Variational Autoencoder

• Some control over distribution of learned Features
• Eg: Decoder as a generative model
• Constraint loss function and a given Probability $\mathcal{D}$
  • Eg: By loss func KL Divergence and prob distribution $$L(X) = n^{-1}\Sigma_i||x_i - D(E(\tilde x))||^2 + \lambda \cdot KL(f_i, d)$
  • Use 2D unit distribution. 0 mean, unit variance
  • Latent vector : $f=\mu +ϵe^{2log\sigma }$
• $$L(X) = n^{-1}\Sigma_i||x_i - D(E(\tilde x))||^2 + \frac{1}{2n}\Sigma_i(e^{log\sigma(x_i)} + \mu(x_i)^2 -1 -log(\sigma (x_i))$
• Encoder predicts mean and std $E(x_i)=(\mu (x_i),log\sigma (x_i))$