On Learning Probabilistic Partial Lexicographic Preference Trees

Proposed by Liu and Truszczynski [1], partial lex-icographic preference trees, PLP-trees, for short, are intuitive and predictive data structures used to model qualitative user preferences over combinatorial domains. In this work, we introduce uncertainty into PLP-trees to propose probabilistic partial lexicographic preference trees, or PPLP-trees. We define such formalism, where uncertainty exhibits in the probability distributions on selecting both the next important feature throughout the model and the preferred value in the domain of every feature. We then define semantics of PPLP-trees in terms of the probability of some object strictly preferred over another object, the probability of some object equivalent with another object, and the probability of some object being optimal. We show that these probabilities can be computed in time polynomial in the size of the tree. To this end, we study the problem of passive learning of PPLP-trees from user examples and demonstrate our learning algorithm, a polynomial time greedy heuristic, bound by a branching factor throughout the construction of the tree.