Zonotope hit-and-run for efficient sampling from projection DPPs
This work addresses a bottleneck in machine learning applications such as summary extraction and recommendation systems by providing an incremental improvement in sampling efficiency for projection DPPs.
The paper tackles the problem of efficiently sampling from projection determinantal point processes (DPPs), which are computationally prohibitive for large-scale applications, by introducing a novel MCMC sampler that achieves faster convergence and greater sample efficiency than previous approaches, as demonstrated in experiments like summary extraction.
Determinantal point processes (DPPs) are distributions over sets of items that model diversity using kernels. Their applications in machine learning include summary extraction and recommendation systems. Yet, the cost of sampling from a DPP is prohibitive in large-scale applications, which has triggered an effort towards efficient approximate samplers. We build a novel MCMC sampler that combines ideas from combinatorial geometry, linear programming, and Monte Carlo methods to sample from DPPs with a fixed sample cardinality, also called projection DPPs. Our sampler leverages the ability of the hit-and-run MCMC kernel to efficiently move across convex bodies. Previous theoretical results yield a fast mixing time of our chain when targeting a distribution that is close to a projection DPP, but not a DPP in general. Our empirical results demonstrate that this extends to sampling projection DPPs, i.e., our sampler is more sample-efficient than previous approaches which in turn translates to faster convergence when dealing with costly-to-evaluate functions, such as summary extraction in our experiments.