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  "Type": "Package",
  "Title": "A Framework to Smooth L1 Penalized Regression Operators using\nNesterov Smoothing",
  "Version": "1.6",
  "Date": "2021-03-18",
  "Author": "Georg Hahn [aut,cre], Sharon M. Lutz [ctb], Nilanjana Laha\n[ctb], Christoph Lange [ctb]",
  "Maintainer": "Georg Hahn <ghahn@hsph.harvard.edu>",
  "Description": "We provide full functionality to smooth L1 penalized\nregression operators and to compute regression estimates\nthereof. For this, the objective function of a user-specified\nregression operator is first smoothed using Nesterov smoothing\n(see Y. Nesterov (2005) <doi:10.1007/s10107-004-0552-5>),\nresulting in a modified objective function with explicit\ngradients everywhere. The smoothed objective function and its\ngradient are minimized via BFGS, and the obtained minimizer is\nreturned. Using Nesterov smoothing, the smoothed objective\nfunction can be made arbitrarily close to the original\n(unsmoothed) one. In particular, the Nesterov approach has the\nadvantage that it comes with explicit accuracy bounds, both on\nthe L1/L2 difference of the unsmoothed to the smoothed\nobjective functions as well as on their respective minimizers\n(see G. Hahn, S.M. Lutz, N. Laha, C. Lange (2020)\n<doi:10.1101/2020.09.17.301788>). A progressive smoothing\napproach is provided which iteratively smoothes the objective\nfunction, resulting in more stable regression estimates. A\nfunction to perform cross validation for selection of the\nregularization parameter is provided.",
  "License": "GPL (>= 2)",
  "RdMacros": "Rdpack",
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  "NeedsCompilation": "no",
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  "Date/Publication": "2021-03-21 06:20:02 UTC",
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    "elasticNet",
    "fusedLasso",
    "graphicalLasso",
    "minimizeFunction",
    "minimizeSmoothedSequence",
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    "objFunctionGradient",
    "objFunctionSmooth",
    "objFunctionSmoothGradient",
    "prsLasso",
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      "page": "crossvalidation",
      "title": "Perform cross validation to select the regularization parameter.",
      "topics": [
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      "topics": [
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      ]
    },
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      "page": "fusedLasso",
      "title": "Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the fused Lasso.",
      "topics": [
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      ]
    },
    {
      "page": "graphicalLasso",
      "title": "Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the graphical Lasso.",
      "topics": [
        "graphicalLasso"
      ]
    },
    {
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      "title": "Minimize the objective function of an unsmoothed or smoothed regression operator with respect to betavector using BFGS.",
      "topics": [
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      ]
    },
    {
      "page": "minimizeSmoothedSequence",
      "title": "Minimize the objective function of a smoothed regression operator with respect to betavector using the progressive smoothing algorithm.",
      "topics": [
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      ]
    },
    {
      "page": "objFunction",
      "title": "Auxiliary function to define the objective function of an L1 penalized regression operator.",
      "topics": [
        "objFunction"
      ]
    },
    {
      "page": "objFunctionGradient",
      "title": "Auxiliary function which computes the (non-smooth) gradient of an L1 penalized regression operator.",
      "topics": [
        "objFunctionGradient"
      ]
    },
    {
      "page": "objFunctionSmooth",
      "title": "Auxiliary function to define the objective function of the smoothed L1 penalized regression operator.",
      "topics": [
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      ]
    },
    {
      "page": "objFunctionSmoothGradient",
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      ]
    },
    {
      "page": "prsLasso",
      "title": "Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the Lasso for polygenic risk scores (prs).",
      "topics": [
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      ]
    },
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      "page": "standardLasso",
      "title": "Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the Lasso.",
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