L1/Lp Regularization of Differences

Lp-regularized optimization by using orthant-wise approach for inducing sparsity

Sparsity induced in the optimized weights effectively works for factorization with robustness to noises and for classification with feature selection. For enhancing the sparsity, L1 regularization is introduced into the objective cost function to be minimized. In general, however, Lp (p<1) regularization leads to more sparse solutions than L1, though Lp regularized problem is difficult to be ef...

Stability Conditions for L1/Lp Regularization

Cross-Cultural Differences and Pragmatic Transfer in English and Persian Refusals

This study aimed to examine cross-cultural differences in performing refusal of requests between Persian native speakers (PNSs) and English native speakers (ENSs) in terms of the frequency of the semantic formulas. Also examined in this study was whether Persian EFL learners would transfer their L1 refusal patterns into the L2, and if there would be a relation between their proficiency level an...

Unifying Framework for Fast Learning Rate of Non-Sparse Multiple Kernel Learning

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations. Our main target in this paper is dense type regularizations including lp-MKL that imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. According to the recent numerical experiments, the sparse regularization does not necessarily show a good p...

Another look at linear programming for feature selection via methods of regularization

We consider statistical procedures for feature selection defined by a family of regularization problems with convex piecewise linear loss functions and penalties of l1 nature. Many known statistical procedures (e.g. quantile regression and support vector machines with l1 norm penalty) are subsumed under this category. Computationally, the regularization problems are linear programming (LP) prob...