Generalized Functional ANOVA Diagnostics for High-Dimensional Functions of Dependent Variables

By Giles Hooker. 2007

273 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

Visualizing the effects of predictor variables in black box supervised learning models (2016, methodology): “Hooker (2007) proposed a functional ANOVA decomposition of f.x/ into component functions {fJ ,ANOVA.xJ / : J ⊆ {1, 2, : : : , d}} by adopting the Stone (1994) approach of using weighted integrals in the function approximation optimality criterion and in the component function orthogonality…”
All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, methodology): “Throughout this section, we will treat f as a pre-specified prediction model of interest (as in Hooker, 2007).”
Auditing Black-Box Models Using Transparent Model Distillation With Side Information (2017, methodology): “that may suffer from bias due to extrapolation off the training manifold [28] or ignored correlations between features [40].”
Learning Global Additive Explanations for Neural Nets Using Model Distillation (2018, methodology): “…distillation with powerful additive models of the ˆ F form is based on two previous research threads: (1) decomposing F into additive ˆ F to understand how F is affected by its inputs (e.g. [22]), and (2) learning an interpretable model (often some form of decision tree) to mimic F (e.g. [11]).”
Please Stop Permuting Features: An Explanation and Alternatives (2019, methodology): “Our VI j still employs permutations, but learns a new model after permuting the features; Mentch and Hooker (2016) found that by maintaining the feature dimension, this made for a better statistical comparison than dropping a feature and re-learning as we have done in VIj .”
A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures (2014, unknown): “…component functions y u,G , u ⊆ { 1 , · · · , N } , of input variables with increasing dimensions. uniqueness of the The existence and uniqueness decomposition in (4.1) have been proven under conditions (C.1) and (C.2) [3], but (4.1) works well in practice under more general assumptions [11, 28].”
Intelligible models for classification and regression (2012, methodology): “Generalized additive models were introduced by the statistics community [14, 15, 22] and have been extended to include LASSO feature selection [18] and to incorporate interaction terms [16].”
Accurate intelligible models with pairwise interactions (2013, background): “One drawback of these meth-ods is that spurious interactions may be reported over low-density regions [15].”
An Efficient Approach for Assessing Hyperparameter Importance (2014, methodology): “Functional Analysis of Variance (ANOVA) Functional analysis of variance (functional ANOVA) is a prominent data analysis method from the statistics literature (Sobol, 1993; Huang, 1998; Jones et al., 1998; Hooker, 2007).”
Generalized Sobol sensitivity indices for dependent variables: numerical methods (2013, unknown): “Inspired by the pioneering work of Stone [17] and Hooker,[18] we showed, under a weak assumption on the inputs distribution, that any model function can be decomposed into a sum of hierarchically orthogonal component functions.”
Definitions, methods, and applications in interpretable machine learning (2019, background): “While feature importance scores can provide useful insights, they also have a number of limitations (80, 82).”
LSTM: A Search Space Odyssey (2015, methodology): “an estimation of uncertainty of those predictions. The obtained marginals can then be used to decompose the variance into additive components using the functional ANalysis Of VAriance (fANOVA) method [46] which provides an insight into the overall importance of hyperparameters and their interactions”
Data-Intensive Science: A New Paradigm for Biodiversity Studies (2009, background): “Once important predictors have been identified, their effects on the response can be studied by summarizing the model, for example, with partial dependence functions (Friedman 2001, Hastie et al. 2001, Hooker 2007).”
Tree Space Prototypes: Another Look at Making Tree Ensembles Interpretable (2016, background): “nostic (not exclusive to tree ensembles) explanations of predictions [10, 11] and feature selection in tree ensembles using, for example, variable importance measures [12] or partial dependence plots [4, 13, 14, 15, 16]. The latter aims at interpretability by targeting sparsity-in-features [17], whe”
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis (2011, methodology): “Notice that a similar result for the Lebesgue measure is given in [18].”
Hyperparameter Importance Across Datasets (2017, background): “Functional ANOVA (Sobol, 1993; Huang, 1998; Jones et al., 1998; Hooker, 2007) decomposes a function ŷ : Θ1× · · · ×Θn → R into additive components that only depend on subsets of the hyperparameters N :”
Explainable Deep Learning: A Field Guide for the Uninitiated (2020, methodology): “In this work, the global additive explanations are constructed by following previous work Hooker (2007) to decompose the black-box model into an additive model such as spline or bagged tree.”