Early stopping in L2Boosting

High-Dimensional $L_2$Boosting: Rate of Convergence

Boosting is one of the most significant developments in machine learning. This paper studies the rate of convergence of L2Boosting, which is tailored for regression, in a high-dimensional setting. Moreover, we introduce so-called “post-Boosting”. This is a post-selection estimator which applies ordinary least squares to the variables selected in the first stage by L2Boosting. Another variant is...

Sparse Boosting

We propose Sparse Boosting (the SparseL2Boost algorithm), a variant on boosting with the squared error loss. SparseL2Boost yields sparser solutions than the previously proposed L2Boosting by minimizing some penalized L2-loss functions, the FPE model selection criteria, through smallstep gradient descent. Although boosting may give already relatively sparse solutions, for example corresponding t...

Boosting additive models using component-wise P-Splines

We consider an efficient approximation of Bühlmann & Yu’s L2Boosting algorithm with component-wise smoothing splines. Smoothing spline base-learners are replaced by P-spline base-learners which yield similar prediction errors but are more advantageous from a computational point of view. In particular, we give a detailed analysis on the effect of various P-spline hyper-parameters on the boosting...

Comparing different stopping criteria for fuzzy decision tree induction through IDFID3

Fuzzy Decision Tree (FDT) classifiers combine decision trees with approximate reasoning offered by fuzzy representation to deal with language and measurement uncertainties. When a FDT induction algorithm utilizes stopping criteria for early stopping of the tree's growth, threshold values of stopping criteria will control the number of nodes. Finding a proper threshold value for a stopping crite...

Consistency for L2Boosting and Matching Pursuit with Trees and Tree-type Basis Functions