Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling

• URL: http://arxiv.org/abs/2508.21255v1
• Date: Thu, 28 Aug 2025 22:58:39 GMT
• Title: Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling
• Authors: Peiqi Zhao, Carlos E. Rodríguez, Ramsés H. Mena, Stephen G. Walker,
• Abstract summary: We introduce a generative modeling framework based on random weighted support points.<n>The proposed method generates diverse and interpretable sample sets from a fixed dataset.<n>We show that our approach produces high-quality and diverse outputs at a fraction of the computational cost of black-box alternatives.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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