{"Package":"gclm","Type":"Package","Title":"Graphical Continuous Lyapunov Models","Version":"0.0.1","Authors@R":"c(\nperson(given = \"Gherardo\", family = \"Varando\", role = c(\"aut\", \"cre\", \"cph\"),\nemail = \"gherardo.varando@gmail.com\",\ncomment = c(ORCID = \"0000-0002-6708-1103\")),\nperson(given = \"Niels Richard\", family = \"Hansen\", role = \"aut\",\ncomment = c(ORCID = \"0000-0003-3883-365X\"))\n)","Description":"Estimation of covariance matrices as solutions of\ncontinuous time Lyapunov equations.\nSparse coefficient matrix and diagonal noise are estimated\nwith a proximal gradient\nmethod for an l1-penalized loss minimization problem.\nVarando G, Hansen NR (2020) .","License":"MIT + file LICENSE","Encoding":"UTF-8","LazyData":"true","RoxygenNote":"7.1.0","URL":"https://github.com/gherardovarando/gclm","BugReports":"https://github.com/gherardovarando/gclm/issues","Suggests":"testthat","NeedsCompilation":"yes","Packaged":"2020-05-25 06:55:33 UTC; gherardo","Author":"Gherardo Varando [aut, cre, cph]\n(),\nNiels Richard Hansen [aut] ()","Maintainer":"Gherardo Varando ","Repository":"CRAN","Date/Publication":"2020-06-04 08:40:07 UTC","repoType":"cran","tarballUrl":"ftp://cran.r-project.org/pub/R/src/contrib/gclm_0.0.1.tar.gz","jsonAuthors":[{"name":"Gherardo Varando","email":"gherardo.varando@gmail.com","maintainer":true},{"name":"Niels Richard Hansen","email":null,"maintainer":false}],"readme":"\n# gclm\n\n`gclm` contains methods to estimate a sparse parametrization of\ncovariance matrix as solution of a continuous time Lyapunov equation\n(CLE):\n\n\\[ B\\Sigma + \\Sigma B^t + C = 0 \\]\n\nSolving the following \$\\ell_1\$ penalized loss minimization\nproblem:\n\n\\[ \\arg\\min L(\\Sigma(B,C)) + \\lambda \\rho_1(B) + \\lambda_C ||C - C_0||^2_F \\]\n\nsubject to \$B\$ stable and \$C\$ diagonal, where \$\\rho_1(B)\$ is the\n\$\\ell_1\$ norm of the off-diagonal elements of \$B\$ and\n\$||C - C_0||^2_F\$ is the squared frobenius norm of the difference\nbetween \$C\$ and a fixed diagonal matrix \$C_0\$ (usually the\nidentity).\n\n## Installation\n\n``` r\ndevtools::install_github(\"gherardovarando/gclm\")\n```\n\n## Usage\n\n``` r\nlibrary(gclm)\n\n### define coefficient matrices\nB <- matrix(nrow = 4, c(-4, 2, 0, 0, \n 0, -3, 1, 0,\n 0, 0, -2, 0.5,\n 0, 0, 0, -1), byrow = TRUE)\nC <- diag(c(1,4,1,4))\n\n### solve continuous Lyapunov equation \n### to obtain real covariance matrix\nSigma <- clyap(B, C) \n\n### obtain observations \nsample <- MASS::mvrnorm(n = 100, mu = rep(0,4),Sigma = Sigma)\n\n\n### Solve minimization\n\nres <- gclm(cov(sample), lambda = 0.3, lambdac = 0.01)\n\nres$B\n```\n\n ## [,1] [,2] [,3] [,4]\n ## [1,] -1.012851 0.3646450 0.0000000 0.0000000\n ## [2,] 0.000000 -0.5771159 0.0000000 0.0000000\n ## [3,] 0.000000 0.0000000 -0.9002638 0.1671158\n ## [4,] 0.000000 0.0000000 0.0000000 -0.3498257\n\n``` r\nres$C\n```\n\n ## [1] 0.3169109 0.8481827 0.5380383 1.2108944\n\nThe CLE can be freely multiplied by a scalar and thus the \$B,C\$\nparametrization can be rescaled. As an example we can impose\n\$C_{11} = 1\$ as in the true \$C\$ matrix, obtaining the estimators:\n\n``` r\nC1 <- res$C / res$C[1]\nB1 <- res$B / res$C[1]\n\nB1 \n```\n\n ## [,1] [,2] [,3] [,4]\n ## [1,] -3.196011 1.150623 0.000000 0.0000000\n ## [2,] 0.000000 -1.821067 0.000000 0.0000000\n ## [3,] 0.000000 0.000000 -2.840747 0.5273274\n ## [4,] 0.000000 0.000000 0.000000 -1.1038614\n\n``` r\nC1\n```\n\n ## [1] 1.000000 2.676407 1.697759 3.820930\n\n#### Solutions along a regularization path\n\n``` r\npath <- gclm.path(cov(sample), lambdac = 0.01)\nt(sapply(path, function(res) c(lambda = res$lambda, \n npar = sum(res$B!=0),\n fp = sum(res$B!=0 & B==0),\n tp = sum(res$B!=0 & B!=0) ,\n fn = sum(res$B==0 & B!=0),\n tn = sum(res$B==0 & B==0),\n errs = sum(res$B!=0 & B==0) + \n sum(res$B==0 & B!=0))))\n```\n\n ## lambda npar fp tp fn tn errs\n ## [1,] 0.85588233 4 0 4 3 9 3\n ## [2,] 0.76078430 4 0 4 3 9 3\n ## [3,] 0.66568626 5 0 5 2 9 2\n ## [4,] 0.57058822 6 0 6 1 9 1\n ## [5,] 0.47549019 6 0 6 1 9 1\n ## [6,] 0.38039215 6 0 6 1 9 1\n ## [7,] 0.28529411 6 0 6 1 9 1\n ## [8,] 0.19019607 6 0 6 1 9 1\n ## [9,] 0.09509804 7 1 6 1 8 2\n ## [10,] 0.00000000 16 9 7 0 0 9\n\n## Related code\n\n - Some inspiration is from the `lyapunov` package\n ().","jobInfo":{"package":"gclm","version":"0.0.1","parsingStatus":"success","parserVersion":1,"parsedAt":"2020-06-04T11:31:08+0000"}}

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