Understanding Conditional Variational Autoencoders

Md Ashiqur Rahman

The variational autoencoder or VAE is a directed graphical generative mannequin which has obtained glorious outcomes and is among the many cutting-edge approaches to generative modeling. It assumes that the info is generated by some random course of, involving an unobserved steady random variable z. it’s assumed that the z is generated from some prior distribution P_θ(z) and the info is generated from some situation distribution P_θ(X|Z), the place X represents that knowledge. The z is typically referred to as the hidden illustration of information X.

Like every other autoencoder structure, it has an encoder and a decoder. The encoder half tries to be taught q_φ(z|x), which is equal to studying hidden illustration of information X or encoding the X into the hidden illustration (probabilistic encoder). The decoder half tries to be taught P_θ(X|z) which decoding the hidden illustration to enter area. The graphical mannequin may be expressed as the next determine.

(source)

The mannequin is educated to reduce the target perform

The primary time period on this loss is the reconstruction error or anticipated unfavourable log-likelihood of the datapoint. The expectation is taken with respect to the encoder’s distribution over the representations by taking just a few samples. This time period encourages the decoder to be taught to reconstruct the info when utilizing samples from the latent distribution. A big error signifies the decoder is unable to reconstruct the info.

The second time period is the Kullback-Leibler divergence between the encoder’s distribution q_φ(z|x) and p(z). This divergence measures how a lot info is misplaced when utilizing q to signify a previous over z and encourages its values to be Gaussian.

Throughout technology, samples from N(0,1) is just fed into the decoder. The coaching and the technology course of may be expressed as the next

A training-time variational autoencoder carried out as a feedforward neural community, the place P(X|z) is Gaussian. Purple exhibits sampling operations which might be non-differentiable. Blue exhibits the loss calculation. (source)
The testing-time variational “autoencoder,” which permits us to generate new samples. The “encoder” pathway is just discarded. (source)

The explanation for such a short description of VAE is, it isn’t the principle focus however very a lot associated to the principle subject.

The one downside for producing knowledge with VAE is we shouldn’t have any management over what sort of knowledge it generates. For instance, if we practice a VAE with the MNIST knowledge set and attempt to generate photos by feeding Z ~ N(0,1) into the decoder, it should additionally produce totally different random digits. If we practice it properly, the pictures might be good however we may have no management over what digit it should produce. For instance, you can’t inform the VAE to supply a picture of digit ‘2’.

For this, we have to have a bit of change to our VAE structure. Let’s say, given an enter Y(label of the picture) we would like our generative mannequin to supply output X(picture). So, the method of VAE might be modified as the next: given remark y, z is drawn from the prior distribution P_θ(z|y), and the output x is generated from the distribution P_θ(x|y, z). Please observe that, for easy VAE, the prior is P_θ(z) and the output is generated by P_θ(x|z).

Visible illustration activity in conditional VAE (source)

So, right here the encoder half tries to be taught q_φ(z|x,y), which is equal to studying hidden illustration of information X or encoding the X into the hidden illustration conditioned y. The decoder half tries to be taught P_θ(X|z,y) which decoding the hidden illustration to enter area conditioned by y. The graphical mannequin may be expressed as the next determine.

(Source)

The neural community structure of Conditional VAE (CVAE) may be represented as the next determine.

X is the picture. Y is the label of the picture which may be in 1 hot-vector illustration.

The implementation of CVAE in Keras is on the market here.

  1. Tutorial on Variational Autoencoders
  2. Auto-Encoding Variational Bayes

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