# Fixed-point algorithms for learning determinantal point processes

arXiv: https://arxiv.org/abs/1508.00792 · HTML: https://mlsanity.com/paper/1508.00792/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2015.

## Built on by (most cited first, 14 of 14)

- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [Gaussian Determinantal Processes: a new model for directionality in data](https://mlsanity.com/paper/2111.09990/) (2021)
- [Hardness of Maximum Likelihood Learning of DPPs](https://mlsanity.com/paper/2205.12377/) (2022)
- [Scalable Sampling for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2201.08417/) (2022)
- [A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence](https://mlsanity.com/paper/2408.01022/) (2024)
- [Revisiting Frank-Wolfe for Structured Nonconvex Optimization](https://mlsanity.com/paper/2503.08921/) (2025)
- [On a class of geodesically convex optimization problems solved via Euclidean MM methods](https://mlsanity.com/paper/2206.11426/) (2022)
- [Learn2Extend: Extending sequences by retaining their statistical properties with mixture models](https://mlsanity.com/paper/2312.01507/) (2023)
- [Disciplined Geodesically Convex Programming](https://mlsanity.com/paper/2407.05261/) (2024)
- [Structured Regularization for Constrained Optimization on the SPD Manifold](https://mlsanity.com/paper/2410.09660/) (2024)
- [Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms](https://mlsanity.com/paper/2507.17545/) (2025)
- [Nonparametric estimation of continuous DPPs with kernel methods](https://mlsanity.com/paper/2106.14210/) (2021)
- [Explicit and Implicit Pattern Relation Analysis for Discovering Actionable Negative Sequences](https://mlsanity.com/paper/2204.03571/) (2022)
- [Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions](https://mlsanity.com/paper/2610.12829/) (2026)

## Abstract (arXiv)

Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique.