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STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, that is, sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.
Journal Article
Bio-ORACLE v2.0: Extending marine data layers for bioclimatic modelling
Motivation: The availability of user-friendly, high-resolution global environmental datasets is crucial for bioclimatic modelling. For terrestrial environments, WorldClim has served this purpose since 2005, but equivalent marine data only became available in 2012, with pioneer initiatives like Bio-ORACLE providing data layers for several ecologically relevant variables. Currently, the available marine data packages have not yet been updated to the most recent Intergovernmental Panel on Climate Change (IPCC) predictions nor to present times, and are mostly restricted to the top surface layer of the oceans, precluding the modelling of a large fraction of the benthic diversity that inhabits deeper habitats. To address this gap, we present a significant update of Bio-ORACLE for new future climate scenarios, present-day conditions and benthic layers (near sea bottom). The reliability of data layers was assessed using a cross-validation framework against in situ quality-controlled data. This test showed a generally good agreement between our data layers and the global climatic patterns. We also provide a package of functions in the R software environment (sdmpredictors) to facilitate listing, extraction and management of data layers and allow easy integration with the available pipelines for bioclimatic modelling. Main types of variable contained: Surface and benthic layers for water temperature, salinity, nutrients, chlorophyll, sea ice, current velocity, phytoplankton, primary productivity, iron and light at bottom. Spatial location and grain: Global at 5 arcmin (c. 0.08° or 9.2 km at the equator). Time period and grain: Present (2000–2014) and future (2040–2050 and 2090–2100) environmental conditions based on monthly averages. Major taxa and level of measurement: Marine biodiversity associated with sea surface and epibenthic habitats. Software format: ASCII and TIFF grid formats for geographical information systems and a package of functions developed for R software.
Journal Article
Oracle database 12c release 2 performance tuning tips and techniques
This book details the latest monitoring, troubleshooting, and optimization methods. Find out how to identify and fix bottlenecks on premises and in the cloud, configure storage devices, execute effective queries, and develop bug-free SQL and PL/SQL code. Testing, reporting, and security enhancements are also covered in this Oracle Press guide.
Book
The Adaptive Lasso and Its Oracle Properties
The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain scenarios where the lasso is inconsistent for variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the ℓ
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penalty. We show that the adaptive lasso enjoys the oracle properties; namely, it performs as well as if the true underlying model were given in advance. Similar to the lasso, the adaptive lasso is shown to be near-minimax optimal. Furthermore, the adaptive lasso can be solved by the same efficient algorithm for solving the lasso. We also discuss the extension of the adaptive lasso in generalized linear models and show that the oracle properties still hold under mild regularity conditions. As a byproduct of our theory, the nonnegative garotte is shown to be consistent for variable selection.
Journal Article
Bio-ORACLE: a global environmental dataset for marine species distribution modelling
Aim: The oceans harbour a great diversity of organisms whose distribution and ecological preferences are often poorly understood. Species distribution modelling (SDM) could improve our knowledge and inform marine ecosystem management and conservation. Although marine environmental data are available from various sources, there are currently no user-friendly, high-resolution global datasets designed for SDM applications. This study aims to fill this gap by assembling a comprehensive, uniform, high-resolution and readily usable package of global environmental rasters. Location: Global, marine. Methods: We compiled global coverage data, e.g. satellite-based and in situ measured data, representing various aspects of the marine environment relevant for species distributions. Rasters were assembled at a resolution of 5 arcmin (c. 9.2 km) and a uniform landmask was applied. The utility of the dataset was evaluated by maximum entropy SDM of the invasive seaweed Codium fragile ssp. fragile. Results: We present Bio-ORACLE (ocean rasters for analysis of climate and environment), a global dataset consisting of 23 geophysical, biotic and climate rasters. This user-friendly data package for marine species distribution modelling is available for download at http://www.bio-oracle.ugent.be. The high predictive power of the distribution model of C. fragile ssp. fragile clearly illustrates the potential of the data package for SDM of shallow-water marine organisms. Main conclusions: The availability of this global environmental data package has the potential to stimulate marine SDM. The high predictive success of the presenceonly model of a notorious invasive seaweed shows that the information contained in Bio-ORACLE can be informative about marine distributions and permits building highly accurate species distribution models.
Journal Article