# Statistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling

arXiv: https://arxiv.org/abs/2004.08085 · HTML: https://mlsanity.com/paper/2004.08085/

## Key facts

- Cited by 7 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 17 Apr 2020.

## Built on by (most cited first, 7 of 7)

- [Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learning](https://mlsanity.com/paper/2112.00423/) (2021)
- [Mean Nystr"om Embeddings for Adaptive Compressive Learning](https://mlsanity.com/paper/2110.10996/) (2021)
- [Transformers as Unsupervised Learning Algorithms: A study on Gaussian Mixtures](https://mlsanity.com/paper/2505.11918/) (2025)
- [Compressive Recovery of Sparse Precision Matrices](https://mlsanity.com/paper/2311.04673/) (2023)
- [Asymmetric compressive learning guarantees with applications to quantized sketches](https://mlsanity.com/paper/2104.10061/) (2021)
- [Batch-less stochastic gradient descent for compressive learning of deep regularization for image denoising](https://mlsanity.com/paper/2310.03085/) (2023)
- [Effective regions and kernels in continuous sparse regularisation, with application to sketched mixtures](https://mlsanity.com/paper/2507.08444/) (2025)

## Abstract (arXiv)

We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The principle of compressive statistical learning is to compress a training collection, in one pass, into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task. We explicitly describe and analyze random feature functions which empirical averages preserve the needed information for compressive clustering and compressive Gaussian mixture modeling with fixed known variance, and establish sufficient sketch sizes given the problem dimensions.