GLASSOc: Penalized precision matrix estimation (c++)
In MGallow/GLASSOO: Lasso Penalized Precision Matrix Estimation

Description Usage Arguments Details Value Author(s) References

Penalized precision matrix estimation using the graphical lasso (glasso) algorithm

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GLASSOc(S, initSigma, initOmega, lam, crit_out = "avg", crit_in = "loss",
  tol_out = 1e-04, tol_in = 1e-04, maxit_out = 10000L,
  maxit_in = 10000L)

`S`	pxp sample covariance matrix (denominator n).
`initSigma`	initialization matrix for estimated covariance matrix Sigma
`initOmega`	initialization matrix for Omega used to initialize the Betas
`lam`	tuning parameter for lasso penalty.
`crit_out`	criterion for convergence in outer (blockwise) loop. Criterion `avg` will loop until the average absolute parameter change is less than `tol_out` times tolerance multiple. Criterion `max` will loop until the maximum change in the estimated Sigma after an iteration over the parameter set is less than `tol_out`. Defaults to `avg`.
`crit_in`	criterion for convergence in inner (lasso) loop. Criterion for convergence. Criterion `loss` will loop until the relative change in the objective for each response after an iteration is less than `tol_in`. Criterion `avg` will loop until the average absolute change for each response is less than `tol_in` times tolerance multiple. Similary, criterion `max` will loop until the maximum absolute change is less than `tol_in` times tolerance multiple. Defaults to `loss`.
`tol_out`	convergence tolerance for outer (blockwise) loop. Defaults to 1e-4.
`tol_in`	convergence tolerance for inner (lasso) loop. Defaults to 1e-4.
`maxit_out`	maximum number of iterations for outer (blockwise) loop. Defaults to 1e4.
`maxit_in`	maximum number of iterations for inner (lasso) loop. Defaults to 1e4.

For details on the implementation of 'GLASSOO', see the vignette https://mgallow.github.io/GLASSOO/.

returns list of returns which includes:

`Iterations`	number of iterations.
`lam`	optimal tuning parameters.
`Omega`	estimated penalized precision matrix.
`Sigma`	estimated covariance matrix.

Matt Galloway gall0441@umn.edu

Friedman, Jerome, Trevor Hastie, and Robert Tibshirani. 'Sparse inverse covariance estimation with the graphical lasso.' Biostatistics 9.3 (2008): 432-441.
Banerjee, Onureen, Ghauoui, Laurent El, and d'Aspremont, Alexandre. 2008. 'Model Selection through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data.' Journal of Machine Learning Research 9: 485-516.
Tibshirani, Robert. 1996. 'Regression Shrinkage and Selection via the Lasso.' Journal of the Royal Statistical Society. Series B (Methodological). JSTOR: 267-288.
Meinshausen, Nicolai and Buhlmann, Peter. 2006. 'High-Dimensional Graphs and Variable Selection with the Lasso.' The Annals of Statistics. JSTOR: 1436-1462.
Witten, Daniela M, Friedman, Jerome H, and Simon, Noah. 2011. 'New Insights and Faster computations for the Graphical Lasso.' Journal of Computation and Graphical Statistics. Taylor and Francis: 892-900.
Tibshirani, Robert, Bien, Jacob, Friedman, Jerome, Hastie, Trevor, Simon, Noah, Jonathan, Taylor, and Tibshirani, Ryan J. 'Strong Rules for Discarding Predictors in Lasso-Type Problems.' Journal of the Royal Statistical Society: Series B (Statistical Methodology). Wiley Online Library 74 (2): 245-266.
Ghaoui, Laurent El, Viallon, Vivian, and Rabbani, Tarek. 2010. 'Safe Feature Elimination for the Lasso and Sparse Supervised Learning Problems.' arXiv preprint arXiv: 1009.4219.
Osborne, Michael R, Presnell, Brett, and Turlach, Berwin A. 'On the Lasso and its Dual.' Journal of Computational and Graphical Statistics. Taylor and Francis 9 (2): 319-337.
Rothman, Adam. 2017. 'STAT 8931 notes on an algorithm to compute the Lasso-penalized Gausssian likelihood precision matrix estimator.'