在凸多面体上构建高效概率模型，支持快速采样与密度估计。
Flows on convex polytopes
- 将多面体映射到单位球，利用球面上的流模型实现变换
- 仅需顶点信息即可构建流模型，精度媲美现有方法
- 适合代谢通量分析等高维多面体分布建模任务
我们提出一种在凸多面体上建模复杂高维分布的框架，利用黎曼流形上的离散与连续归一化流最新进展。证明任意满维多面体与单位球同胚，通过在球面上定义流并映射回原多面体实现建模。当仅有顶点表示时，采用最大熵重心坐标与Aitchison几何构造流。实验受代谢通量分析启发，结果表明该方法在密度估计、采样精度上表现优异，且训练和推理速度快。
原文摘要 · Abstract (English)
We present a framework for modeling complex, high-dimensional distributions on convex polytopes by leveraging recent advances in discrete and continuous normalizing flows on Riemannian manifolds. We show that any full-dimensional polytope is homeomorphic to a unit ball, and our approach harnesses flows defined on the ball, mapping them back to the original polytope. Furthermore, we introduce a strategy to construct flows when only the vertex representation of a polytope is available, employing maximum entropy barycentric coordinates and Aitchison geometry. Our experiments take inspiration from applications in metabolic flux analysis and demonstrate that our methods achieve competitive density estimation, sampling accuracy, as well as fast training and inference times.
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