one could be constructed. Certain constructive proofs exist, but they tend to require highly complicated (i.e. fractal) functions, and thus are not suitable for modeling approaches. Therefore, the generalized additive model drops the outer sum, and demands instead that the function belong to a simpler class,

where is a smooth monotonic function. Writing for the inverse of , this is traditionally written as

: .

When this function is approximating the expectation

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