For questions about the Wasserstein metric/distance (or Kantorovich–Rubinstein metric), which is a metric (distance function) defined between probability distributions.
Questions tagged [wasserstein-metric]
6 questions
7
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2 answers
Why is KL divergence used so often in Machine Learning?
The KL Divergence is quite easy to compute in closed form for simple distributions -such as Gaussians- but has some not-very-nice properties. For example, it is not symmetrical (thus it is not a metric) and it does not respect the triangular…
Federico Taschin
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3
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1 answer
Are there some notions of distance between two policies?
I want to determine some distance between two policies $\pi_1 (a \mid s)$ and $\pi_2 (a \mid s)$, i.e. something like $\vert \vert \pi_1 (a \mid s) - \pi_2(a \mid s) \vert \vert$, where $\pi_i (a\mid s)$ is the vector $(\pi_i (a_1 \mid s), \dots,…
Felix P.
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3
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1 answer
What is the reason for mode collapse in GAN as opposed to WGAN?
In this article I am reading:
$D_{KL}$ gives us inifity when two distributions are disjoint. The value of $D_{JS}$ has sudden jump, not differentiable at $\theta=0$. Only Wasserstein metric provides a smooth measure, which is super helpful for a…
craft
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votes
1 answer
Why do we use a linear interpolation of fake and real data to penalize the gradient of discriminator in WGAN-GP
I'm trying to better frame/summarize the formulations and motivations behind Wasserstein GAN with gradient penalty, based on my understanding.
For the basic GAN we are trying to optimize the following quantity:
$$\min_\theta \max_\phi \mathbb{E}_{x…
James Arten
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vote
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WGAN-GP Loss formalization
I have to write the formalization of the loss function of my network, built following the WGAN-GP model. The discriminator takes 3 consecutive images as input (such as 3 consecutive frames of a video) and must evaluate if the intermediate image is a…
Gibser
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Under what conditions can one find the optimal critic in WGAN?
The Kantorovich-Rubinstein duality for the optimal transport problem implies that the Wasserstein distance between two distributions $\mu_1$ and $\mu_2$ can be computed as (equation 2 in section 3 in the WGAN paper)
$$W(\mu_1,\mu_2)=\underset{f\in…
Subho
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