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Determinantal point processes (DPPs) are distributions over sets of itemsthat model diversity using kernels. Their applications in machine learninginclude summary extraction and recommendation systems. Yet, the cost ofsampling from a DPP is prohibitive in large-scale applications, which hastriggered an effort towards efficient approximate samplers. We build a novelMCMC sampler that combines ideas from combinatorial geometry, linearprogramming, and Monte Carlo methods to sample from DPPs with a fixed samplecardinality, also called projection DPPs. Our sampler leverages the ability ofthe hit-and-run MCMC kernel to efficiently move across convex bodies. Previoustheoretical results yield a fast mixing time of our chain when targeting adistribution that is close to a projection DPP, but not a DPP in general. Ourempirical results demonstrate that this extends to sampling projection DPPs,i.e., our sampler is more sample-efficient than previous approaches which inturn translates to faster convergence when dealing with costly-to-evaluatefunctions, such as summary extraction in our experiments.

Zonotope hit-and-run for efficient sampling from projection DPPs