DD-PREF: A Language for Expressing Preferences over Sets

In many application domains, it is useful to be able to represent and reason about a user's preferences over sets of objects. We present a representation language, DD-PREF (for Diversity and Depth PREFerences), for specifying the desired diversity and depth of sets of objects where each object is represented as a vector of feature values. A strong diversity preference for a particular feature indicates that the user would like the set to include objects whose values are evenly dispersed across the range of possible values for that feature. A strong depth preference for a feature indicates that the user is interested in specific target values or ranges. Diversity and depth are complementary, but are not necessarily opposites. We define an objective function that, when maximized, identifies the subset of objects that best satisfies a statement of preferences in DD-PREF. Exhaustively searching the space of all possible subsets is intractable for large problem spaces; therefore, we also present an efficient greedy algorithm for generating preferred object subsets. We demonstrate the expressive power of DD-PREF and the performance of our greedy algorithm by encoding and applying qualitatively different preferences for multiple tasks on a blocks world data set. Finally, we provide experimental results for a collection of Mars rover images, demonstrating that we can successfully capture individual preferences of different users, and use them to retrieve high-quality image subsets.