# Training Gaussian Mixture Models at Scale via Coresets

arXiv: https://arxiv.org/abs/1703.08110 · HTML: https://mlsanity.com/paper/1703.08110/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2017.

## Built on by (most cited first, 30 of 38)

- [DataComp: In search of the next generation of multimodal datasets](https://mlsanity.com/paper/2304.14108/) (2023)
- [Efficient Dataset Distillation Using Random Feature Approximation](https://mlsanity.com/paper/2210.12067/) (2022)
- [Self-Guided Noise-Free Data Generation for Efficient Zero-Shot Learning](https://mlsanity.com/paper/2205.12679/) (2022)
- [Graph Condensation for Inductive Node Representation Learning](https://mlsanity.com/paper/2307.15967/) (2023)
- [Probabilistic Bilevel Coreset Selection](https://mlsanity.com/paper/2301.09880/) (2023)
- [Learning-Augmented k-means Clustering](https://mlsanity.com/paper/2110.14094/) (2021)
- [Towards Optimal Lower Bounds for k-median and k-means Coresets](https://mlsanity.com/paper/2202.12793/) (2022)
- [Triangle and Four Cycle Counting with Predictions in Graph Streams](https://mlsanity.com/paper/2203.09572/) (2022)
- [Unlocking the Potential of Federated Learning: The Symphony of Dataset Distillation via Deep Generative Latents](https://mlsanity.com/paper/2312.01537/) (2023)
- [Training Data Subset Selection for Regression with Controlled Generalization Error](https://mlsanity.com/paper/2106.12491/) (2021)
- [Coresets for Vertical Federated Learning: Regularized Linear Regression and K-Means Clustering](https://mlsanity.com/paper/2210.14664/) (2022)
- [Dimensionality Reduction for Wasserstein Barycenter](https://mlsanity.com/paper/2110.08991/) (2021)
- [Refined Coreset Selection: Towards Minimal Coreset Size under Model Performance Constraints](https://mlsanity.com/paper/2311.08675/) (2023)
- [Efficient Data Subset Selection to Generalize Training Across Models: Transductive and Inductive Networks](https://mlsanity.com/paper/2409.12255/) (2024)
- [Learning-Augmented Algorithms for Online Linear and Semidefinite Programming](https://mlsanity.com/paper/2209.10614/) (2022)
- [Coresets for Decision Trees of Signals](https://mlsanity.com/paper/2110.03195/) (2021)
- [Data Summarization via Bilevel Optimization](https://mlsanity.com/paper/2109.12534/) (2021)
- [Coresets for Time Series Clustering](https://mlsanity.com/paper/2110.15263/) (2021)
- [A Novel Sequential Coreset Method for Gradient Descent Algorithms](https://mlsanity.com/paper/2112.02504/) (2021)
- [Robust and Fully-Dynamic Coreset for Continuous-and-Bounded Learning (With Outliers) Problems](https://mlsanity.com/paper/2107.00068/) (2021)
- [Extending Contrastive Learning to Unsupervised Coreset Selection](https://mlsanity.com/paper/2103.03574/) (2021)
- [A sampling-based approach for efficient clustering in large datasets](https://mlsanity.com/paper/2112.14793/) (2021)
- [Robustness-preserving Lifelong Learning via Dataset Condensation](https://mlsanity.com/paper/2303.04183/) (2023)
- [Optimal Sample Selection Through Uncertainty Estimation and Its Application in Deep Learning](https://mlsanity.com/paper/2309.02476/) (2023)
- [Data Selection for ERMs](https://mlsanity.com/paper/2504.14572/) (2025)
- [DUSE: A Data Expansion Framework for Low-resource Automatic Modulation Recognition based on Active Learning](https://mlsanity.com/paper/2507.12011/) (2025)
- [Learning-Augmented Moment Estimation on Time-Decay Models](https://mlsanity.com/paper/2603.02488/) (2026)
- [ALLWAS: Active Learning on Language models in WASserstein space](https://mlsanity.com/paper/2109.01691/) (2021)
- [Coresets for Relational Data and The Applications](https://mlsanity.com/paper/2210.04249/) (2022)
- [Byzantine-tolerant distributed learning of finite mixture models](https://mlsanity.com/paper/2407.13980/) (2024)

## Abstract (arXiv)

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being independent of the data set size. Hence, one can harness computationally intensive algorithms to compute a good approximation on a significantly smaller data set. More importantly, such coresets can be efficiently constructed both in distributed and streaming settings and do not impose restrictions on the data generating process. Our results rely on a novel reduction of statistical estimation to problems in computational geometry and new combinatorial complexity results for mixtures of Gaussians. Empirical evaluation on several real-world datasets suggests that our coreset-based approach enables significant reduction in training-time with negligible approximation error.