Explicit Density Approximation for Neural Implicit Samplers Using a Bernstein-Based Convex Divergence

Authors: José Manuel de Frutos, Pablo M. Olmos, Manuel A. Vázquez, Joaquín Míguez
Venue: AISTATS 2026 · Spotlight
Links: AISTATS Spotlight · OpenReview · arXiv · PDF · Code

Overview

We introduce dual-ISL, a rank-based objective obtained by reversing the roles of the target and model distributions in ISL. This formulation is convex in the model density and provides a likelihood-free route to training neural implicit samplers while retaining strong regularity properties.

A key result is an explicit density approximation: the rank-based discrepancy admits an interpretation as an approximation of the density ratio in a Bernstein polynomial basis. This leads to closed-form truncated density estimates, convergence guarantees, and a natural sliced extension for multivariate data.

Relation to GANs and adversarial generative modeling

GANs and many other implicit generative models are trained through adversarial objectives because the model density is unavailable. Dual-ISL addresses the same likelihood-free setting without requiring an adversarial discriminator. Its convex formulation offers a different route to training neural implicit samplers and is therefore relevant to researchers looking for GAN alternatives, discriminator-free generative modeling, or more stable objectives for sample-based generators.

The explicit density approximation also provides additional interpretability compared with standard GAN training: the method yields a tractable Bernstein-polynomial approximation linked to the model/target density ratio, while retaining a sample-based training procedure.

Topics

dual-ISL · neural implicit samplers · implicit generative models · generative adversarial networks (GANs) · GAN training · adversarial training · GAN alternatives · discriminator-free generative modeling · mode collapse · training stability · explicit density approximation · Bernstein polynomials · convex divergence · likelihood-free learning · sliced divergences · density-ratio approximation

Abstract

The canonical abstract and conference record are available on OpenReview and the AISTATS Spotlight page.

BibTeX

@inproceedings{defrutos2026explicit,
  title={Explicit Density Approximation for Neural Implicit Samplers Using a Bernstein-Based Convex Divergence},
  author={de Frutos, Jos\'e Manuel and Olmos, Pablo M. and V\'azquez, Manuel A. and M\'iguez, Joaqu\'in},
  booktitle={Proceedings of the 29th International Conference on Artificial Intelligence and Statistics},
  year={2026},
  note={Spotlight}
}

Recommended citation: José Manuel de Frutos, Pablo M. Olmos, Manuel A. Vázquez, and Joaquín Míguez. (2026). "Explicit Density Approximation for Neural Implicit Samplers Using a Bernstein-Based Convex Divergence." AISTATS 2026, Spotlight.
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