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PreprintCC BY 4.0arXiv

MiniMMD: Minimization of MMD for Sampling, Inference and Integration

  • Zonghao Chen
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Abstract

Many problems in computational statistics and machine learning can be formulated as approximating a target distribution by minimizing a discrepancy over a restricted class of candidate distributions. This minimum-discrepancy viewpoint appears, for example, in numerical integration, sampling, generative modelling, and statistical inference, but these instances are often studied separately in the literature. This thesis develops the first unified treatment of these many problems through the minimization of the maximum mean discrepancy (MMD), a kernel-based discrepancy between probability measures. The central theme is that MMD is not only a statistically meaningful distance between probability distributions, but also a tractable optimization objective to design practical and efficient algorithms. This thesis summarizes the recent theoretical and empirical advancements of such minimum-MMD based algorithms.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026minimmd,
  title = {{MiniMMD: Minimization of MMD for Sampling, Inference and Integration}},
  author = {Zonghao Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38122},
  eprint = {2610.38122},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38122},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - MiniMMD: Minimization of MMD for Sampling, Inference and Integration
AU  - Zonghao Chen
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38122
UR  - https://arxiv.org/abs/2610.38122
AB  - Many problems in computational statistics and machine learning can be formulated as approximating a target distribution by minimizing a discrepancy over a restricted class of candidate distributions. This minimum-discrepancy viewpoint appears, for example, in numerical integration, sampling, generative modelling, and statistical inference, but these instances are often studied separately in the literature. This thesis develops the first unified treatment of these many problems through the minimization of the maximum mean discrepancy (MMD), a kernel-based discrepancy between probability measures. The central theme is that MMD is not only a statistically meaningful distance between probability distributions, but also a tractable optimization objective to design practical and efficient algorithms. This thesis summarizes the recent theoretical and empirical advancements of such minimum-MMD based algorithms.
ER  -