Robust Statistics: The Approach Based on Influence Functions

By Christopher Jennison. 1987

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Citations in the corpus

Learning from untrusted data (2016, neutral): “We refer the reader to Huber and Ronchetti (2009) and Hampel et al. (2011) for recent surveys.”
Behavior of Machine Learning Algorithms in Adversarial Environments (2010, background): “Here I summarize these concepts, but for a full treatment of these topics, refer to the books by Huber [1981], Hampel et al. [1986], and Maronna et al.”
The Dependent Wild Bootstrap (2010, background): “For an approximately linear statistic T(ρn), it admits an expansion in a neighborhood of F, that is, T(ρn) = T(F) + n−1 ∑nt=1 IF(Xt;F) + Rn, where IF(x;F) is the influence function (Hampel et al. 1986) defined by IF(x;F) = lim ↓0[T{(1 − )F + δx} − T(F)]/ and Rn is the remainder term.”
ICLabel: An automated electroencephalographic independent component classifier, dataset, and website (2019, methodology): “This version was used because movement artifacts are a common occurrence in EEG datasets and the sample median is more robust to outliers than the sample mean (Hampel et al., 2011).”
Datamodels: Predicting Predictions from Training Data (2022, methodology): “In particular, a recent line of work aims to compute the empirical influence (Hampel et al., 2011) of training points xi on predictions f(xj), i.e., Infl[xi → xj ] := P (model trained on S is correct on xj)− P (model trained on S \ {xi} is correct on xj) , where randomness is taken over the…”
Revisiting Methods for Finding Influential Examples (2021, methodology): “Influence functions (IFs) (Hampel 1986) are a core component of classic statistical theory and can be seen as approximations of leave one out (for convex functions), first used by Koh and Liang (2017) in the context of deep neural networks, and defined as: 1https://keras.io/api/datasets/mnist/.”
A Monte Carlo comparison of the Type I and Type II error rates of tests of multivariate normality (2005, background): “[51] for being ‘wasteful and superfluous’ and in Horswell [4] for being ‘haphazardly selected’.”