Alternating conditional expectations: Difference between revisions

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In [[statistics]], '''Alternating conditionalConditional expectations'''Expectations ('''ACE)''') is an [[algorithm]] used in [[regression analysis]] to find the optimal transformations betweenfor both the outcome ([[response variable|response]]) variable and predictorthe variablesinput in(predictor) [[regression analysis]]variables.<ref>Breiman, L. and Friedman, J. H. [http://apps.dtic.mil/dtic/tr/fulltext/u2/a123908.pdf Estimating optimal transformations for multiple regression and correlation]. J. Am. Stat. Assoc., 80(391):580–598, September 1985b. {{PD-notice}}</ref>

For example, in a model that tries to predict house prices based on size and ___location, ACE helps by figuring out if, for instance, transforming the size (maybe taking the square root or logarithm) or the ___location (perhaps grouping locations into categories) would make the relationship easier to model and lead to better predictions. The algorithm iteratively adjusts these transformations until it finds the ones that maximize the predictive power of the regression model.

==Introduction==

In [[statistics]], a nonlinear transformation of variables is commonly used in practice in regression problems. Alternating conditional expectations (ACE) is one of the methods to find those transformations that produce the best fitting [[additive model]]. Knowledge of such transformations aids in the interpretation and understanding of the relationship between the response and predictors.

ACE transforms the response variable <math>Y</math> and its predictor variables, <math>X_i</math> to minimize the [[Fraction of variance unexplained|fraction of variance not explained]]. The transformation is nonlinear and is iteratively obtained from data.