Victor-Emmanuel Brunel: Negative Association and Discrete Determinantal Point Processes

Discrete Determinantal Point Processes (DPPs) form a class of probability distributions that can describe the random selection of items from a finite or countable collection. They naturally arise in many problems in probability theory, and they have gained a lot of attention in machine learning, due to both their modeling flexibility and their tractability. In the finite case, a DPP is parametrized by a matrix, whose principal minors are the weights given by the DPP to each possible subset of items. When the matrix is symmetric, the DPP has a very special property, called Negative Association. Thanks to this property, symmetric DPPs enforce diversity within the randomly selected items, which is a feature that is sought for in many applications of Machine Learning, such as recommendation systems.