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

Key points

• We learn data-adapted dictionaries through sparse autoencoder parameterizations, producing fast, scalable representations of probability measures as sparse finite-dimensional codes.1
• The resulting framework combines the rich, geometric structure of optimal transport with the interpretability and efficiency of sparse representation learning.1
• We also prove generalization bounds for sparse dictionary learning objectives on broad classes of $L^2$-valued measure embeddings, expressed in terms of the metric complexity of the atom class.1
• For optimal transport and entropic transport map dictionaries, we derive new covering number bounds that yield explicit rates.1

Sources (1)

• [1]Sparse Dictionary Learning for Measure-Valued Data via Linearized Optimal Transport: Efficient Algorithms and Sample Complexity
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 9, 03:15 AM

  We study dictionary learning for probability measure-valued data by embedding measures into Hilbert spaces using features derived from optimal transport geometry.

  We learn data-adapted dictionaries through sparse autoencoder parameterizations, producing fast, scalable representations of probability measures as sparse finite-dimensional codes.

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