  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.
