Efficient Sampling for k-Determinantal Point Processes
This work addresses the scalability problem for researchers and practitioners using DPPs to model diversity in applications like recommendation systems or document summarization, though it is an incremental improvement over existing sampling methods.
The paper tackles the computational bottleneck of cubic-complexity matrix operations in sampling from k-Determinantal Point Processes (k-DPPs) for large datasets, proposing a two-stage method using coresets that achieves more accurate samples than previous approaches.
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks such as sampling. In light of this, we propose a new method for approximate sampling from discrete $k$-DPPs. Our method takes advantage of the diversity property of subsets sampled from a DPP, and proceeds in two stages: first it constructs coresets for the ground set of items; thereafter, it efficiently samples subsets based on the constructed coresets. As opposed to previous approaches, our algorithm aims to minimize the total variation distance to the original distribution. Experiments on both synthetic and real datasets indicate that our sampling algorithm works efficiently on large data sets, and yields more accurate samples than previous approaches.