I've recently come across the ALE algorithm and I'm currently trying to get my head around Judea Pearl's theories incl. the "Ladder of Causation" and I'm struggling to understand how the two relate.

In ALE you are nudging values for a single variable to the upper and lower edge of a bin to see how this changes the prediction of a rung 1 model (i.e. a model purely based on correlations). Amongst other things Daniel W. Apley and Jingyu Zhu claim that "paired differencing is what blocks out the effect of the correlated nuisance variable" and I have seen examples where the ALE plot really shows a "trend" between Y and a given variable almost opposite of what the raw data suggests (i.e. what a simple rung 1 correlation would find).

In Pearl's "Ladder of Causation" rung 1 is concerned with correlation/association in observed data, rung 2 with (experimental) interventions and rung 3 with counterfactuals.

So while the difference between rung 2 and 3 is nicely explained here I'm pretty much confused already about rung 2 alone and my question is: can the "nudging" in ALE be considered a (rung 2) intervention even though it is not a physical experiment but relying on a (rung 1) model or are you basically stuck at rung 1 even when interpreting ALE plots "the right way" (see Fig. 11)?


1 Answer 1


This is a very interesting consideration. I cannot claim to give a definitive answer, but I will offer my thoughts. As far as I understand, in the terminology of your question, ALE nudging is nothing more than Rung 1 of the ladder of causation: correlation/association.

It is important to understand that ALE does not attempt to directly describe the true relationship between input variables and an outcome. Rather, ALE describes a model's characterization of the relationship between input variables and the outcome. Any statistical or machine learning model is, on its own, nothing more than a mathematical relationship between variables. At that level, any model is fundamentally correlational. This is what ALE describes. Although its manipulations of controlling for effects by bounding them might superficially resemble experimental manipulations, these are simply mathematical tricks to account for interactions among variables.

To advance on the ladder of causality, the research design needs to incorporate elements outside of the mathematical model such as random assignment and temporal precedence. ALE is agnostic to such measures. It only describes the mathematical, correlational model.

  • $\begingroup$ Thanks, I guess this is in good agreement with my initial intuition. Some of the more counter-intuitive ALE curves gave raise to the hope that there might be some magic I was not aware of... $\endgroup$
    – MarkH
    Dec 18, 2023 at 22:47

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