A Greedy Homotopy Method for Regression with Nonconvex Constraints

Constrained least squares regression is an essential tool for high-dimensional data analysis. Given a partition $\mathcal{G}$ of input variables, this paper considers a particular class of nonconvex constraint functions that encourage the linear model to select a small number of variables from a small number of groups in $\mathcal{G}$. Such constraints are relevant in many practical applications, such as Genome-Wide Association Studies (GWAS). Motivated by the efficiency of the Lasso homotopy method, we present RepLasso, a greedy homotopy algorithm that tries to solve the induced sequence of nonconvex problems by solving a sequence of suitably adapted convex surrogate problems. We prove that in some situations RepLasso recovers the global minima of the nonconvex problem. Moreover, even if it does not recover global minima, we prove that in relevant cases it will still do no worse than the Lasso in terms of support and signed support recovery, while in practice outperforming it. We show empirically that the strategy can also be used to improve over other Lasso-style algorithms. Finally, a GWAS of ankylosing spondylitis highlights our method's practical utility

Magma sources involved in the 2002 Nyiragongo eruption, as inferred from an InSAR analysis

International audienceOn 17 January 2002, Nyiragongo volcano erupted along a 20 km-long fracture network extending from the volcano to the city of Goma. The event was captured by InSAR data from the ERS-2 and RADARSAT-1 satellites. A combination of 3D numerical modeling and inversions is used to analyze these displacements. Using Akaike Information Criteria, we determine that a model with two subvertical dikes is the most likely explanation for the 2002 InSAR deformation signal. A first, shallow dike, 2 km high, is associated with the eruptive fissure, and a second, deeper dike, 6 km high and 40 km long, lies about 3 km below the city of Goma. As the deep dike extends laterally for 20 km beneath the gas-rich Lake Kivu, the interaction of magma and dissolved gas should be considered as a significant hazard for future eruptions. A likely scenario for the eruption is that the magma supply to a deep reservoir started ten months before the eruption, as indicated by LP events and tremor. Stress analysis indicates that the deep dike could have triggered the injection of magma from the lake and shallow reservoir into the eruptive dike. The deep dike induced the opening of the southern part of this shallow dike, to which it transmitted magma though a narrow dike. This model is consistent with the geochemical analysis, the lava rheology and the pre- and post-eruptive seismicity. We infer low overpressures (1-10 MPa) for the dikes. These values are consistent with lithostatic crustal stresses close to the dikes and low magma pressure. As a consequence, the dike direction is probably not controlled by stresses but rather by a reduced tensile strength, inherited from previous rift intrusions. The lithostatic stresses indicate that magmatic activity is intense enough to relax tensional stresses associated with the rift extension

The 2007 rifting event in Northern Tanzania studied by C and L-band interferometry

peer reviewe

Jacques Foccart et les mauvais conseils de Félix Houphouët-Boigny

Un des premiers « faits d'armes », si l'on ose ainsi dire, de Jacques Foccart fut son soutien à la sécession du Katanga et à un dirigeant africain des plus douteux, Moïse Tschombé, auquel le général de Gaulle fit l'honneur d'être reçu à Paris en novembre 1964. Les éléments les moins recommandables des réseaux de Foccart, notamment du célèbre SAC (le service d'ordre gaulliste dont il fut l'un des animateurs) se retrouvèrent pour appuyer la sécession katangaise, qui fut ponctuée, on s'en souvie..