Flexible Modeling of Diversity with Strongly Log-Concave Distributions
This work addresses the need for more flexible diversity modeling in machine learning, offering incremental improvements over existing strongly Rayleigh methods.
The paper tackled the problem of modeling diversity with strongly log-concave distributions, which extend strongly Rayleigh distributions to allow easier control over diversity, and developed sampling and mode-finding tools with theoretical guarantees like mixing time bounds and optimization guarantees.
Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lack an easy control over how they express diversity. We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance. We develop two fundamental tools needed to apply SLC distributions to learning and inference: sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds. For mode finding, we establish a weak log-submodularity property for SLC functions and derive optimization guarantees for a distorted greedy algorithm.