Conditional Generative Models

Preface

We can extend mixture models and VAE's to be conditional distributions: \(p(\mathbf{x | y})\) for some inputs \(\mathbf{y}\).

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Mixture Models

The parameters of the mixture models are now functions with input \(\mathbf{y}\). ie.

\[ p(x | \mathbf{y}) = c_{1}(\mathbf{y}) \cdot \mathcal{N}(\mu_{1}(\mathbf{y}), \sigma_{1}^2(\mathbf{y}))+ c_{2}(\mathbf{y}) \cdot \mathcal{N}(\mu_{2}(\mathbf{y}), \sigma_{2}^2(\mathbf{y})) \]

represents a conditional mixture distributions with two components, that models \(x \in \mathbb{R}\) conditioned on inputs \(\mathbf{y}\).

We can then approximate these functions: \(c_{i}(\mathbf{y}), \ \mu_{i}(\mathbf{y}), \ \sigma_{i}(\mathbf{y})\), using any function approximation technique; RBF Network, Neural Network, other fixed representations, etc.

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Conditional VAEs

Conditional Variational Autoencoders (CVAE)

References

Variational Autoencoder (VAE) Generative Models Simple Generative Models, Mixture Models Radial Basis Function Networks (RBF) Evaluating Generative Models