Understanding negative partial dependency values

Question

What does a negative partial dependency value (centered/mean value), such as a change from -0.8 to -0.7 with an increase in input, indicate for a parameter?

Does this mean the parameter has a negative relationship with the output, or does it imply that the predictions are generally lower than average?

Answer 1

Just some initial context: Partial dependence plots show the average relationship between a given feature $x_A$ and the response $y$ within the fixed, joint distribution of all the other inputs $x_B, \dots, x_Z$. That said, when displaying the actual plot, we might choose to display the changes relative to an overall central tendency (e.g. the median) or just display the raw values. In the plot shown, this is not defined, so I will answer for both cases:

1. If we are showing the centred values: The partial dependency values being consistently negative is a strong indication that the feature value tends to pull the model's predictions below the average across a wide range of the feature's values. Something like "number of cigarettes smoked (our $x_A$) and overall lung health" (our $y$), at no point smoking cigarettes improves lung health on average so all other things being equal, the PDP values for number of cigarettes smoked will always be negative. (i.e. below our central tendency)
2. If we are showing the raw values of the PDPs: We predict negative values on average across all values of feature $x_A$, that is not a problem, our dataset may be like that after all. (e.g. predicting temperature in Antarctica)

Small caveat: Univariate PDPs are good for small fast investigations but do consider looking at some interactions of our $x_A$ feature with other features. Especially on larger ML models (e.g. GBMs with hundreds of base learners) we might have strong heterogenous interaction effects.