Projection Pursuit Regression

By Jerome H. Friedman, Werner Stuetzle. 1981

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Citations in the corpus

Additive models with trend filtering (2017, methodology): “The book by Hastie & Tibshirani (1990) is the definitive practical guide for additive models for exponential family data distributions, i.e., generalized additive models. More recent work on additive models is focused on high-dimensional nonparametric estimation, and here the natural goal is to indu”
Kernel dimension reduction in regression (2009, background): “The problem of sufficient dimension reduction (SDR) for regression is that of finding a subspace S such that the projection of the covariate vector X onto S captures the statistical dependency of the response Y on X .”
Breaking the Curse of Dimensionality with Convex Neural Networks (2014, background): “differentiable optimization problem, techniques based on gradient descent may not ﬁnd the global optimum. If the number of hidden units is ﬁxed, thi s is a parametric problem. (e) Projection pursuit (Friedman and Stuetzle, 1981): f(x) = Pk j=1 fj(w ⊤ j x) where k is the number of projections. This m”
Empirical likelihood confidence regions in a partially linear single‐index model (2006, methodology): “Zhu and L. Xue (1994), Speckman (1988), Hdrdle et al.”
Nonparametric inference with generalized likelihood ratio tests (2007, methodology): “The additive models, proposed by Friedman and Stuetzle (1981) and Hastie and Tibshirani (1990), have been widely used in multivariate nonparametric modeling.”
Non-linear regression models for Approximate Bayesian Computation (2008, unknown): “Compared to other regression models, neural networks share many properties of projection pursuit regression (Friedman and Stuetze 1981), which may then lead to equivalent performances.”
Neural Networks and the Bias/Variance Dilemma (1992, methodology): “…regularization methods (see, e.g., Wahba 1982) and the closely related method of sieves (Grenander 1981; Geman and Hwang 1982), projection pursuit (Friedman and Stuetzle 1981; Huber 19851, recursive partitioning methods such as "CART," which stands for "Classification and Regression Trees"…”
Fast nonnegative deconvolution for spike train inference from population calcium imaging. (2009, methodology): “Template matching, projection pursuit regression [42], and matching pursuit [43] are examples of such a greedy approach (Greenberg et al’s algorithm [12] could also be considered a special case of such a greedy approach, as could the “peeling” approach described by [44]).”
Semiparametric Regression of Multidimensional Genetic Pathway Data: Least‐Squares Kernel Machines and Linear Mixed Models (2007, unknown): “Methods such as multivariate kernel smoothing (Wand and Jones, 1995), projection pursuit regression (Friedman and Stuetzle, 1981), and multivariate adaptive regression splines (MARS) (Friedman, 1991), are usually computationally expensive.”
The Elements of Statistical Learning (2003, methodology): “A signi cant portion of the theoretical development for this methodology has been done by these authors, (see, e.g., Hastie and Tibshirani 1991; De Veaux 1992; Friedman and Stuetzle 1981; Friedman 1991).”
Metrics and Models for Handwritten Character Recognition (1998, methodology): “This model can be seen as an extension of the polychotomous logistic regression model and is similar in structure and flavor to the projection pursuit regression models of Friedman and Stuetzle (1981). There is a large literature on such models (Ripley, 1996; Bishop, 1995), with many possibilities f”
Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, unknown): “The PP index can be used for supervised analysis [164,166–168] , clustering analysis [161,162,169,170] , and regression analysis [171,172] .”
Heterogeneous Peer Effects and Rank Concerns: Theory and Evidence (2017, unknown): “Equation 3 is a semiparametric single-index model (Hall 1989, Ichimura 1993, Horowitz 2010).”
Generalized Additive Models (1986, unknown): “Cross-validation for span selection is discussed in Friedman and Stuetzle (1982). Note that if we used the observed residual error RSS = (1/n) n (Y -s (xi))2 to choose w, (s.”