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Summary. Variable selection can be challenging, particularly in situations with a large number of predictors with possibly high correlations, such as gene expression data. In this paper, a new method called the OSCAR (Octagonal Shrinkage and Clustering Algorithm for Regression) is proposed to simultaneously select variables while grouping them into predictive clusters. In addition to improving prediction accuracy and interpretation, these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior. The technique is based on penalized least squares with a geometrically intuitive penalty function that shrinks some coefficients to exactly zero. Additionally, this penalty yields exact equality of some coefficients, encouraging correlated predictors that have a similar effect on the response to form predictive clusters represented by a single coefficient. The proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and model complexity, while yielding the additional grouping information.

We address the problem of sparse selection in linear models. A number of non-convex penalties have been proposed for this purpose, along with a variety of convex-relaxation algorithms for finding good solutions. In this paper we pursue the coordinate-descent approach for optimization, and study its convergence properties. We characterize the properties of penalties suitable for this approach, study their corresponding threshold functions, and describe a df-standardizing reparametrization that assists our pathwise algorithm. The MC+ penalty (Zhang 2010) is ideally suited to this task, and we use it to demonstrate the performance of our algorithm. 1

SUMMARY Gaussian graphical models explore dependence relationships between random variables, through the estimation of the corresponding inverse covariance matrices. In this paper we develop an estimator for such models appropriate for data from several graphical models that share the same variables and some of the dependence structure. In this setting, estimating a single graphical model would mask the underlying heterogeneity, while estimating separate models for each category does not take advantage of the common structure. We propose a method that jointly estimates the graphical models corresponding to the different categories present in the data, aiming to preserve the common structure, while allowing for differences between the categories. This is achieved through a hierarchical penalty that targets the removal of common zeros in the inverse covariance matrices across categories. We establish the asymptotic consistency and sparsity of the proposed estimator in the high-dimensional case, and illustrate its performance on a number of simulated networks. An application to learning semantic connections between terms from webpages collected from computer science departments is included.

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96 (2001) 1348–1360] and [Ann. Statist. 32 (2004) 928–961] which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem, which should be properly handled by the ideal method. Many existing variable selection methods fail to achieve both goals simultaneously. In this paper, we propose the adaptive elastic-net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Under weak regularity conditions, we establish the oracle property of the adaptive elastic-net. We show by simulations that the adaptive elastic-net deals with the collinearity problem better than the other oracle-like methods, thus enjoying much improved finite sample performance.

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Abstract: We present a weighted-Lasso method to infer the parameters of a first-order vector auto-regressive model that describes time course expression data generated by directed gene-to-gene regulation networks. These networks are assumed to own prior internal structures of connectiv-ity which drive the inference method. This prior structure can be either derived from prior biological knowledge or inferred by the method itself. We illustrate the performance of this structure-based penalization both on synthetic data and on two canonical regulatory networks, first yeast cell cycle regulation network by analyzing Spellman et al’s dataset and second E. coli S.O.S. DNA repair network by analysing U. Alon’s lab data.

Objective. Electronic medical records (EMRs) are a rich data source for discovery research but are underutilized due to the difficulty of extracting highly accurate clinical data. We assessed whether a classification algorithm incorporating narrative EMR data (typed physician notes) more accurately classifies subjects with rheumatoid arthritis (RA) compared with an algorithm using codified EMR data alone. Methods. Subjects with>1 International Classification of Diseases, Ninth Revision RA code (714.xx) or who had anti–cyclic citrullinated peptide (anti-CCP) checked in the EMR of 2 large academic centers were included in an “RA Mart ” (n 29,432). For all 29,432 subjects, we extracted narrative (using natural language processing) and codified RA clinical information. In a training set of 96 RA and 404 non-RA cases from the RA Mart classified by medical record review, we used narrative and codified data to develop classification algorithms using logistic regression. These algorithms were applied to the entire RA Mart. We calculated and compared the positive predictive value (PPV) of these algorithms by reviewing the records of an additional 400 subjects classified as having RA by the algorithms. Results. A complete algorithm (narrative and codified data) classified RA subjects with a significantly higher PPV of 94% than an algorithm with codified data alone (PPV of 88%). Characteristics of the RA cohort identified by the complete algorithm were comparable to existing RA cohorts (80 % women, 63 % anti-CCP positive, and 59 % positive for erosions). Conclusion. We demonstrate the ability to utilize complete EMR data to define an RA cohort with a PPV of 94%, which was superior to an algorithm using codified data alone.

In this paper, we aim at recovering an unknown signal x0 from noisy measurements y = Φx0 +w, where Φ is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we impose an analysis sparsity prior. More precisely, the recovery is cast as a convex optimization program where the objective is the sum of a quadratic data fidelity term and a regularization term formed of the ℓ 1-norm of the correlations between the sought after signal and atoms in a given (generally overcomplete) dictionary. The ℓ 1-sparsity analysis prior is weighted by a regularization parameter λ> 0. In this paper, we prove that any minimizers of this problem is a piecewise-affine function of the observations y and the regularization parameter λ. As a byproduct, we exploit these properties to get an objectively guided choice of λ. In particular, we develop an extension of the Generalized Stein Unbiased Risk Estimator (GSURE) and show that it is an unbiased and reliable estimator of an appropriately defined risk. The latter encompasses special cases

Motivation: Gene regulatory networks, in which edges between nodes describe interactions between transcriptional regulators and their target genes, determine the coordinated spatiotemporal expression of genes. Especially in higher organisms, context-specific combinatorial regulation by transcription factors (TFs) is believed to determine cellular states and fates. TF-target gene interactions can be studied using high-throughput techniques such as ChIP-chip or ChIP-Seq. These experiments are time and cost intensive, and further limited by, for instance, availability of high affinity TF anti-bodies. Hence, there is a practical need for methods that can predict TF-TF and TF-target gene interactions in silico, i.e. from gene expression and DNA sequence data alone. We propose GEMULA, a novel approach based on linear models to predict TF-gene expression associations and TF-TF interactions from experimental data. GEMULA is based on linear models, fast and considers a wide range of biologically plausible models that describe gene expression data as a function of predicted TF binding to gene promoters. Results: We show that models inferred with GEMULA are able to explain roughly 70 % of the observed variation in gene expression in the yeast heat shock response. The functional relevance of the inferred TF-TF interactions in these models are validated by different sources of independent experimental evidence. We also have applied GEMULA to an in vitro model of neuronal outgrowth. Our findings confirm existing knowledge on gene regulatory interactions underlying neuronal outgrowth, but importantly also generate new insights into the temporal dynamics of this gene regulatory network that can now be addressed experimentally.