Probability density functions

In all previous chapters, we have always supposed that our datasets were drawn from an implicit data-generating process p_data and all the algorithms assumed x_i ∈ X as independent and identically distributed (IID) and uniformly sampled. We were supposing that X represented p_data with enough accuracy so that an algorithm could learn to generalize with limited initial knowledge. In this chapter, instead, we are interested in directly modeling p_data without any specific restriction (for example, a Gaussian mixture model achieves this goal by imposing a constraint on the structure of the distributions). Before discussing some very powerful approaches, it's helpful to briefly recap the properties of a generic continuous probability density function p(x) defined on a measurable subset X ℜn (to avoid confusion, we are going to indicate...