Penalized wavelet monotone regression

In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex op- timization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular we investigate a penalized wavelet monotone regression estimator. We establish the rate of convergence of this estimator, and illustrate its finite sample performance via a simulation study. We also compare its performance with that of a recently proposed constrained estimator. An illustration to some real data is given

Optimization with Sparsity-Inducing Penalties

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view

A Feature Selection Method for Multivariate Performance Measures

Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for classification error. In this paper, we propose a generalized sparse regularizer. Based on the proposed regularizer, we present a unified feature selection framework for general loss functions. In particular, we study the novel feature selection paradigm by optimizing multivariate performance measures. The resultant formulation is a challenging problem for high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed to solve this problem, and the convergence is presented. In addition, we adapt the proposed method to optimize multivariate measures for multiple instance learning problems. The analyses by comparing with the state-of-the-art feature selection methods show that the proposed method is superior to others. Extensive experiments on large-scale and high-dimensional real world datasets show that the proposed method outperforms $l_1$-SVM and SVM-RFE when choosing a small subset of features, and achieves significantly improved performances over SVM$^{perf}$ in terms of $F_1$-score

Competition and Enterprise Performance in Transition Economies: Evidence from a Cross-country Survey

This paper uses a survey of 3,300 firms in 25 transition countries to shed light on the factors that influence restructuring by firms and their subsequent performance as measured by growth in sales and in sales per employee over a three-year period. We begin by surveying what a decade of transition has taught us about the factors that determine how firms respond to the new market environment. We go on to analyse the impact on performance of ownership, soft budget constraints, the general business environment and a range of measures of the intensity of competition as perceived by a firm. We find that competition has an important and non-monotonic effect on the growth of sales and of labour productivity: some degree of perceived market power is associated with higher sales growth, but competitive pressure is also important. Similar competition effects are found upon firms' decisions to develop and improve their products, but market power has an unambiguously negative impact on purely defensive (cost-reducing) restructuring activity. New firms have grown relatively fast, but among old firms ownership per se has no significant relationship to performance (though state-owned firms have engaged in significantly less development of new products). Soft budget constraints have a broadly negative and the business environment a broadly positive impact on restructuring and performance.http://deepblue.lib.umich.edu/bitstream/2027.42/39760/3/wp376.pd