I'm looking for a measure to analysis the uncertainty observed in a set of variables (with multivariate Gaussian distribution). So, I've tried conventional Shanon entropy (differential entropy) which results into the following equation for MVG distributions:


**H(s) = ln(sqrt((2πe)^k\*det(cov)))**


**H(s) = 0.5\*[k\*ln(2πe)+sum(log(eigs))]**


Where, Sigma(Σ) is the covariance matrix. Thus, it's just a constant term plus sum of logarithm of eigenvalues of covariance matrix. But, when I've a small eigenvalue among eigenvalues, the small value affects the whole thing dramatically. In other words, this measure is not robust to small eigenvalues. On the other hand if I use sum of eigenvalues itself (instead of logarithmic scales), I won't face this issue. I was wondering if there is any other measures of uncertainty which may result in to sum of eigs instead of sum of log(eigs)?



Robust entropy-like measure for analyzing uncertainity

> 
> I was wondering if there is any other measures of uncertainty
>  which may result in to sum of eigs instead of sum of log(eigs)?
> 
> 
> 


This is also known as the "total variance" and is the sum of the diagonals of the covariance matrix.


