mlsanityData to 14 Oct 2026

Bilateral Distribution Compression: Reducing Both Data Size and Dimensionality

arXiv 2509.17543 ↗First posted 22 Sep 2025stat.ML cs.LG stat.MEcited by 0

Not on the map. Why?

Abstract (arXiv)

Existing distribution compression methods reduce the number of observations in a dataset by minimising the Maximum Mean Discrepancy (MMD) between original and compressed sets, but modern datasets are often large in both sample size and dimensionality. We propose Bilateral Distribution Compression (BDC), a two-stage framework that compresses along both axes while preserving the underlying distribution, with overall linear time and memory complexity in dataset size and dimension. Central to BDC is the Decoded MMD (DMMD), which we introduce to quantify the discrepancy between the original data and a compressed set decoded from a low-dimensional latent space. BDC proceeds by (i) learning a low-dimensional projection using the Reconstruction MMD (RMMD), and (ii) optimising a latent compressed set with the Encoded MMD (EMMD). We show that this procedure minimises the DMMD, guaranteeing that the compressed set faithfully represents the original distribution. Experiments show that BDC can achieve comparable or superior downstream task performance to ambient-space compression at substantially lower cost and with significantly higher rates of compression.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 28 of its 83 references that are in the map. First posted on arXiv 22 Sep 2025.

Builds on

28 of 83 references.

References · 28

  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  2. 2017GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networkscited by 834
  3. 2016Deep Transfer Learning with Joint Adaptation Networkscited by 612
  4. 2021Dataset Condensation with Distribution Matchingcited by 365
  5. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 364
  6. 2018Riemannian Adaptive Optimization Methodscited by 194
  7. 2020The Computational Limits of Deep Learningcited by 193
  8. 2019Maximum Mean Discrepancy Gradient Flowcited by 127
  9. 2023Generalizing Dataset Distillation via Deep Generative Priorcited by 126
  10. 2023Improved Distribution Matching for Dataset Condensationcited by 124
  11. 2020A Measure-Theoretic Approach to Kernel Conditional Mean Embeddingscited by 86
  12. 2020Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transformcited by 80
16 more
  1. 2021Scikit-dimension: a Python package for intrinsic dimension estimationcited by 68
  2. 2023Engression: Extrapolation through the Lens of Distributional Regressioncited by 51
  3. 2023M3D: Dataset Condensation by Minimizing Maximum Mean Discrepancycited by 49
  4. 2021Kernel Thinningcited by 47
  5. 2017Characteristic and Universal Tensor Product Kernelscited by 41
  6. 2016Support pointscited by 39
  7. 2021Generalized Kernel Thinningcited by 29
  8. 2022Statistical exploration of the Manifold Hypothesiscited by 29
  9. 2021Distribution Compression in Near-linear Timecited by 19
  10. 2021Empirical comparison between autoencoders and traditional dimensionality reduction methodscited by 13
  11. 2024Distributional Principal Autoencoderscited by 11
  12. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  13. 2021Bayesian data selectioncited by 6
  14. 2020Optimisation of Large Wave Farms using a Multi-strategy Evolutionary Frameworkcited by 5
  15. 2025Distributional Autoencoders Know the Scorecited by 3
  16. 2025Conditional Distribution Compression via the Kernel Conditional Mean Embeddingcited by 1

Built on by

Not cited yet.