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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)?

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Since this was already on the front-page, I retagged with some ArXiV tags –  David White Sep 29 '11 at 0:36
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up vote -1 down vote accepted

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.

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Is this "total variance" measure used as a measure of uncertainty in literature? –  Soroosh Sep 14 '11 at 23:14
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