# Flexible Modeling of Diversity with Strongly Log-Concave Distributions

arXiv: https://arxiv.org/abs/1906.05413 · HTML: https://mlsanity.com/paper/1906.05413/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

## Built on by (most cited first, 6 of 6)

- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [Submodular + Concave](https://mlsanity.com/paper/2106.04769/) (2021)
- [Some Inapproximability Results of MAP Inference and Exponentiated Determinantal Point Processes](https://mlsanity.com/paper/2109.00727/) (2021)
- [Diverse Probabilistic Trajectory Forecasting with Admissibility Constraints](https://mlsanity.com/paper/2302.03462/) (2023)
- [Mixtures of All Trees](https://mlsanity.com/paper/2302.14202/) (2023)
- [Computational Complexity of Normalizing Constants for the Product of Determinantal Point Processes](https://mlsanity.com/paper/2111.14148/) (2021)

## Abstract (arXiv)

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.