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

## TL;DR

This paper introduces a novel generative modeling approach using random weighted support points inspired by Bayesian methods, offering an interpretable, scalable, and efficient alternative to neural network-based models like GANs and DDPMs.

## Contribution

It develops a new framework for generative modeling based on random weighted support points with a theoretical foundation and an efficient optimization algorithm, avoiding neural networks.

## Key findings

- Produces high-quality, diverse samples on MNIST and CelebA-HQ
- Achieves comparable results at lower computational cost
- Generates interpolative samples that preserve data structure

## 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.