The Influence Curve and Its Role in Robust Estimation

By Frank Hampel. 1974

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Citations in the corpus

Adversarial Training for Large Neural Language Models (2020, methodology): “In this subsection, we assess the impact of adversarial pre-training on the model’s robustness against adversarial attacks, using three standard adversarial NLP benchmarks: ANLI (Nie et al., 2019), HELLASWAG (Zellers et al., 2019) and adversarial SQuAD (Jia and Liang, 2017).”
Generalized random forests (2016, methodology): “We tackle this problem using the method of influence functions as described by Hampel (1974); in particular, we are motivated by the analysis of Newey (1994a).”
Robustness and Regularization of Support Vector Machines (2008, methodology): “For example, the In-ﬂuence Function approach, proposed in Hampel (1974) and Hampel et al. (1986), measures the impact of an inﬁnitesimal amount of contamination of the original distribution on the quantity of interest.”
SMART: Robust and Efficient Fine-Tuning for Pre-trained Natural Language Models through Principled Regularized Optimization (2019, neutral): “Note that the idea of measuring the local Lipschitz continuity is similar to the local shift sensitivity criterion in existing literature on robust statistics, which dates back to 1960’s (Hampel, 1974; Huber, 2011).”
Robust kernel density estimation (2008, methodology): “The proposed method achieves robustness by combining a traditional kernel density estimator with ideas from M -estimation (Huber, 1964; Hampel, 1974).”
Detection of single influential points in OLS regression model building (2001, methodology): “The diagnostic APi is related to the elements of the extended projection matrix H∗ by the expression APi = 1 − Hii − ê2N,i = 1 −Hm,ii.”
Analysis of Robust Quasi-deviances for Generalized Linear Models (2004, methodology): “Its influence function (Hampel 1974) is proportional to ψ (see Hampel, Ronchetti, Rousseeuw, and Stahel 1986), which is bounded with respect to y if ν(y, µ) is bounded, and with respect to x if w(x) is suitably chosen to down-weight leverage points.”
Welfare Rankings in the Presence of Contaminated Data (2002, methodology): “For any T this idea can be made more precise by introducing the influence function IF ( Hampel 1968, 1974 ), obtained by taking the derivative with respect to e of the statistic at F (z) e when e → 0:”
On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition (2004, unknown): “…in a mathematical way, e.g. the minimax approach (Huber, 1964), the sensitivity curve (Tukey, 1977), the approach based on influence functions (Hampel, 1974, Hampel et al., 1986), the maxbias curve (Huber, 1964, Hampel et al., 1986), and the finite sample breakdown point (Donoho and Huber,…”
Robustness in Data Analysis: Criteria and Methods (2001, background): “The local measures of robustness From the influence function, the following robustness measures can be defined (Hampel, 1968; Hampel, 1974): THE SUPREMUM OF THE ABSOLUTE VALUE γ∗(T, F) = sup x |IF(x; T, F)|, (1.”
Highly Robust Estimation of the Autocovariance Function (2000, methodology): “The in¯uence function (Hampel, 1974) is an important tool to describe the robustness properties of an estimator.”
On Directional Regression for Dimension Reduction (2007, methodology): “The random object S∗(F ) is called the influence function (see, e.g., Hampel 1974; Fernholz 1983; Serfling 1980, sec.”