Exterior Distance Function (EDF)
We introduce and study exterior distance function (EDF) and correspondent exterior point method (EPM) for convex optimization. The EDF is a classical Lagrangian for an equivalent problem obtained from the initial one by monotone transformation of both the objective function and the constraints. The constraints transformation is scaled by a positive scaling parameter. Thus, the EDF is a particular realization of the Nonlinear Rescaling (NR) principle. Along with the ‘center’, the EDF has two extra tools: the barrier (scaling) parameter and the vector of Lagrange multipliers. We show that EPM generates primal – dual sequence, which converges to the primal – dual solution in value under minimum assumption on the input data. Moreover, the convergence is taking place under any fixed interior point as a ‘center’ and any fixed positive scaling parameter, just due to the Lagrange multipliers update. If the second order sufficient optimality condition is satisfied, then the EPM converges with Q-linear rate under any fixed interior point as a ‘center’ and any fixed, but large enough positive scaling parameter. …

Bootstrap Lasso + Partial Ridge (LPR)
For high-dimensional sparse linear models, how to construct confidence intervals for coefficients remains a difficult question. The main reason is the complicated limiting distributions of common estimators such as the Lasso. Several confidence interval construction methods have been developed, and Bootstrap Lasso+OLS is notable for its simple technicality, good interpretability, and comparable performance with other more complicated methods. However, Bootstrap Lasso+OLS depends on the beta-min assumption, a theoretic criterion that is often violated in practice. In this paper, we introduce a new method called Bootstrap Lasso+Partial Ridge (LPR) to relax this assumption. LPR is a two-stage estimator: first using Lasso to select features and subsequently using Partial Ridge to refit the coefficients. Simulation results show that Bootstrap LPR outperforms Bootstrap Lasso+OLS when there exist small but non-zero coefficients, a common situation violating the beta-min assumption. For such coefficients, compared to Bootstrap Lasso+OLS, confidence intervals constructed by Bootstrap LPR have on average 50% larger coverage probabilities. Bootstrap LPR also has on average 35% shorter confidence interval lengths than the de-sparsified Lasso methods, regardless of whether linear models are misspecified. Additionally, we provide theoretical guarantees of Bootstrap LPR under appropriate conditions and implement it in the R package ‘HDCI.’ …

KnowNER
KnowNER is a multilingual Named Entity Recognition (NER) system that leverages different degrees of external knowledge. A novel modular framework divides the knowledge into four categories according to the depth of knowledge they convey. Each category consists of a set of features automatically generated from different information sources (such as a knowledge-base, a list of names or document-specific semantic annotations) and is used to train a conditional random field (CRF). Since those information sources are usually multilingual, KnowNER can be easily trained for a wide range of languages. In this paper, we show that the incorporation of deeper knowledge systematically boosts accuracy and compare KnowNER with state-of-the-art NER approaches across three languages (i.e., English, German and Spanish) performing amongst state-of-the art systems in all of them. …