Robust statistics: the approach based on influence functions

By Frank Hampel, Elvezio Ronchetti, Peter J. Rousseeuw, Werner A. Stahel. 1986

Subfields: Statistics and Probability, Safety, Robustness & Interpretability

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Citations in the corpus

Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI (2019, neutral): “As stated in [165–167] , stability is a must-have when drawing interpretations from a certain model.”
Proper local scoring rules (2011, background): “Equation (7) delivers an M -estimator [Huber (1981), Hampel et al. (1986)].”
How to Explain Individual Classification Decisions (2009, background): “A classical example is the outlier sensitivity in statistics (Hampel, Ronchetti, Rousseeuw, and Stahel, 1986).”
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.”
Being Robust (in High Dimensions) Can Be Practical (2017, neutral): “See [HR09] and [HRRS86] for further background.”
Adaptive vertex fitting (2007, background): “The resulting estimator can be regarded as an M-estimator [9], the result of minimizing an objective function of the form”
Optical Flow Estimation (2006, background): “LS estimators are not suitable when the distribution of gradient constraint errors is heavy-tailed, as they are sensitive to small numbers of measurement outliers [24, 32].”
A Framework for Robust Subspace Learning (2003, methodology): “Our formulation here is based on the techniques of robust M-estimation developed in the statistics community (Hampel et al., 1986; Huber, 1981).”
Continual Graph Learning (2020, unknown): “on influence function [Hampel et al., 2011], in addition to two intuitive experience selection schemes.”
Airavat: Security and Privacy for MapReduce (2010, background): “Differential privacy guarantees are somewhat similar to robust or secure statistical estimation, which provides statistical computations with low sensitivity to any single input ( e.g. , see [21, 23, 24]).”
Inferential Aspects of the Skew Exponential Power Distribution (2004, methodology): “First, an initial t was computed using a Huber Ã function with tuning constant 1.345; then a nal t was derived using a bisquare Ã function with tuning constant 4.685 (see Hampel et al. 1986, secs.”
Robust statistics for outlier detection (2011, methodology): “The outlier map 23 plots the standardized LTS residuals versus robust distances (7) based on (for instance) the MCD estimator, which is applied to the x -variables only.”