On the (In)tractability of Computing Normalizing Constants for the Product of Determinantal Point Processes

The last few lectures have been about online combinatorial optimization, learning bandits, etc. Today we will switch gears to talk about probabilistic models of diversity. These models increase the probability of sets that are more spread out and diverse. For example, consider the problem of detecting where the people are in a given picture. Ideally, you would expect people to be spatially far from each other, and not standing on top of each other. We want probabilistic models that capture negative correlations, i.e., including an element a makes it less likely to include another element b.