Consider the following two paragraphs taken from the paper titles Generative Adversarial Nets by Ian J. Goodfellow et.al
We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1.......
#2: Excerpt from Introduction
The promise of deep learning is to discover rich, hierarchical models that represent probability distributions over the kinds of data encountered in artificial intelligence applications, such as natural images, audio waveforms containing speech, and symbols in natural language corpora.
here we saw the word distribution thrice. It is very common to encounter the phrase data distribution in machine learning papers. For the types of data we use in artificial intelligence, there can be infinite random samples. We collect some instances and form a dataset, based on which we try to get the data distribution.
Even most of the literature uses the phrases data distribution or probability distribution. I personally never came across papers that explicitly talk about the random vector for the probability distribution under consideration. What can be the reason for it? Why won't research papers give the list of random variables for the distribution they are discussing? Is it immaterial or is it obvious from the context?
Note: For example, if our discussion is about a 'human face images' dataset and if we use the phrase 'data distribution' then should I assume random variables to be 'pixels' of the image or high-level features like 'eyes, ears, etc.,' or some other? Or is it immaterial? If immaterial, then what should I need to perceive about probability distribution? Should I imagine it as an arbitrary random vector?