After selection with the Group LASSO (or generalized variants such as the overlapping, sparse, or standardized Group LASSO), inference for the selected parameters is unreliable in the absence of adjustments for selection bias. In the penalized Gaussian regression setup, existing approaches provide adjustments for selection events that can be expressed as linear inequalities in the data variables. Such a representation, however, fails to hold for selection with the Group LASSO and substantially obstructs the scope of subsequent post-selective inference. Key questions of inferential interest, e.g., inference for the effects of selected variables on the outcome, remain unanswered. In the present paper, we develop a consistent, post-selective, Bayesian method to address the existing gaps by deriving a likelihood adjustment factor and an approximation thereof that eliminates bias from the selection of groups. Experiments on simulated data and data from the Human Connectome Project demonstrate that our method recovers the effects of parameters within the selected groups while paying only a small price for bias adjustment.

There is substantial interest in developing machine-based methods that reliably distinguish patients from healthy controls using high dimensional correlation maps known as functional connectomes (FC's) generated from resting state fMRI. To address the dimensionality of FC's, the current body of work relies on feature selection techniques that are blind to the spatial structure of the data. In this paper, we propose to use the fused Lasso regularized support vector machine to explicitly account for the 6-D structure of the FC (defined by pairs of points in 3-D brain space). In order to solve the resulting nonsmooth and large-scale optimization problem, we introduce a novel and scalable algorithm based on the alternating direction method. Experiments on real resting state scans show that our approach can recover results that are more neuroscientifically informative than previous methods.

UNLABELLED: DNA watermarks are used for hiding messages or for authenticating genetically modified organisms. Recently, we presented an algorithm called DNA-Crypt for generating DNA-based watermarks that can be integrated into the genome by using the characteristics of the degenerative genetic code. DNA-Crypt generates the watermark by replacing single bases and thus creating synonymous codons that encrypt the hidden information. Mutations within the integrated DNA sequence can be corrected using several mutation correction codes, to keep the hidden information intact. This method has successfully been tested in asexually replicating organisms like bacteria or yeast, where the watermark is duplicated with every cell division. It has been shown that DNA watermarks produced by DNA-Crypt do not influence the transcription or translation of a protein. In sexually reproducing diploid organisms, additional problems can occur, e.g. recombination events can destroy hidden information. Using population predictions as well as statistical analyses we identified a coupled Y-chromosomal/mitochondrial DNA watermarking procedure as the most appropriate for diploid organisms. We developed a mitochondria adapted version of DNA-Crypt, which is called Project Mito that can be used in combination with the original program. AVAILABILITY: http://www.uni-muenster.de/Biologie.NeuroVer/Tumorbiologie/DNA-Crypt/index.html