Wasserstein Projection Pursuit of Non-Gaussian Signals

• URL: http://arxiv.org/abs/2302.12693v1
• Date: Fri, 24 Feb 2023 15:36:51 GMT
• Title: Wasserstein Projection Pursuit of Non-Gaussian Signals
• Authors: Satyaki Mukherjee, Soumendu Sundar Mukherjee, Debarghya Ghoshdastidar
• Abstract summary: We consider the problem of locating interesting directions in a $k$-dimensional non-Gaussian subspace of interesting features in a high-dimensional data cloud. Under a generative model, we prove rigorous statistical guarantees on the accuracy of approxing this unknown subspace. Our results operate in the regime where the data dimensionality is comparable to the sample size.
• Score: 8.789656856095947
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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