This CMU machine learning textbook says
Both principles have been widely used to derive and to justify a vast range of machine learning algorithms, from Bayesian networks, to linear regression, to neural network learning.
it seems that to derive and to justify are different.
could someone give an example to illustrate the difference between to derive and to justify?
for example, the derivation of linear regression is A while the justification of linear regression is B, and what the difference between A and B is.
"Derive" is a mathematical term, which refers to transforming a set of ideas and equations into another set of mathematical equations by the rules of mathematics.
"Justify" is a broader and weaker term. You could justify some result by checking that its limiting cases make sense, or that in some conditions it reduces to a known (and accepted) result, and so forth.
"Justify" is sometimes used to explain why a single step (not a full derivation) is valid. You say that some distribution of weights in a network approximate a Gaussian distribution by means of the central limit theorem. You needn't "derive" the result, just set certain conditions and show some limiting case.
Frankly.... I wouldn't worry or spend time thinking about the distinction between these words.