Residuals and Influence in Regression

By S. Chatterjee, R. Dennis Cook, Sanford Weisberg. 1982

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Citations in the corpus

Coresets via Bilevel Optimization for Continual Learning and Streaming (2020, neutral): “Following [34] and using the result of [14], under twice differentiability and strict convexity of the inner loss, the empirical influence function at k is ∂θ ∗ ∂ε ∣∣ ε=0 =− ( ∂(2) ∑n i=1 w ∗ S,i`i(θ ∗) ∂θ∂θ> )−1 ∇θ`k(θ).”
What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation (2020, background): “A famous proxy for the classical leave-one-one influence is the influence function [12].”
Improving Question Answering Model Robustness with Synthetic Adversarial Data Generation (2021, methodology): “Influence Functions We use influence functions (Cook and Weisberg, 1982; Koh and Liang, 2017) to estimate the effect on the validation loss of including a synthetic example as explored by Yang et al.”
Fitting Linear Mixed-Effects Models Using lme4 (2014, background): “The hat matrix The hat matrix, H, is a useful object in linear model diagnostics (Cook and Weisberg 1982).”
Data Shapley: Equitable Valuation of Data for Machine Learning (2019, background): “LOO is often approximated by leverage or inﬂuence score, which measures how the predictor changes when the weight of one point changes slightly (Cook & Weisberg, 1982).”
G-DAug: Generative Data Augmentation for Commonsense Reasoning (2020, methodology): “Fortu-nately, the validation loss change can be efﬁciently approximated through the use of inﬂuence functions (Atkinson et al., 1983; Koh and Liang, 2017 The main result from previous work (Atkinson et al., 1983; Koh and Liang, 2017) tells us that the inﬂuence of upweighting a training example x by…”
Certified Data Removal from Machine Learning Models (2019, background): “is also known as the influence function of the training point (xn, yn) on the parameter vector w∗ (Cook and Weisberg, 1982; Koh and Liang, 2017).”
A local influence approach to sensitivity analysis of incomplete longitudinal ordinal data (2001, background): “The best known perturbation schemes are based on case-deletion (Cook and Weisberg, 1982) in which the effect is studied of completely removing cases from the analysis.”
Robust Computation of Linear Models by Convex Relaxation (2012, background): “4 Screening for Outliers Another common approach is to remove possible outliers and then estimate the underlying subspace by PCA [15,66,67].”
Model selection procedures in social research: Monte-Carlo simulation results (2008, methodology): “As such, we explored the underlying data structure of each of our six models using standard regression diagnostics for linearity and heteroscedasticity, casebased model criticism tools for goodness-of-fit, leverage, and influence [4]; as well as several methods for assessing multivariate normality a”
Identifying multiple influential observations in linear regression (2005, background): “These residuals are also known as internally and externally Studentized residuals respectively (see Cook & Weisberg, 1982 ) in the literature.”
Influence Diagnostics for Elliptical Multivariate Linear Regression Models (2003, methodology): “Diagnostic methods for the normal linear regression model have been amply investigated in the statistical literature (see, for instance, Belsley et al, 1980 ; Cook, 1982 ; Chatterjee and Hadi, 1988 ).”
Adolescent Self-Esteem and Gender: Exploring Relations to Sexual Harassment, Body Image, Media Influence, and Emotional Expression (2001, methodology): “Outliers were checked by reviewing numerical ranges and by using the Cook's D distance procedure (Cook and Weisberg, 1982), resulting in the deletion of 4 cases.”
Robust continuum regression (2005, background): “However, even the influence function of classical continuum regression itself has not yet been established, except in the special cases of δ = 0 [20] and δ = 0.”
Product Fit Uncertainty in Online Markets: Nature, Effects, and Antecedents (2014, unknown): “Furthermore, we did not detect inﬂu-ential observations or outliers using Cook’s distance (Cook 1977, Cook and Weisberg 1982) following Belsley et al. (1980).”
The Generalized Birnbaum–Saunders Distribution and Its Theory, Methodology, and Application (2008, methodology): “An important diagnostics technique of the global influence method is the Cook's distance; see Cook and Weisberg ( 1982 ).”
Diagnostic Checks for Multilevel Models (2008, background): “Such measures are called externally studentized residuals [11] or deletion residuals [2].”