Empirical vs Analytical?
I have been reading some literature on Machine Learning and whenever I try to brush up my mathematical concepts, I come across an avid use of the terms empirical (ex. we can 'empirically' prove it, 'empirical' distribution)
and the term analytical (ex: the concept of matrix inversion helps us 'analytically' solve the eqn : Ax = b)
I see that they are used in complimentary scenarios but I am not able to find any concrete definitions of these terms in the mathematical sense. Can someone help clarify the differences between these?
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$\begingroup$From dictionary meanings:
empirical: based on, concerned with, or verified by observation or experience.
analytical: based on analysis or logic.
Besides this, there are technical terms.
The empirical distribution for a random variable based on a finite set of observations gives each observed value the probability consisting of the fraction of observations that have that value.
An analytical expression is a formula that can be written down using the basic arithmetic operations (+-*/^) and "well-known" functions. Not to be confused with analytic function.
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