InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets

[howardyclo]

Metadata

• Authors: Xi Chen, Yan Duan, +3 authors Pieter Abbeel
• Organization: UC Berkeley & OpenAI
• Conference: NIPS 2016
• Paper: https://arxiv.org/pdf/1606.03657.pdf
• 3rd Party Code: https://github.com/eriklindernoren/PyTorch-GAN#infogan

Abstract

InfoGAN, an information-theoretic extension to the GAN that is able to learn disentangled representations in a completely unsupervised manner. (Related to #33)

Vanilla GAN

• Objective: min_{G} max_{D} V(D, G) = E_{x ~ P_data} [log D(x)] + E_{z ~ noise} [log(1-D(G(z)))]
• Problem: Input noise vector z has no restrictions on the manner in which the generator may use this noise. As a result, it is possible that the noise will be used by the generator in a highly entangled way, causing the individual dimensions of z to not correspond to semantic features of the data.

InfoGAN

• Decompose the input noise vector z into 2 parts:
  • Incompressible noise z (interpret as an uncertainty of dataset that cannot be encoded to meaningful factors of variation)
  • Disentangled latent code c = {c_1, c_2, ..., c_L} (Encode factors of variation of dataset)
  • Note both vectors are learned in an unsupervised manner.
  • Problem: The generator may ignore the latent code: P_G(x|c) = P_G(x).
  • Apply regularization by maximizing mutual information: I(c; G(z,c)).
• Mutual information I(X;Y):
  • Measures the “amount of information” learned from knowledge of random variable Y about the other random variable X.
  • I(X;Y) = H(X) − H(X|Y) = H(Y) − H(Y|X), where H(.) is entropy.
  • I(X;Y) is the reduction of uncertainty in X when Y is observed. If X and Y are independent, then I(X;Y) = 0, because knowing one variable reveals nothing about the other.
  • Given any x ∼ P_G(x), we want P_G(c|x) to have a small entropy. In other words, the information in the latent code c should not be lost in the generation process (Address the above problem).
• Objective: min_{G} max_{D} V_I(D, G) = V(D, G) - λ I(c; G(z,c))

Variational Mutual Information Maximization

• Problem: I(c; G(z, c)) is hard to maximize directly as it requires access to the posterior P(c|x).
• Obtain a lower bound if it by defining an auxiliary Q(c|x) to approximate P(c|x).

• TODO: Upload lower bound derivation image in my macbook & change faster-rcnn folder name (lol)