Regularization of Wavelet Approximations

By Anestis Antoniadis, Jianqing Fan. 2001

541 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aef392806619ce9543a483edd66e966bcb27cdaf

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In Computational Mechanics

In Computer Vision and Pattern Recognition

In Mathematical Physics

Citations in the corpus

AMlet, RAMlet, and GAMlet: Automatic Nonlinear Fitting of Additive Models, Robust and Generalized, With Wavelets (2004, background): “Many generalizations of Waveshrink have been proposed to handle the non-equispaced situation (see, e.g., Antoniadis and Fan 2001 and the references therein).”
When is there a representer theorem? Vector versus matrix regularizers (2008, unknown): “…not apply to a family of “mixed” matrix norms that have been used in both statistics and machine learning, in formulations such as the “group Lasso” [Antoniadis and Fan, 2001, Argyriou et al., 2006, Bakin, 1999, Grandvalet and Canu, 1999, Lin and Zhang, 2003, Obozinski et al., 2006, Yuan and…”
The Role of Pseudo Data for Robust Smoothing with Application to Wavelet Regression (2007, methodology): “Methods for wavelet thresholding with irregularly spaced data have been studied by different authors Kovac and Silverman (2000), Antoniadis and Fan (2001) and more recently Lee and Meng (2005). The proposed algorithm can be coupled with any of these methods to perform irregularly spaced data robust ”
HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS (2011, unknown): “…technique, which takes the form of b | | Rothman, Levina and Zhu (2009) and Cai and Liu (2011) studied a more general thresholding function of Antoniadis and Fan (2001), which admits the form σ ij ( θ ij ) = s ( σ ij ), and also allows for soft-thresholding. b It is easy to apply the more…”
Ultrahigh dimensional feature selection: beyond the linear model (2009, background): “Unlike the L 1 penalty, SCAD and MC penalty functions have ﬂat tails, which are fundamental in reducing biases due to penalization (Antoniadis & Fan, 2001; Fan & Li, 2001).”
Challenges of Big Data Analysis (2013, unknown): “Popular choices of the penalty function Pλ, γ (·) include the hard-thresholding penalty [80,81], softthresholding penalty [6,82], smoothly clipped absolution deviation (SCAD, [8]) and minimax concavity penalty (MCP, [10]).”
Generalized Thresholding of Large Covariance Matrices (2009, background): “For more details on the relationship between penalty functions and resulting thresholding rules, see Antoniadis and Fan (2001). The simplest example of generalized thresholding is the hard thresholding rule,”
A data-driven block thresholding approach to wavelet estimation (2009, background): “See, for example, Donoho and Johnstone (1994a), Gao (1998) and Antoniadis and Fan (2001).”
Sufficient dimension reduction based on an ensemble of minimum average variance estimators (2011, background): “See, for example, Donoho and Johnstone (1994) and Antoniadis and Fan (2001). The Haar basis is obviously dense in B and hence characterizes the central subspace.”
Projective image restoration using sparsity regularization (2013, background): “These properties are very important for establishing sparsity regularization [4].”
Nonconcave penalized likelihood with a diverging number of parameters (2004, methodology): “For example, Antoniadis and Fan (2001) used this approach in wavelet analysis, and Fan and Li (2002) applied the technique to the Cox proportional hazards model and the frailty model.”
High dimensional thresholded regression and shrinkage effect (2014, background): “Antoniadis and Fan (2001) obtained comprehensive oracle inequalities and universal thresholding parameters for a wide class of general penalty functions, in the wavelets setting.”
Multiscale methods for data on graphs and irregular multidimensional situations (2009, background): “(1999), Kovac and Silverman (2000), Antoniadis and Fan (2001), Pensky and Vidakovic (2001), Nason (2002) and Kohler (2003). Herrick (2000) extended the interpolation method of Kovac and Silverman (2000) to two dimensions but found the resulting procedure too computationally intensive to be of any pr”