressing probabilistic polynomial-time protocol steps, a specification method based on a compositional form of equivalence, and a logical basis for reasoning about equivalence. The process calculus is a variant of CCS, with bounded replication and probabilistic polynomial-time expressions allowed in messages and boolean tests. To avoid inconsistency between security and nondeterminism, messages are scheduled probabilistically instead of nondeterministically. We prove that evaluation of any process expression halts in probabilistic polynomial time and define a form of asymptotic protocol equivalence that allows security properties to be expressed using observational equivalence, a standard relation from programming language theory that involves quantifying over all possible environments that might interact with the protocol. We develop a form of probabilistic bisimulation and use it to establish the soundness of an equational proof system based on observational equivalences. The proof system is illustrated by a formation derivation of the assertion, well-known in cryptography, that El Gamal encryption’s semantic security is equivalent to the (computational) Decision Diffie-Hellman assumption. This example demonstrates the power of probabilistic bisimulation and equational reasoning for protocol security.