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Learning Signed Determinantal Point Processes through the Principal Minor Assignment Problem

by   Victor-Emmanuel Brunel, et al.

Symmetric determinantal point processes (DPP's) are a class of probabilistic models that encode the random selection of items that exhibit a repulsive behavior. They have attracted a lot of attention in machine learning, when returning diverse sets of items is sought for. Sampling and learning these symmetric DPP's is pretty well understood. In this work, we consider a new class of DPP's, which we call signed DPP's, where we break the symmetry and allow attractive behaviors. We set the ground for learning signed DPP's through a method of moments, by solving the so called principal assignment problem for a class of matrices K that satisfy K_i,j=± K_j,i, i≠ j, in polynomial time.


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