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arXiv Machine Learning

Sparse Dictionary Learning for Measure-Valued Data via Linearized Optimal Transport: Efficient Algorithms and Sample Complexity

The paper introduces a dictionary learning framework for probability measure-valued data by embedding measures into Hilbert spaces using features derived from optimal transport geometry. It learns data‑adapted dictionaries through sparse autoencoder parameterizations, yielding fast, scalable representations of probability measures as sparse finite‑dimensional codes. The authors demonstrate the method on hyperspectral images, geometric point clouds, and document embeddings from large language models, and provide generalization bounds and covering number results for optimal transport and entropic transport map dictionaries.

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