I have trained a logistic regression model with 4 possible output labels. I want to determine the overall feature importance for each feature irrespective of a specific output label. In case of binary classification, we can simply infer feature importance using feature coefficients. However, when the output labels are more than 2, things get a bit tricky. For multinomial logistic regression, multiple one vs rest classifiers are trained. For example, if there are 4 possible output labels, 3 one vs rest classifiers will be trained. Each classifier will have its own set of feature coefficients. While calculating feature importance, we will have 3 coefficients for each feature corresponding to a specific output label. Is there a way to aggregate these coefficients into a single feature importance value? Can we just take the mean or weighted mean of these coefficients to get a single feature importance value?
The most relevant question to this problem I found is https://stackoverflow.com/questions/60060292/interpreting-variable-importance-for-multinomial-logistic-regression-nnetmu However, this question has no answers yet and it uses log-linear model instead of logistic regression.