论文标题
通过不断发展的措施卷积的对抗性最佳运输
Adversarial Optimal Transport Through The Convolution Of Kernels With Evolving Measures
论文作者
论文摘要
提出了一种新型算法来解决基于样本的最佳运输问题。推动前进条件的对抗性配方使用一种测试功能作为自适应内核与潜在变量$ b $上不断发展的概率分布$ν$之间的卷积。通过其模拟近似于$ b^i（t）$ $ν$的模拟，测试功能的参数化减少以确定这些样品的流量。在离散时间步骤中离散的流量$ t_n $是由基本地图的组成构建的。最佳运输还遵循双重性，必须遵循测试功能的梯度。测试函数作为分布的蒙特卡洛模拟的表示使算法鲁棒至维度，并且其在不记忆的流动下的演变可从简单的参数转换产生丰富的复杂图。用数值示例说明了该算法。
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability distribution $ν$ over a latent variable $b$. Approximating this convolution by its simulation over evolving samples $b^i(t)$ of $ν$, the parameterization of the test function reduces to determining the flow of these samples. This flow, discretized over discrete time steps $t_n$, is built from the composition of elementary maps. The optimal transport also follows a flow that, by duality, must follow the gradient of the test function. The representation of the test function as the Monte Carlo simulation of a distribution makes the algorithm robust to dimensionality, and its evolution under a memory-less flow produces rich, complex maps from simple parametric transformations. The algorithm is illustrated with numerical examples.
