Table of Contents
Why use Wasserstein distance?
Why Wasserstein Distance Unlike other distance metrics like KL-divergence, Wasserstein distance provide a meaningful and smooth representation of the distance between distributions.
How is Wasserstein metric calculated?
The 2-Wasserstein metric is computed like 1-Wasserstein, except instead of summing the work values, you sum the squared work values and then take the square root. The 3-Wasserstein would be the cube root of the sum of cubed work values, and so on.
What is a Wasserstein Gan?
Wasserstein GAN, or WGAN, is a type of generative adversarial network that minimizes an approximation of the Earth-Mover’s distance (EM) rather than the Jensen-Shannon divergence as in the original GAN formulation.
Why Wasserstein is better than JS or KL divergence?
The reason why Wasserstein distance is better than JS or KL divergence is that when two distributions are located in lower dimensional manifolds without overlaps, Wasserstein distance can still provide a meaningful and smooth representation of the distance in-between.
Is Wasserstein an F divergence?
Given a p-Wasserstein metric or an f-divergence, which is defined between two probability mea- sures of the same dimension, we show that it naturally defines two different distances for probability measures µ and ν on spaces of different dimensions — we call these the embedding distance and projection distance …
What is mode collapse Gan?
Mode collapse happens when the generator can only produce a single type of output or a small set of outputs. This may happen due to problems in training, such as the generator finds a type of data that is easily able to fool the discriminator and thus keeps generating that one type.
What is integral probability metric?
Abstract. Given two probability measures, P and Q defined on a measurable space, S , the integral probability metric (IPM) is defined as γF(P,Q)=sup{∣∣∣∫SfdP−∫SfdQ∣∣∣:f∈F}, γ F ( P , Q ) = sup { | ∫ S f d P − ∫ S f d Q | : f ∈ F } , where F is a class of real-valued bounded measurable functions on S .
How does a GAN work?
Generative adversarial networks (GANs) are algorithmic architectures that use two neural networks, pitting one against the other (thus the “adversarial”) in order to generate new, synthetic instances of data that can pass for real data. They are used widely in image generation, video generation and voice generation.
What is Nash equilibrium in GAN?
In game theory, the GAN model converges when the discriminator and the generator reach a Nash equilibrium. This is the optimal point for the minimax equation below. The Nash equilibrium is x=y=0. This is the only state where the action of your opponent does not matter.