Simultaneous Regression Shrinkage, Variable Selection, and Supervised Clustering of Predictors with OSCAR

By Howard D. Bondell, Brian J. Reich. 2008

533 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Molecular Biology, Statistics and Probability

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Citations in the corpus

On Security and Sparsity of Linear Classifiers for Adversarial Settings (2016, background): “In this case, the (cid:96) ∞ regularizer bounds the weights’ maximum absolute value as (cid:107) w (cid:107) ∞ = max j =1 ,..., d | w j | [20]: As the standard SVM, this classiﬁer is not sparse; however, the above learning problem can be solved using a simple linear programming approach.”
Learning Multi-Level Task Groups in Multi-Task Learning (2015, background): “TDof is originated from the degree of freedom used in the feature grouping literatures such as (Bondell and Reich 2008), and is defined as the number of ‘unequal’ columns in W, where two columns wi and wj are defined to be ‘equal’, denoted by wi ' wj , if ‖wi − wj‖2 ≤ ε0 for some threshold constant ”
The BerHu penalty and the grouped effect (2012, background): “es. Such a reasoning leads to a bound quantifying the grouping eect of the Elastic Net ([35]). Such a property was generalized to the adaptive Elastic Net in [6] and also proved for the algorithm of [3]. The goal of the following theorem is to provide a quantitative description for the grouping eect”
SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax (2015, background): “We remark that a preprint [34] considers statistical properties of a generalization of OSCAR [17] that coincides with SLOPE.”
Collinearity: a review of methods to deal with it and a simulation study evaluating their performance (2013, methodology): “Some other methods were consistent, but at a higher RMSE level (Hoeffding/Ward & Spearman/average clustering, seqreg, LRR, OSCAR, randomForest, BRT 570 and SVM).”
Feature Selection (2016, background): “(96) where u and v are sparse vectors with only two non-zero entries such that ui = uj = 1 2, vi = −vj = 1 2. Theformulation of the GOSCARis more general than the OSCARalgorithm which is proposed in (Bondell and Reich, 2008). OSCARalgorithm assumes that all features form a complete graph whose entri”
On Decomposing the Proximal Map (2013, background): “This norm ‖ · ‖oct is proposed in [21] for feature grouping, but Corollary 5 appears to be new.”
Predicting diabetes-related hospitalizations based on electronic health records (2018, background): “[24, 25] The remainder of the paper is organized as follows.”
Homogeneity pursuit in panel data models: Theory and application (2018, methodology): “One approach is to use finite mixture models; see Sun (2005), Kasahara and Shimotsu (2009), and Browning and Carro (2010). Another approach adapts the K-means algorithm to panel data models; see Lin and Ng (2012), Sarafidis and Weber (2015), Bonhomme and Manresa (2015), and Ando and Bai (2016).”
Group Sparsity and Geometry Constrained Dictionary Learning for Action Recognition from Depth Maps (2013, background): “Group sparsity encourages the sparse coefficients in the same group to be zero or nonzero simultaneously [2, 4, 26].”
Feature Selection for Classification: A Review (2014, methodology): “The GOSCAR formulation is closely related to OSCAR in [4].”
Sieve Estimation of Time-Varying Panel Data Models With Latent Structures (2019, methodology): “The latter approach is adopted by Ng and Lin (2012) in linear panel data models with additive fixed effects, by Bonhomme and Manresa (2015) for linear models with grouped additive effects, and by Ando and Bai (2016) in linear panel data models with grouped interactive fixed effects.”