论文标题
凸电势流：具有最佳运输和凸优化的通用概率分布
Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization
论文作者
论文摘要
基于流的模型是设计具有可拖动密度的概率模型的强大工具。本文介绍了凸电势流（CP-Flow），这是一种受最佳传输（OT）理论启发的可逆模型的自然参数化。 CP-Flows是强烈凸出神经潜在功能的梯度图。凸度意味着可逆性，并使我们能够求助于凸优化以求解凸共轭以进行有效反转。为了实现最大的似然训练，我们得出了Jacobian对数确定因子的新梯度估计器，该梯度涉及使用共轭梯度方法求解反Hessian矢量产物。梯度估计器具有恒定的内存成本，可以通过降低凸优化常规的误差耐度水平来有效地公正。从理论上讲，我们证明CP-Flows是通用密度近似器，并且在OT意义上是最佳的。我们的经验结果表明，CP-Flow在密度估计和变异推断的标准基准方面竞争性能。
Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal transport (OT) theory. CP-Flows are the gradient map of a strongly convex neural potential function. The convexity implies invertibility and allows us to resort to convex optimization to solve the convex conjugate for efficient inversion. To enable maximum likelihood training, we derive a new gradient estimator of the log-determinant of the Jacobian, which involves solving an inverse-Hessian vector product using the conjugate gradient method. The gradient estimator has constant-memory cost, and can be made effectively unbiased by reducing the error tolerance level of the convex optimization routine. Theoretically, we prove that CP-Flows are universal density approximators and are optimal in the OT sense. Our empirical results show that CP-Flow performs competitively on standard benchmarks of density estimation and variational inference.
