Partial dependence, individual conditional expectation, accumulated local effects क्या है?

The partial dependence of a model $f$ on feature $j$ is $\mathrm{PD}_j(v) = n^{-1}\sum_i f(v, x_{i,-j})$: the average prediction with feature $j$ set to $v$ for every observation (Friedman, 2001). The individual conditional expectation (ICE) curves are the terms of that average, one curve per observation (Goldstein and co-authors, 2015). Accumulated local effects (ALE) average, within narrow intervals of feature $j$, the change in prediction when $j$ moves across the interval for the observations that lie in it, and accumulate those changes (Apley and Zhu, 2020).