Fixed-point algorithms for learning determinantal point processes
This work addresses the computational bottleneck in learning DPPs, which are used for modeling probabilities over subsets in machine learning applications, though it appears incremental as it improves upon existing methods rather than introducing a new paradigm.
The paper tackled the problem of learning the kernel of determinantal point processes (DPPs) from data, and developed a new fixed-point algorithm that is simpler, achieves comparable or better local maxima, and runs an order of magnitude faster on large problems.
Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique.