另一部分代表了两个分布形状上的差异。现在返回去看上面KL时候举的那个例子，它们之间的Wasserstein dista...
刚才的例子也告诉我们，Wasserstein distance是可以定义两个support不重合，甚至一点交集都没有的分布之间的距离的，而KL在这种情况并不适用。维基中也给出了两个正态分布的Wasserstein distance (p=2时候) 的公式，大家可以去看一下，正好是两部分的和，一部分代表了中心间的几何距离，另一部分代表了两个分布形状上...
Here, we propose a new information-geometrical theory that is a unified framework connecting the Wasserstein distance and Kullback-Leibler (KL) divergence. We primarily considered a discrete case consisting of $n$ elements and studied the geometry of the probability simplex $S_{n-1}$, which is...
2 WGAN 之前在《关于GAN的一些笔记》中写到了 Wasserstein distance 相较于 JS/KL divergence 的优越性。就算PG,PdataPG,Pdata之间没有重叠也可以衡量两个分布的距离。 当然,W(P,Q)=infγ∈Π(Pdata,PG)E(x,y)∼γ[∥x−y∥]W(P,Q)=infγ∈Π(Pdata,PG)E(x,y)∼γ[‖x−y‖]这种形式...
python实现: 7.推土机距离(Wassersteindistance、Earth Mover's Distance...熵就越大。分布越有序(或者说分布越集中),信息熵就越小。 欧氏距离损失经常用在线性回归问题(求解的是连续问题)中,而交叉熵损失经常用在逻辑回归问题(求解的是离散的分类问题)上,用来作为预测值和真实标签 ...
之前在《关于GAN的一些笔记》中写到了 Wasserstein distance 相较于 JS/KL divergence 的优越性。就算 $P_G, P_{data}$ 之间没有重叠也可以衡量两个分布的距离。 当然,$W(P,Q) = \inf\limits_{\gamma \in \Pi(P_{data},P_G)} E_{(x,y) \sim \gamma}[\left \| x-y \righ...
在学习Wasserstein距离,首先回顾在机器学习算法中,衡量两个分布相似程度的指标常常是KL散度(Kullback-Leibler Divergence)以及JS散度 (Jensen-Shannon Divergence)。 KL散度 KL散度描述的是,评价训练所得的概率分布p与目标分布q之间的距离,可以表示为 机器学习的算法最终的目的是缩小 ...
Since pioneering work of Hinton et al., knowledge distillation based on Kullback-Leibler Divergence (KL-Div) has been predominant, and recently its variants have achieved compelling performance. However, KL-Div only compares probabilities of the corresponding category between the teacher and student whi...
In information geometry, [17] studied the connec- tions between the Wasserstein distance and the Kullback-Leibler (KL) divergence employed by early GANs. They exploit the fact that by regularizing the Wasser- stein distance with entropy, the entropy relaxed Wasserstein distance introduces a ...
It is shown in [3] that KL-divergence, Jenson-Shannon and Wasserstein distance do not generalize, in the sense that the population distance cannot be approximated by an empir- ical distance when there are only a polynomial number of samples. To improve generalization, one popu...