Generalized Additive Models

By Trevor J. Hastie, Robert Tibshirani. 2014

11,920 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Artificial Intelligence, Statistics and Probability

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Citations in the corpus

A Survey on Explainable Artificial Intelligence (XAI): Toward Medical XAI (2019, methodology): “Subspace Explanations) [84] X X classiﬁers generally perform better at deeper layer, that is, at larger k. General Additive Models. Linear model is generalized by the Generalized Additive Model (GAM) [101], [102] with standard form g(E[y]) = 0 + f j(x j) where gis the link function. The equation is ”
Distill-and-Compare: Auditing Black-Box Models Using Transparent Model Distillation (2017, methodology): “can be visualized in graphs such as Figure 2 that plot xi on the x-axis and hi(xi)on the y-axis. For classification,дis the logistic function. For regression, дis the identityfunction.ForclassicalGAMS[19],featurecontributionsh(·) are fitted using splines; for iGAM, they are fitted using ensembles of”
Peeking Inside the Black Box: Visualizing Statistical Learning With Plots of Individual Conditional Expectation (2013, positive): “As an illustration, consider the following additive data generating model We simulate 1000 independent ( X i , Y i ) pairs according to the above and ﬁt a generalized additive model ( GAM , Hastie and Tibshirani, 1986) via the R package gam (Hastie, 2013).”
Partially Interpretable Estimators (PIE): Black-Box-Refined Interpretable Machine Learning (2021, methodology): “The popular choices of the basis function ψjk include Bsplines and cubic splines; the details can be found in (Hastie & Tibshirani, 1990), for example.”
Neural Additive Models: Interpretable Machine Learning with Neural Nets (2020, neutral): “Methodologically, NAMs belong to a model family called Generalized Additive Models (GAMs) [14].”
Convex-constrained Sparse Additive Modeling and Its Extensions (2017, methodology): “Additive modeling [HT90] is a class of convenient tools to combat the curse of dimensionality, by making further assumption that the regression function m can be decomposed (approximately) into a sum of univariate component functions, each acting on a separate covariate.”
Additive models with trend filtering (2017, positive): “In general, given data Y ∈ Rn with E(Y ) = η, Cov(Y ) = σ2I, and an estimator η̂ of η, recall that we define the effective degrees of freedom of η̂ as [Efron, 1986, Hastie and Tibshirani, 1990]: df(η̂) = 1 σ2 n∑ i=1 Cov ( η̂i(Y ), Y i ) , where η̂(Y ) = (η̂1(y), . . . , η̂n(Y )).”
Interpretable Decision Sets: A Joint Framework for Description and Prediction (2016, background): “For example, prototype vector machines [4], regression models [36, 35], generalized additive models [16, 40, 26, 27], Bayesian case models [19] mind-the-gap models [20], and scoring systems [37] have all been proposed as interpretable models.”
Fused Lasso Additive Model (2014, positive): “We assume E[ y i | x i ] = g =1 f j ( x ij ) , where g is a speciﬁed function and each f j is an unknown function that we wish to estimate [Hastie and Tibshirani, 1986].”
Sparse Partially Linear Additive Models (2014, background): “Generalized partially linear additive models (GPLAMs) [1] provide an attractive middle ground between the simplicity of generalized linear models (GLMs) [2] and the flexibility of generalized additive models (GAMs) [3].”
On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, background): “The sequence of eigenvalues ( µ m ) m > 1 is an important quantity that appears in the analysis of kernel methods ( Hastie and Tibshirani, 1990; Caponnetto and De Vito, 2007; Harchaoui et al., 2008; Bach, 2013; El Alaoui and Mahoney, 2014).”
Control functionals for Monte Carlo integration (2014, background): “emulation (Oakley and O’Hagan, 2002) and machine learning applications (e.g. Rasmussen and Williams, 2006). 2.5.1 An analytic expression for ^ D 0 (D 1) A Gaussian process (GP) is a linear smoother (Hastie and Tibshirani, 1990) whose conjugacy properties enable the derivation of an analytic expressi”
Breaking the Curse of Dimensionality with Convex Neural Networks (2014, neutral): “(b) Generalized additive models: f(x) = ∑d j=1 fj(xj), which are generalizations of the above by summing functions fj : R → R which may not be affine (Hastie and Tibshirani, 1990; Ravikumar et al., 2008; Bach, 2008a).”
Monotonic Calibrated Interpolated Look-Up Tables (2015, neutral): “We give a brief overview of related work in interpretable machine learning, then survey related work in learning monotonic functions.”
Varying Index Coefficient Models (2015, methodology): “By treating Zβl as a covariate Ul and letting Xl ≡ 1 for all 1 ≤ l ≤ d, model (4) may be regarded as an additive model (Hastie and Tibshirani (1990) and Wang and Yang (2007)), and moreover by letting ml (·) ≡ ml for some l, it is a partially linear additive model (PLAM, Wang et al.”