1
$\begingroup$

I know KL divergence tries to measure how different 2 probability distributions are.

I know high correlation values between 2 sets of variables imply they are highly dependent on each other.

Will the probability distributions associated with both sets of variables have low KL divergence between them, i.e.: will they be similar?

$\endgroup$
1
$\begingroup$

Not necessarily, e.g. $Y=cX$ and $X\sim N(0,1),\ c>0$, which means $Y\sim N(0,c^2)$. The KL divergence between two univariate normals can be calculated as laid out in here, and yields: $$KL(p_x||p_y)=2\log c+\frac{1}{2c^2}-{1\over2}$$

This can be arbitrarily large as $c$ changes but the correlation is always $1$.

$\endgroup$
1
  • $\begingroup$ Thank you for the explanation, however my naive intuition believed me to think that having high correlation implies that the data is sampled from similar distributions. $\endgroup$ – unholy_me Apr 9 '20 at 16:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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