For a partial dependence plot this is computed as the slope of a linear regression line that is fit to the data points of the plot.
Motivation: We want to find partial dependence functions that show a strong trend, either up or down.
The score of a partial dependence plot is computed as the difference between the highest and lowest value of the function for that plot. Formula: max f(x) - min f(x)
Motivation: We want to find predictors that have a strong absolute effect, i.e., are not showing a "flat line". There is not necessarily a trend, e.g., it could go up and down repeatedly.
This measure describes the variation among sequential values of a partial dependence profile. Thus, sequential variation is particularly well suited for finding oscillating patterns. For example, you can use sequential variation to find the oscillating patterns of occurrence exhibited by irruptive winter migrants like Common Redpoll.
Motivation: We want to find plots where the probability of observing the bird varies strongly for consecutive (and hence similar) values of the predictor. This could discover strong trends in one direction, but also "oscillating" signals that go up and down (like odd versus even year trends).