A Robust Minimax Approach to Classification

By Gert R. G. Lanckriet, Laurent El Ghaoui, C. Bhattacharyya, Michael I. Jordan. 2002

534 citations recorded by the source corpus.

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Citations in the corpus

Analysis of classifiers’ robustness to adversarial perturbations (2015, methodology): “For a specific disturbance model on the data samples, the robust optimization approach for constructing robust classifiers seeks to minimize the worst possible empirical error under such disturbances (Lanckriet et al., 2003; Xu et al., 2009).”
Adversarial Examples Detection in Deep Networks with Convolutional Filter Statistics (2016, background): “It is relevant to robust learning (e.g. [14]), however robust learning usually seek to directly optimize the minimax loss under adversarial conditions, instead of outputting an abstain option.”
Robustness of classifiers: from adversarial to random noise (2016, methodology): “The robustness properties of SVM classifiers have been studied in [19] for example, and robust optimization approaches for constructing robust classifiers have been proposed to minimize the worst possible empirical error under noise disturbance [1, 10].”
Analysis of universal adversarial perturbations (2017, background): “Several works have focused on the analysis of the robustness properties of SVM classiﬁers (e.g., [3]) and new approaches for constructing robust classiﬁers (based on robust optimization) have been proposed [4], [5].”
On Robustness and Regularization of Structural Support Vector Machines (2014, background): “A number of other authors have explored the application of robust optimization to classification problems (e.g., (Lanckriet et al., 2003; El Ghaoui et al., 2003; Bhattacharyya et al., 2004; Shivaswamy et al., 2006)).”
A Minimax Approach to Supervised Learning (2016, methodology): “We evaluated the performance of the minimax SVM on six binary classification datasets from the UCI repository, compared to these five benchmarks: Support Vector Machines (SVM) [24], Discrete Chebyshev Classifiers (DCC) [3], Minimax Probabilistic Machine (MPM) [2], Tree Augmented Naive Bayes (TAN) [2”
Regularization via Mass Transportation (2017, methodology): “[44] extend the minimax probability machine to account for estimation errors in the mean vectors and covariance matrices.”
Classifier evaluation and attribute selection against active adversaries (2010, methodology): “In that case, the Stackelberg solution concept for adversarial classification corresponds to the minimax solution studied in depth by many authors (Lanckriet et al. 2003; El Ghaoui et al. 2003).”
Theory and Applications of Robust Optimization (2010, background): “The basic problem setup is as follows: one has a collection of data vectors associated with two classes, x and y , with Lanckriet et al. [96] approach this problem ﬁrst from the approach of distributional robustness.”
Class Imbalance, Redux (2011, background): “Alternatively, this objective can be viewed as learning under the minimax assumption, in which case we attempt to minimize the maximum loss under an arbitrary covariate shift [15].”