# Wasserstein Projection Pursuit of Non-Gaussian Signals

arXiv: https://arxiv.org/abs/2302.12693 · HTML: https://mlsanity.com/paper/2302.12693/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 4 of 4)

- [Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors](https://mlsanity.com/paper/1512.02337/) (2015)
- [Optimal Spectral Recovery of a Planted Vector in a Subspace](https://mlsanity.com/paper/2105.15081/) (2021)
- [Statistical-Computational Trade-offs in Tensor PCA and Related Problems via Communication Complexity](https://mlsanity.com/paper/2204.07526/) (2022)
- [Overparametrized linear dimensionality reductions: From projection pursuit to two-layer neural networks](https://mlsanity.com/paper/2206.06526/) (2022)

## Built on by (most cited first, 3 of 3)

- [Contrast-Free ICA and Causal Inference via Wasserstein Distances to the Gaussian](https://mlsanity.com/paper/2607.12832/) (2026)
- [Linear Independent Component Analysis via Optimal Transport](https://mlsanity.com/paper/2607.14081/) (2026)
- [Search Dimension in Unlabeled Projection Pursuit: A Scaling Law for Subspace Restriction](https://mlsanity.com/paper/2609.37917/) (2026)

## Abstract (arXiv)

We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a k-dimensional non-Gaussian subspace of interesting features. We use a projection pursuit approach -- we search for mutually orthogonal unit directions which maximise the 2-Wasserstein distance of the empirical distribution of data-projections along these directions from a standard Gaussian. Under a generative model, where there is a underlying (unknown) low-dimensional non-Gaussian subspace, we prove rigorous statistical guarantees on the accuracy of approximating this unknown subspace by the directions found by our projection pursuit approach. Our results operate in the regime where the data dimensionality is comparable to the sample size, and thus supplement the recent literature on the non-feasibility of locating interesting directions via projection pursuit in the complementary regime where the data dimensionality is much larger than the sample size.