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: <math> e^2(\theta,\varphi_1,\dots,\varphi_p)=\frac{\mathbb{E}\left[\theta(Y)-\sum_{i=1}^p \varphi_i(X_i)\right]^2}{\mathbb{E}[\theta^2(Y)]}</math>
Generally, the optimal transformations that minimize the unexplained part are difficult to compute directly. As an alternative, ACE is an iterative method to calculate the optimal transformations. The procedure of ACE has the following steps:
# Hold <math>\
-->gives <math>\theta_1(Y)=\mathbb{E}\left[\sum_{i=1}^p \varphi_i(X_i)\Bigg|Y\right]</math>
# Normalize <math>\theta_1(Y)</math> to unit variance.
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