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

The other War on Terror revealed: global governmentality and the Financial Action Task Force's campaign against terrorist financing

Abstract. Despite initial fanfare surrounding its launch in the White House Rose Garden, the War on Terrorist Finances (WOTF) has thus far languished as a sideshow, in the shadows of military campaigns against terrorism in Afghanistan and Iraq. This neglect is unfortunate, for the WOTF reflects the other multilateral cooperative dimension of the US-led ‘war on terror’, quite contrary to conventional sweeping accusations of American unilateralism. Yet the existing academic literature has been confined mostly to niche specialist journals dedicated to technical, legalistic and financial regulatory aspects of the WOTF. Using the Financial Action Task Force (FATF) as a case study, this article seeks to steer discussions on the WOTF onto a broader theoretical IR perspective. Building upon emerging academic works that extend Foucauldian ideas of governmentality to the global level, we examine the interwoven overlapping national, regional and global regulatory practices emerging against terrorist financing, and the implications for notions of government, regulation and sovereignty

Oracle Inequalities and Optimal Inference under Group Sparsity

We consider the problem of estimating a sparse linear regression vector $\beta^*$ under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern, namely the set of variables is partitioned into prescribed groups, only few of which are relevant in the estimation process. This group sparsity assumption suggests us to consider the Group Lasso method as a means to estimate $\beta^*$. We establish oracle inequalities for the prediction and $\ell_2$ estimation errors of this estimator. These bounds hold under a restricted eigenvalue condition on the design matrix. Under a stronger coherence condition, we derive bounds for the estimation error for mixed $(2,p)$-norms with $1\le p\leq \infty$. When $p=\infty$, this result implies that a threshold version of the Group Lasso estimator selects the sparsity pattern of $\beta^*$ with high probability. Next, we prove that the rate of convergence of our upper bounds is optimal in a minimax sense, up to a logarithmic factor, for all estimators over a class of group sparse vectors. Furthermore, we establish lower bounds for the prediction and $\ell_2$ estimation errors of the usual Lasso estimator. Using this result, we demonstrate that the Group Lasso can achieve an improvement in the prediction and estimation properties as compared to the Lasso.Comment: 37 page