标题： CINDES：分类诱导神经密度估计器和模拟器 显示英文标题

标题： CINDES: Classification induced neural density estimator and simulator

摘要： 基于神经网络的方法在（无）条件密度估计中最近引起了广泛关注，因为各种神经密度估计器在真实数据实验中表现优于传统方法。 尽管取得了这些经验上的成功，但由于需要确保非负性和单位质量约束，实现起来可能具有挑战性，理论理解仍然有限。 特别是，当底层密度表现出低维结构时，这些估计器是否能够自适应地实现更快的收敛速率尚不清楚。 本文通过提出一种与结构无关的神经密度估计器来弥补这些差距，该估计器具有（i）易于实现和（ii）可证明的自适应性，在真实密度具有低维组合结构时能够获得更快的收敛速度。 我们工作的另一个主要贡献是表明所提出的估计器可以自然地融入生成采样流程中，尤其是在基于得分的扩散模型中，当底层密度具有结构时，它能够实现可证明的更快收敛。 我们通过广泛的模拟和一个真实数据应用验证了其性能。 显示英文摘要

摘要： Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator that is (i) straightforward to implement and (ii) provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application.