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What is the influence function used for binary classification in the R package partkit, specifically for the conditional tree (ctree). I could not find any details in the R package documentation. In the vigente I found this paragraph about classification:

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But the function $e_J(Y_i)$ is not defined. What is $e_J(Y_i)$? and is it the influence function used for the function ctree?

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The function is defined at the top of page 10 in vignette("ctree", package = "partykit"), albeit briefly: $e_K(k)$ is the unit vector of length $K$ with $k$-th element being equal to one.

As an example, if you do classification with $J = 4$ classes and the second class is observed in observation $i$ with $Y_i = 2$, then $e_J(Y_i) = (0, 1, 0, 0)^\top$.

See also the following for more explanations: What is the test statistics used for a conditional inference regression tree?

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