lqa-package: Fitting GLMs based on penalized likelihood inference.
In lqa: Penalized Likelihood Inference for GLMs

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The lqa package is designed to fit Generalized Linear Models (GLMs) based on penalized likelihood inference. That is we assume our objective to be

\min_{\mathbf{b}} - \ell (\mathbf{b}) + P_λ (\boldsymbol{β}),

where \ell(\mathbf{b}) is the log-likelihood of the underlying GLM with unknown coefficient vector \mathbf{b} = (β_0, \boldsymbol{β}^\top)^\top and the penalty term has structure

P_{λ} (\boldsymbol{β}) = ∑_{j=1}^J p_{λ,j} (|\mathbf{a}_j^\top \boldsymbol{β}|)

with known vectors of constants \mathbf{a}_j. The subscript \boldsymbol{λ} illustrates the dependency on a vector of tuning parameters. This structure allows for many different penalty terms, including polytopes (such as lasso, fused lasso, LICB) and quadratic penalties (ridge, penalreg etc.).

The main important fitting procedure is the LQA algorithm. Alternatively, you can apply GBlockBoost (including RidgeBoost as special case when you use the arguments penalty = ridge and componentwise = TRUE) or ForwardBoost. However, the P-IRLS algorithm is also implemented (indirectly) as this is a special case of the LQA algorithm. See Ulbricht (2010) or the accompanying ‘User’s Guide' for further details.