# Generative Adversarial Nets (GANs)

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1. The problem statement that is addressed by GANs.
Can we build a generative model to create a new faked distribution, so that a discriminator (human) cannot tell it’s fake given the observed distribution?
Here is an interactive 2D sketch:

The potential applications include edge2image, labels2image, dataset augmentation, denoising, and filtering.
2. Generator G, input: 2D noise, and initial parameters $\theta$ of a multilayer perceptron; output: faked data
Discriminator D, input: faked data X from the generator G; output: a single scalar representing the probability that the X comes from the observed data rather than G.
We train D to maximize the probablity of assigning the correct lable; train D to minimize that the faked data is corrected by G.
3. The two-player minimax game with value function V(G, D):
$$\min_G \max_D V(D, G) = E_{x~p_{data(X)}}[\log D(x)] +E_{z~p_z(z)} [\log (1 – D(G(z)) ]$$
4.