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Workshop: NeurIPS 2022 Workshop on Score-Based Methods

Dimension reduction via score ratio matching

Michael Brennan · Ricardo Baptista · Youssef Marzouk


We propose a method to detect a low-dimensional subspace where a non-Gaussian target distribution departs from a known reference distribution (e.g., a standard Gaussian). We identify this subspace from gradients of the log-ratio between the target and reference densities, which we call the score ratio. Given only samples from the target distribution, we estimate these gradients via score ratio matching, with a tailored parameterization and a regularization method that expose the low-dimensional structure we seek. We show that our approach outperforms standard score matching for dimension reduction of in-class distributions, and that several benchmark UCI datasets in fact exhibit this type of low dimensionality.

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