Why Deep Generative Modeling?

Before we start thinking about (deep) generative modeling, let us consider a simple example. Imagine we have trained a deep neural network that classifies images ( \(\mathbf {x} \in \mathbb {Z}^{D}\) ) of animals ( \(y \in \mathcal {Y}\) , and \(\mathcal {Y} = \{cat, dog, horse\}\) ). Further, let us assume that this neural network is trained really well so that it always classifies a proper class with a high probability p(y|x). So far so good, right? The problem could occur though. As pointed out in [1], adding noise to images could result in completely false classification. An example of such a situation is presented in Fig. 1.1 where adding noise could shift predicted probabilities of labels; however, the image is barely changed (at least to us, human beings).