Some Comments on Cp

By Colin L. Mallows. 2000

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Citations in the corpus

True Few-Shot Learning with Language Models (2021, methodology): “Prior work has developed other model selection criteria such as the Akaike Information Criterion [AIC; 42], Watanabe-Akaike Information Criterion [WAIC; 41], and Mallows’ C p [43].”
Generalized random forests (2016, methodology): “In the case of estimating the effect of a binary treatment, Athey and Imbens (2016) study sample-splitting trees, and propose an unbiased, model-free estimate of err (C1, C2) using an overfitting penalty in the spirit of Mallows (1973).”
The Dantzig selector: Statistical estimation when P is much larger than n (2005, neutral): “le selection strategy—hence, the name. There is of course a huge literature on model selection, and many procedures motivated by a wide array of criteria have been proposed over the years—among which [1, 7, 26, 31, 36]. By and large, the most commonly discussed approach—the “canonical selection proc”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, neutral): “See also related simulation experiments for random designs from the Gaussian ensemble in [7]. Note that a traditional frequentist criterion is to penalize larger subsets Aby the Mallow’s CL criterion [145], which is equal to A→ tr(XAX⊤ A + λI)−1XAX⊤ A, which is not a submodular function. 6.7 Best su”
Parametric or nonparametric? A parametricness index for model selection (2011, neutral): “e.g., [17, 27, 39, 43, 46, 48–51, 54, 57, 61, 63, 67, 71, 74, 75]) have been established mostly in terms of either selection consistency or an asymptotic optimality. It is well known that AIC [2], Cp [47] and FPE [1, 58] have an asymptotic optimality property which says the accuracy of the estimator”
Theory of classification : a survey of some recent advances (2005, background): “The notion that ideal penalties should be rooted in sharp risk estimates goes back to the pioneering works of Akaike [6] and Mallows [150].”
‘All models are wrong...’: an introduction to model uncertainty (2012, methodology): “Interestingly, Mallows (1973) warns against using ‘his’ Cp method as a model selection tool, instead of a method for selecting a set of models with good predictive performance.”
Robust regression: an inferential method for determining which independent variables are most important (2018, neutral): “calledMallow’s [19]Cp criterion, cannot be recommended [22].”
Risk bounds for the non-parametric estimation of Lévy processes (2006, background): “ on the collection of linear models {Sm,m ∈ M}. Methods ofestimation basedonthe minimization ofpenaltyfunctions havealong history in the literature on regression and density estimation (for instance, [1, 22], and [28]). The general idea is to choose, among a given collection of parametric models, th”