Second Order Cone Programming Approaches for Handling Missing and Uncertain Data

By Pannagadatta K. Shivaswamy, C. Bhattacharyya, Alex Smola. 2006

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “For instance, Song et al. (2007b) considers a supervised feature selection as maximizing a dependence between the subsets of covariate X ′, obtained from backward elimination algorithm (Guyon and Elisseeff 2003), and the target Y , e.”
Robustness and generalization (2010, methodology): “Robust optimization was introduced in machine learning tasks to handle exogenous noise (Bhattacharyya et al. 2004; Shivaswamy et al. 2006; Globerson and Roweis 2006), i.e., the learning algorithm only has access to inaccurate observation of training samples.”
A distributional interpretation of robust optimization (2010, background): “, Shivaswamy etc [6], Lanckriet etc [7], El Ghaoui and Lebret [5], Ben-Tal etc [8], [9], and Boyd etc [10]); see the recent monograph by Ben-Tal and co-authros [11] for a detailed survey.”
Supervised classification and mathematical optimization (2013, methodology): “In [1, 214], data in the two groups are assumed to be given by random variables, with known mean and covariance matrices.”
Theory and Applications of Robust Optimization (2010, methodology): “[91] who consider SOCP approaches for handling missing and uncertain data, and also Caramanis and Mannor [40], where robust optimization is used to obtain a model for uncertainty in the label of the training data.”
Learning with Marginalized Corrupted Features (2013, methodology): “Others (Bhattacharyya et al., 2004; Shivaswamy et al., 2006; Trafalis & Gilbert, 2007; Xu et al., 2009) also use minimax approaches that minimize the loss under a worst-case scenario, but corrupt the data by adding a constant that is uniformly drawn from [−u, u] to each of the features.”
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)).”
Regularization via Mass Transportation (2017, background): “Shivaswamy et al. [35] study linear classiﬁcation problems trained with incomplete and noisy features, where each training sample is modeled by an ambiguous distribution with known ﬁrst and second-order moments.”
Support Measure Data Description for group anomaly detection (2015, background): “However, there is a growing interest in machine learning methods for datasets whose individual observations are clusters, groups or sets of points in R [32, 33, 20, 19, 25, 35, 10, 34, 26, 15, 18].”
Optimization for machine learning (2010, background): “In (Shivaswamy et al., 2006), the authors consider two varieties of such chance constraints for i = 1, .”
Robust Regression and Lasso (2008, methodology): “In that paper, and in most of the subse q ent research in this area and the more general area of Robust Optimization (see [12, 13] and re ferences therein) the disturbance is taken to be either row-wise and uncorrelated [14], or given b y bounding the Frobenius norm of the disturbance matrix [11].”
Robust Optimization (2021, methodology): “The approach has been further developed in [105].”
Expected kernel for missing features in support vector machines (2011, methodology): “introduced a generalization of the SVM so that the margin-maximization takes into account the uncertainty due to missing features or noise [5].”