2
$\begingroup$

I've been reading about Independent Component Analysis and the FastICA algorithm. The wiki page for FastICA states:

FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyvärinen at Helsinki University of Technology.[1][2] Like most ICA algorithms, FastICA seeks an orthogonal rotation of prewhitened data, through a fixed-point iteration scheme, that maximizes a measure of non-Gaussianity of the rotated components. Non-gaussianity serves as a proxy for statistical independence, which is a very strong condition and requires infinite data to verify.

I understand that non-gaussianity can serve as a proxy for independence due to the central limit theorem, but why is it that independence itself requires infinite data to verify?

$\endgroup$

1 Answer 1

3
$\begingroup$

Independence, like many other concepts in statistics, is a feature of a population rather than a sample. You can't conclude much with certainty about a population from only a finite random sample, since you could always be arbitrarily unlucky in your choice of sample.

$\endgroup$
3
  • $\begingroup$ Ah, didn't realize the answer was that simple. Great, thanks. $\endgroup$
    – Austin
    Dec 5, 2017 at 18:42
  • 1
    $\begingroup$ Yes, but by that reasoning everything requires "infinite data." (except when sampling from finite populations). Thus, either the quotation is a meaningless triviality or else something else was meant. $\endgroup$
    – whuber
    Dec 5, 2017 at 18:42
  • 3
    $\begingroup$ @whuber I tend towards thinking "meaningless triviality", but it's possible that the author meant something else. $\endgroup$ Dec 5, 2017 at 18:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.