An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors

Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group selection. Nonconvex penalties such as SCAD and MCP have been proposed and s...

An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression

We propose and study a new iterative coordinate descent algorithm (QICD) for solving nonconvex penalized quantile regression in high dimension. By permitting different subsets of covariates to be relevant for modeling the response variable at different quantiles, nonconvex penalized quantile regression provides a flexible approach for modeling high-dimensional data with heterogeneity. Although ...

Penalized likelihood regression for generalized linear models with nonquadratic penalties

One popular method for fitting a regression function is regularization: minimize an objective function which enforces a roughness penalty in addition to coherence with the data. This is the case when formulating penalized likelihood regression for exponential families. Most smoothing methods employ quadratic penalties, leading to linear estimates, and are in general incapable of recovering disc...

An Iterative Algorithm for Automatic Fitting of Continuous Piecewise Linear Models

Continuous piecewise linear models constitute useful tools to extract the basic features about the patterns of growth in complex time series data. In this work, we present an iterative algorithm for continuous piecewise regression with automatic change-points estimation. The algorithm requires an initial guess about the number and positions of the change-points or hinges, which can be obtained ...

Fitting Models to Grouped Data