# Expectation-Maximization for Learning Determinantal Point Processes

arXiv: https://arxiv.org/abs/1411.1088 · HTML: https://mlsanity.com/paper/1411.1088/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2014.

## Built on by (most cited first, 20 of 20)

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- [Learning Neural Set Functions Under the Optimal Subset Oracle](https://mlsanity.com/paper/2203.01693/) (2022)
- [Learning from the Dark: Boosting Graph Convolutional Neural Networks with Diverse Negative Samples](https://mlsanity.com/paper/2210.00728/) (2022)
- [Graph Convolutional Neural Networks with Diverse Negative Samples via Decomposed Determinant Point Processes](https://mlsanity.com/paper/2212.02055/) (2022)
- [Neural Estimation of Submodular Functions with Applications to Differentiable Subset Selection](https://mlsanity.com/paper/2210.11033/) (2022)
- [Hardness of Maximum Likelihood Learning of DPPs](https://mlsanity.com/paper/2205.12377/) (2022)
- [Advances in Set Function Learning: A Survey of Techniques and Applications](https://mlsanity.com/paper/2501.14991/) (2025)
- [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)
- [From DPPs to k-DPPs: identifiability analysis via spectral decomposition](https://mlsanity.com/paper/2605.25526/) (2026)
- [Enhancing Neural Subset Selection: Integrating Background Information into Set Representations](https://mlsanity.com/paper/2402.03139/) (2024)
- [Learning Set Functions with Implicit Differentiation](https://mlsanity.com/paper/2412.11239/) (2024)
- [Explicit and Implicit Pattern Relation Analysis for Discovering Actionable Negative Sequences](https://mlsanity.com/paper/2204.03571/) (2022)
- [Duality induced by an embedding structure of determinantal point process](https://mlsanity.com/paper/2404.11024/) (2024)
- [Advancing Optimal Subset Oracle via Learning Relaxation of Neural Set Functions](https://mlsanity.com/paper/2607.11555/) (2026)
- [Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions](https://mlsanity.com/paper/2610.12829/) (2026)

## Abstract (arXiv)

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard. Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix, or learning weights for a linear combination of DPPs with fixed kernel matrices. In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure. We test our method on a real-world product recommendation task, and achieve relative gains of up to 16.5% in test log-likelihood compared to the naive approach of maximizing likelihood by projected gradient ascent on the entries of the kernel matrix.