Union Support Recovery in High-Dimensional Multivariate Regression

Abstract

Standard Form 298 (Rev. 8-98)Prescribed by ANSI Std. Z39.18Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Once released in the environment, either through detonation, casing breakage, or by slow leaks from unexploded ordnance (UXO), nitrogenous energetic compounds (NEC, such as TNT, HMX, RDX) may sorb onto particulates, partition to dissolved organic matter, or remain dissolved in aqueous media. Our hypothesis was that NEC would be transient in coastal ecosystems. This was based primarily on the understanding that microbial growth in these systems is typically nitrogen-limited and there are few examples of nitrogen based organic compounds that are not rapidly metabolized in these environments. During 14 sampling events in coastal waterways from 2002 to 2007, we measured TNT mineralization rates in surface sediment and water samples that were often the same as, or within one order of magnitude of, the rate of total heterotrophic bacterial metabolism. These rates were often similar to those of other organic compounds that are transient in natural ecosystems due to their use in bacterial metabolism, such as petroleum hydrocarbons and amino acids. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) SPONSOR / MONITOR'S ACRONYM(S) 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR / MONITOR'S REPORT NUMBER(S)

Multi-Task Feature Selection on Multiple Networks via Maximum Flows

“…In multi-task settings, we compare Multi-SConES to multi-task Lasso [23] and multi-task Grace. Since Grace is for single-task feature selection, we construct an artificial dataset including a given network using the reformulation in Lemma 1 of [18], followed by applying multi-task Lasso to the dataset (Supplementary Note C).…”

“…Several multi-task versions of Lasso, in which related tasks are coupled with each other, have been proposed as well: Multi-Task Lasso [23] uses an ℓ 2 -norm on each weight across all tasks to reward solutions, where the same features are selected for all tasks. Graph-Guided Fused Lasso [16] extends this idea by coupling the weight vectors of correlated tasks: the more correlated two tasks are, the more solutions in which they have similar weight vectors are rewarded.…”

Conditions for Consistency of a Log-Likelihood-Based Information Criterion in Normal Multivariate Linear Regression Models under the Violation of the Normality Assumption

“…A variable selection through the candidate models in (1.1) is equivalent to extracting the subset of relevant explanatory variables that are active in at least one response variable, which is referred to as the support union problem (see Obozinski et al (2008Obozinski et al ( , 2011), and a result from the variable selection helps to provide a faster and more cost-effective model, and a better understanding of the underlying process that generated the data.…”

Adaptive Multi-task Sparse Learning with an Application to fMRI Study

“…The task of conducting variable selection can always be achieved via learning the sparsity pattern of parameters. In the multi-task learning setting, it is often assumed that parameters for different tasks share the same sparsity pattern [2,18]. To achieve such an effect, a popular approach is to adopt a joint sparsity regularization to encourage groupwise sparsity across multiple tasks.…”