# Feature Importance based on a Logistic Regression Model

I was training a Logistic Regression model over a fairly large dataset with ~1000 columns.

I did apply scaling of features using MinMaxScaler.

I was wondering how to interpret the coefficients generated by the model and find something like feature importance in a Tree based model.

Should I re-scale the coefficients back to original scale to interpret the model properly?

It will be great if someone can shed some light on how to interpret the Logistic Regression coefficients correctly.

Let's assume that our logistic regression model has coefficients {$$a_i$$}, relating to the different (scaled) variables {$$x_i$$}.
A change of $$\Delta x_i$$ in the variable $$x_i$$ will result in an increase (or decrease, if $$a_i$$ is negative) of $$a_i \Delta x_i$$ in $$log({\hat p_i \over {1-\hat p_i}})$$, i.e. the logit function of $$\hat p_i$$, where $$\hat p_i$$ is the predicted probability that the i-th example is in the positive class.
So, if the variables are scaled, you can say that if $$a_i$$ is larger, then $$x_i$$ is more important in the model.