General formulation of HDMR component functions with independent and correlated variables

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Visualizing the effects of predictor variables in black box supervised learning models (2016, background): “Follow-up work in Li and Rabitz (2012), Chastaing and Prieur (2012), and Rahman (2014) improved the solution techniques, sometimes restricting the component ANOVA functions to be expansions in basis functions such as polynomials and splines, but these are more restrictive (perhaps negating the…”
Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment (2017, methodology): “For different input parameters, the output is calculated as [123]”
A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures (2014, unknown): “Li and Rabitz [14] proposed combining hierarchically selected univariate orthogonal polynomials and regression, applied to input-output data, to approximate the component functions of the generalized ADD.”
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis (2011, unknown): “[22] proposed a numerical method to compute the decomposition components given by Hooker.”
Generalized Sobol sensitivity indices for dependent variables: numerical methods (2013, unknown): “The following section is devoted to an original estimation scheme of the HOFD components based on two tools: extended bases [19] and penalized regression.”