On the Consistency of Feature Selection using Greedy Least Squares Regression

By Tong Zhang. 2009

177 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Molecular Biology

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Citations in the corpus

Forward stability and model path selection (2021, neutral): “…on assessing consistency and establishing conditions under which it can be guaranteed that the estimated tuning parameter(s) cor-respondingtothechosen ˆ f m convergestotheirtrueoroptimal values [see e.g. Zhao and Yu (2006); Bach (2008); Zhang (2009) or Fan and Lv (2010) for a thorough overview].”
Stability selection (2008, background): “Keywords: High dimensional data; Resampling; Stability selection; Structure estimation”
Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming (2010, background): “[6], [25], [10], [5], [30], [8], [27], and [29] contain other fundamental results obtained for related problems; see [4] for further references.”
Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise (2011, methodology): “Zhang (2009) considered model selection consistency of the OMP algorithm and showed that under suitable stopping conditions, OMP will return a subset of the true support and the number of unselected nonzero components can be bounded.”
Targeted Undersmoothing. (2017, methodology): “2Alternatives to the lasso estimator with similar properties include the Dantzig selector (see [19]), forward stepwise regression (see [54], [57], [48], [28], [37] ), SCAD (see [30]), and many others.”
Abnormal event detection in crowded scenes using sparse representation (2013, methodology): “Thus, we can use either weighted L1 minimization in [7] or the improved version of WOMP in Alg.3 to solve Eq.”
Selection of time instants and intervals with Support Vector Regression for multivariate functional data (2020, methodology): “Particularly, in the regression area, we can highlight (Andersen and Bro, 2010; Karagiannopoulos et al., 2007; Li et al., 2009; Mehmood et al., 2012; Van Dijck and Van Hulle, 2006; Yang and Ong, 2011; Zhang, 2009).”
Identifying a Minimal Class of Models for High-dimensional Data (2015, background): “For p > n, it turns out that practically strong and unverifiable conditions are needed to achieve (5) for popular regularization based estimators (Zhao and Yu, 2006; Meinshausen and Bühlmann, 2006; Huang et al., 2008; Jia and Yu, 2010; Tropp, 2004; Zhang, 2009).”
Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection (2011, methodology): “Our problem formulation appears somewhat similar to the problem of sparse recovery (Zhang, 2008; 2009; Zhao & Yu, 2006; Candès et al., 2005); however, note that in sparse recovery, it is generally assumed that the prediction vector is truly (almost)k-sparse, and the aim is to recover the exact coeff”
Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization (2012, methodology): “Similar or even more stringent lower bounds are required throughout the literature on support recovery in a noisy setup [9, 12, 33, 54, 59, 60], and are typically already needed to ensure that the variables in S are ranked at the top (cf.”
Structured sparsity through convex optimization (2011, background): “…date: April 23, 2012 A striking consequence of assuming that w∗ has many zero components is that for the three criteria, consistency is achievable even when p is much larger than n (Zhao and Yu, 2006; Wainwright, 2009; Bickel, Ritov and Tsybakov, 2009; Zhang, 2009).”