# Compressive Statistical Learning with Random Feature Moments

arXiv: https://arxiv.org/abs/1706.07180 · HTML: https://mlsanity.com/paper/1706.07180/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2017.

## Built on by (most cited first, 11 of 11)

- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [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)
- [Compressive Recovery of Sparse Precision Matrices](https://mlsanity.com/paper/2311.04673/) (2023)
- [Sketch and shift: a robust decoder for compressive clustering](https://mlsanity.com/paper/2312.09940/) (2023)
- [Asymmetric compressive learning guarantees with applications to quantized sketches](https://mlsanity.com/paper/2104.10061/) (2021)
- [Compressive Independent Component Analysis: Theory and Algorithms](https://mlsanity.com/paper/2110.08045/) (2021)
- [M2M: A general method to perform various data analysis tasks from a differentially private sketch](https://mlsanity.com/paper/2211.14062/) (2022)
- [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)
- [Compressive Meta-Learning](https://mlsanity.com/paper/2508.11090/) (2025)

## Abstract (arXiv)

We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed 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. A near-minimizer of the risk is computed from the sketch through the solution of a nonlinear least squares problem. We investigate sufficient sketch sizes to control the generalization error of this procedure. The framework is illustrated on compressive PCA, compressive clustering, and compressive Gaussian mixture Modeling with fixed known variance. The latter two are further developed in a companion paper.