Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912558751940608 |
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| author | Zhao, Peiqi Rodríguez, Carlos E. Mena, Ramsés H. Walker, Stephen G. |
| author_facet | Zhao, Peiqi Rodríguez, Carlos E. Mena, Ramsés H. Walker, Stephen G. |
| contents | Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer a compact yet informative representation of the original data. We build on this idea to introduce a generative modeling framework based on random weighted support points, where the randomness arises from a weighting scheme inspired by the Dirichlet process and the Bayesian bootstrap. The proposed method generates diverse and interpretable sample sets from a fixed dataset, without relying on probabilistic modeling assumptions or neural network architectures. We present the theoretical formulation of the method and develop an efficient optimization algorithm based on the Convex--Concave Procedure (CCP). Empirical results on the MNIST and CelebA-HQ datasets show that our approach produces high-quality and diverse outputs at a fraction of the computational cost of black-box alternatives such as Generative Adversarial Networks (GANs) or Denoising Diffusion Probabilistic Models (DDPMs). These results suggest that random weighted support points offer a principled, scalable, and interpretable alternative for generative modeling. A key feature is their ability to produce genuinely interpolative samples that preserve underlying data structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling Zhao, Peiqi Rodríguez, Carlos E. Mena, Ramsés H. Walker, Stephen G. Machine Learning Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer a compact yet informative representation of the original data. We build on this idea to introduce a generative modeling framework based on random weighted support points, where the randomness arises from a weighting scheme inspired by the Dirichlet process and the Bayesian bootstrap. The proposed method generates diverse and interpretable sample sets from a fixed dataset, without relying on probabilistic modeling assumptions or neural network architectures. We present the theoretical formulation of the method and develop an efficient optimization algorithm based on the Convex--Concave Procedure (CCP). Empirical results on the MNIST and CelebA-HQ datasets show that our approach produces high-quality and diverse outputs at a fraction of the computational cost of black-box alternatives such as Generative Adversarial Networks (GANs) or Denoising Diffusion Probabilistic Models (DDPMs). These results suggest that random weighted support points offer a principled, scalable, and interpretable alternative for generative modeling. A key feature is their ability to produce genuinely interpolative samples that preserve underlying data structure. |
| title | Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.21255 |