On integration over distribution.
When I read various journal articles related to machine learning, I often face integrals over distribution.
In an article I am reading now, for example, a risk function associated with distribution is defined by
,
where
X and Y are a feature space and a label space, respectively.
is a given model parameterized by ,
is a loss function, and
is the data generating distributions.
In addition to the above case and the others (even not related to this field), I have seen many times integration formulas over distributions. However, whenever I encountered them, I couldn't grasp what it is.
Rather, I am familiar with the following equation:
where fL(x) is a cost (or reward) function achieved by an event x, and pX(x) is a probability that an event x occurred.
Can someone please let me know what the integral over a distribution means?