Breakdown-Point for Spatially and Temporally Correlated Observations

Genton, Marc G.

doi:10.1007/978-3-642-57338-5_12

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…A variety of extensions of the BDP concept have been proposed in the literature. Stromberg and Ruppert [1992] and Sakata and White [1995] proposed BDPs for regression, Sakata and White [1998] suggested a BDP definition for location-scale estimators while Genton [1998] propose the spatial BDP for variogram estimators and Genton and Lucas [2003] and Genton [2003] introduce a BDP for dependent samples (time series). Donoho and Stodden [2006], Donoho [2006] propose a BDP for model selection and Kanamori et al [2004] study the BDP for SVMs and Hennig [2008] transferred the BDP concept to the dissolution point concept for clustering.…”

Section: The Breakdown Point Conceptmentioning

confidence: 99%

Quantitative robustness of instance ranking problems

Werner¹

2021

Preprint

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Instance ranking problems intend to recover the true ordering of the instances in a data set with a variety of applications in for example scientific, social and financial contexts. Robust statistics studies the behaviour of estimators in the presence of perturbations of the data resp. the underlying distribution and provides different concepts to characterize local and global robustness. In this work, we concentrate on the global robustness of parametric ranking problems in terms of the breakdown point which measures the fraction of samples that need to be perturbed in order to let the estimator take unreasonable values. However, existing breakdown point notions do not cover ranking problems so far. We propose to define a breakdown of the estimator as a sign-reversal of all components which causes the predicted ranking to be inverted, therefore we call our concept the order-inversal breakdown point (OIBDP). We will study the OIBDP, based on a linear model, for several different ranking problems that we carefully distinguish and provide least favorable outlier configurations, characterizations of the order-inversal breakdown point as well as sharp asymptotic upper bounds. We also outline the case of SVM-type ranking estimators.

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Section: The Breakdown Point Conceptmentioning

confidence: 99%

Quantitative robustness of instance ranking problems

Werner¹

2021

Preprint

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“…There are already a lot of BDP concepts in literature, for example for regression (Stromberg and Ruppert [1992] and Sakata and White [1995]), for location-scale estimators (Sakata and White [1998]), for time series (Genton and Lucas [2003], Genton [2003]) and for variogram estimators (Genton [1998]). Donoho and Stodden [2006] propose a BDP for model selection while Kanamori et al [2004] studied the BDP for SVMs.…”

Section: The Breakdown Point Conceptmentioning

confidence: 99%

Trimming Stability Selection increases variable selection robustness

Werner¹

2021

Preprint

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Contamination can severely distort an estimator unless the estimation procedure is suitably robust. This is a well-known issue and has been addressed in Robust Statistics, however, the relation of contamination and distorted variable selection has been rarely considered in literature. As for variable selection, many methods for sparse model selection have been proposed, including Stability Selection which is a meta-algorithm based on some variable selection algorithm in order to immunize against particular data configurations. We introduce the variable selection breakdown point that quantifies the number of cases resp. cells that have to be contaminated in order to let no relevant variable be detected. We show that particular outlier configurations can completely mislead model selection and argue why even cell-wise robust methods cannot fix this problem. We combine the variable selection breakdown point with resampling, resulting in the Stability Selection breakdown point that quantifies the robustness of Stability Selection. We propose a trimmed Stability Selection which only aggregates the models with the lowest in-sample losses so that, heuristically, models computed on heavily contaminated resamples should be trimmed away. We provide a short simulation study that reveals both the potential of our approach as well as the fragility of variable selection, even for an extremely small cell-wise contamination rate.

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“…We consider two common types of observation outliers: additive outliers (AO) and innovations outliers (IO ;Fox 1972;Genton 2003;Lucas 2003, 2005). In an AO model, we observe…”

Section: B the Effects Of Observation Outliersmentioning

confidence: 99%

Observation Quality Control with a Robust Ensemble Kalman Filter

Roh

Genton

Jun

et al. 2013

Monthly Weather Review

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Current ensemble-based Kalman filter (EnKF) algorithms are not robust to gross observation errors caused by technical or human errors during the data collection process. In this paper, the authors consider two types of gross observational errors, additive statistical outliers and innovation outliers, and introduce a method to make EnKF robust to gross observation errors. Using both a one-dimensional linear system of dynamics and a 40-variable Lorenz model, the performance of the proposed robust ensemble Kalman filter (REnKF) was tested and it was found that the new approach greatly improves the performance of the filter in the presence of gross observation errors and leads to only a modest loss of accuracy with clean, outlier-free, observations.

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Breakdown-Point for Spatially and Temporally Correlated Observations

Cited by 6 publications

References 15 publications

Quantitative robustness of instance ranking problems

Quantitative robustness of instance ranking problems

Trimming Stability Selection increases variable selection robustness

Observation Quality Control with a Robust Ensemble Kalman Filter

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