论文标题
广义切成薄片的距离的快速近似
Fast Approximation of the Generalized Sliced-Wasserstein Distance
论文作者
论文摘要
一般切片的Wasserstein距离是切成薄片的Wasserstein距离的变体，它通过给定的定义函数利用非线性投影的功率，以更好地捕获概率分布的复杂结构。与切成薄片的Wasserstein距离相似，将广义切成薄片的Wasserstein定义为对随机投影的期望，该预测可以通过蒙特卡洛方法近似。但是，在高维设置中，该近似值的复杂性可能很昂贵。为此，我们建议在定义函数是多项式函数，圆形函数和神经网络类型函数时，通过使用随机投影的浓度来形成一般切片的瓦斯泰因距离的确定性和快速近似值。我们的近似取决于重要结果，即高维随机矢量的一维投影大约是高斯。
Generalized sliced Wasserstein distance is a variant of sliced Wasserstein distance that exploits the power of non-linear projection through a given defining function to better capture the complex structures of the probability distributions. Similar to sliced Wasserstein distance, generalized sliced Wasserstein is defined as an expectation over random projections which can be approximated by the Monte Carlo method. However, the complexity of that approximation can be expensive in high-dimensional settings. To that end, we propose to form deterministic and fast approximations of the generalized sliced Wasserstein distance by using the concentration of random projections when the defining functions are polynomial function, circular function, and neural network type function. Our approximations hinge upon an important result that one-dimensional projections of a high-dimensional random vector are approximately Gaussian.
