Robust entropy-like measure for analyzing uncertainity - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T00:44:04Z http://mathoverflow.net/feeds/question/75444 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75444/robust-entropy-like-measure-for-analyzing-uncertainity Robust entropy-like measure for analyzing uncertainity Soroosh 2011-09-14T20:39:21Z 2011-10-13T01:22:12Z <p>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:</p> <p><strong>H(s) = ln(sqrt((2πe)^k*det(cov)))</strong></p> <p><strong>H(s) = 0.5*[k*ln(2πe)+sum(log(eigs))]</strong></p> <p>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)?</p> http://mathoverflow.net/questions/75444/robust-entropy-like-measure-for-analyzing-uncertainity/75457#75457 Answer by psd for Robust entropy-like measure for analyzing uncertainity psd 2011-09-14T22:53:30Z 2011-09-14T22:53:30Z <blockquote> <p>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)?</p> </blockquote> <p>This is also known as the "total variance" and is the sum of the diagonals of the covariance matrix.</p>