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@@ -48,8 +48,8 @@ therefore given by \\\vert E(\Omega) \vert\\.
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where \\\xi \in \[0,1\]\\ is a tuning parameter. Setting \\\xi = 0\\
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reduces EBIC to the classic BIC.
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4. HBIC: High dimensional Bayesian information criterion ([Wang, Kim,
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and Li 2013](#ref-wang2013calibrating); [Fan et al.
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4. HBIC: High dimensional Bayesian information criterion ([Wang et al.
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2013](#ref-wang2013calibrating); [Fan et al.
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2017](#ref-fan2017high))
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\\ \hat{\Omega}\_{\mathrm{HBIC}} = {\arg\min}\_{\Omega} \left\\
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Akaike, Hirotogu. 1973. “Information Theory and an Extension of the
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Maximum Likelihood Principle.” In *Second International Symposium on
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Information Theory*, edited by Boris Nikolaevich Petrov and Frigyes
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Csáki, 267–81. Budapest, Hungary: Akadémiai Kiadó.
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Csáki. Akadémiai Kiadó.
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Chen, Jiahua, and Zehua Chen. 2008. “Extended Bayesian Information
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Criteria for Model Selection with Large Model Spaces.” *Biometrika* 95
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Foygel, Rina, and Mathias Drton. 2010. “Extended Bayesian Information
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Criteria for Gaussian Graphical Models.” In *Advances in Neural
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Information Processing Systems 23 (NIPS 2010)*, edited by J. Lafferty,
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C. Williams, J. Shawe-Taylor, R. Zemel, and A. Culotta, 604–12. Red
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Hook, NY, USA: Curran Associates, Inc.
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<https://dl.acm.org/doi/10.5555/2997189.2997257>.
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C. Williams, J. Shawe-Taylor, R. Zemel, and A. Culotta. Curran
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Associates, Inc. <https://dl.acm.org/doi/10.5555/2997189.2997257>.
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Schwarz, Gideon. 1978. “Estimating the Dimension of a Model.” *The
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Annals of Statistics* 6 (2): 461–64.

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## Penalties
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1. Lasso: Least absolute shrinkage and selection operator ([Tibshirani
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1996](#ref-tibshirani1996regression); [Friedman, Hastie, and
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Tibshirani 2008](#ref-friedman2008sparse))
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1996](#ref-tibshirani1996regression); [Friedman et al.
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2008](#ref-friedman2008sparse))
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\\\lambda p(\omega\_{ij}) = \lambda\vert\omega\_{ij}\vert.\\
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2. Adaptive lasso ([Zou 2006](#ref-zou2006adaptive); [Fan, Feng, and Wu
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2. Adaptive lasso ([Zou 2006](#ref-zou2006adaptive); [Fan et al.
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2009](#ref-fan2009network))
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\\ \lambda p\_\gamma(\omega\_{ij}) =
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\arctan\left(\frac{\vert\omega\_{ij}\vert}{\gamma}\right), \quad \gamma
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\> 0. \\
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4. Exp: Exponential type penalty ([Wang, Fan, and Zhu
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4. Exp: Exponential type penalty ([Wang et al.
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2018](#ref-wang2018variable))
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\\ \lambda p\_\gamma(\omega\_{ij}) =
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\\ \lambda p\_\gamma(\omega\_{ij}) =
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\lambda\vert\omega\_{ij}\vert^\gamma, \quad 0 \< \gamma \< 1. \\
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6. LSP: Log-sum penalty ([Candès, Wakin, and Boyd
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6. LSP: Log-sum penalty ([Candès et al.
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2008](#ref-candes2008enhancing))
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\\ \lambda p\_\gamma(\omega\_{ij}) =
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\gamma\lambda. \end{cases} \quad \gamma \> 1. \\
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8. SCAD: Smoothly clipped absolute deviation ([Fan and Li
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2001](#ref-fan2001variable); [Fan, Feng, and Wu
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2009](#ref-fan2009network))
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2001](#ref-fan2001variable); [Fan et al. 2009](#ref-fan2009network))
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\\ \lambda p\_\gamma(\omega\_{ij}) = \begin{cases}
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\lambda\vert\omega\_{ij}\vert & \text{if } \vert\omega\_{ij}\vert \leq

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authors.md

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- **[Shiying Xiao](http://shiying-xiao.com)**. Author, maintainer.
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[](https://orcid.org/0000-0002-8846-3258)
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- **[Jun Yan](https://statcomp.org)**. Author.
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[](https://orcid.org/0000-0003-4401-7296)
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- **[Panpan Zhang](https://panpan-zhang.com)**. Author.
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[](https://orcid.org/0000-0002-8211-5930)
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## Citation
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Source:
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[`DESCRIPTION`](https://github.com/Carol-seven/grasps/blob/main/DESCRIPTION)
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Xiao S (2025). *grasps: Groupwise Regularized Adaptive Sparse Precision
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Solution*. R package version 0.1.0,
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Xiao S, Yan J, Zhang P (2026). *grasps: Groupwise Regularized Adaptive
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Sparse Precision Solution*. R package version 0.1.0,
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<https://github.com/Carol-seven/grasps>.
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@Manual{,
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title = {grasps: Groupwise Regularized Adaptive Sparse Precision Solution},
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author = {Shiying Xiao},
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year = {2025},
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author = {Shiying Xiao and Jun Yan and Panpan Zhang},
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year = {2026},
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note = {R package version 0.1.0},
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url = {https://github.com/Carol-seven/grasps},
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}

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