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About this paper
Onur Teymur, Jackson Gorham, Marina Riabiz, Chris. J. Oates
Researchers from Newcastle University and the Alan Turing Institute developed non-myopic and mini-batching algorithms for optimal quantization of probability measures using Maximum Mean Discrepancy (MMD) from finite candidate sets. These methods demonstrate superior statistical efficiency, achieving lower MMD values for a given number of points, and improve computational tractability for large datasets, especially in tasks like MCMC thinning.
Key insights
- Non-myopic selection strategies (simultaneously choosing multiple points) are statistically more efficient than myopic greedy approaches, leading to better overall approximations.
- The proposed non-myopic and mini-batch algorithms for MMD/KSD quantization from finite candidate sets are theoretically consistent and come with finite-sample error bounds, which are notably independent of the number of points selected simultaneously.
- Mini-batching effectively addresses the scalability challenges of non-myopic MMD minimization, making it computationally tractable for large candidate sets without sacrificing statistical efficiency.
Summary by alphaXiv.
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