Using the coefficient of variation to detect feature importance - but what if mean and sd are correlated? I would like to have an estimate for the importance of a feature - the rough idea would be to define importance as the ratio between the mean and standard deviation. In other words, a feature is important if it has a high mean and a low standard deviation. So far so good - there is the coefficient of variation which is very close to what I need. In my case, however, the mean of each feature is highly correlated with the standard deviation. Using the coefficient of variation would therefore not be a good measure, because it would "reward" features with low mean too much but features with a high mean too less.
Here's a figure to get an intuition for my problem (the x-axis lists each feature the y-axis represents the value, lines are representing mean with +/- sd):

Is there a way to correct for this correlation between mean and sd?
EDIT: Each feature on the figure below is a brain region/node. Mean and SD represent energy values over various state transitions for each node.

Coefficient of variation has severe problems in the best of cases, due to its assumption that the origin for the measurement is zero.  So CV is not to be used for variable importance.  Use a general measure such as explained variation, i.e., $R^2$ or pseudo $R^2$ or the proportion of -2 log-likelihood $\chi^2$ explained by a part of the model.  Other measures are described here.  These approaches also easily handle the case where the variable has more than one parameter in the model (e.g., quadratic effect).
