Stat Stories: Normalizing Flows as an Application of Variable Transformation

While other statistical methods such as Generative Adversarial Networks (GAN) and Variational AutoEncoders (VAN) have been able to perform dramatic results on difficult tasks such as learning distributions of images, and other complicated datasets, they do not allow evaluation of density estimation and calculation of probability density of new data points. In such a sense, Normalizing Flows proves to be eloquent. The method can perform density estimation and sampling as well as variational inferences. Consider a transformation u g(x; θ), i.e., g is parametrized by parameter vector θ.