I'm having trouble with the Machine Learningmachine learning vocabulary, especially with the concept of Random Variablesrandom variables.
My question is very simple, givenGiven a sample X $X$ (x1,x2,...xnwith features $x_1, x_2, \dots, x_n$) that you train your algorithm on (or predict), what is the Random Variable random variable? Is it X $X$? Or is it any of its feature x1,x2,...xn $x_1, x_2, \dots, x_n$?
The thing is it's often not clearQuoting The Deep Learning book (at least for me) in ML litteracy, for instance quoting The Deep Learning Book fromby Ian Goodfellow):
A random variable is a variable that can take on different values randomly. We typically denote the random variable itself with a lowercase letter in plain typeface
Where as in the definition of a Random Variable in the Wikipedia article:
A random variable is a measurable function from a set of possible outcomes to a measurable space E
Then we also have the definition of multivariate random variable
A multivariatemultivariate random variable is a column vector (or its transpose, which is a row vector) whose components are scalar-valued random variables on the same probability space as each other.
Should a sample be in fact considered as a multivariate random variable ?
