Ultra-high Dimensional Multiple Output Learning With Simultaneous Orthogonal Matching Pursuit: A Sure Screening Approach

We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in \cite{fan08sis}, is an efficient and highly scalable way to remove many irrelevant variables from the set of all variables, while retaining all the relevant variables. S-OMP can be applied to problems with hundreds of thousands of variables and once the number of variables is reduced to a manageable size, a more computationally demanding procedure can be used to identify the relevant variables for each of the regression outputs. To our knowledge, this is the first attempt to utilize relatedness of multiple outputs to perform fast screening of relevant variables. As our main theoretical contribution, we prove that, asymptotically, S-OMP is guaranteed to reduce an ultra-high number of variables to below the sample size without losing true relevant variables. We also provide formal evidence that a modified Bayesian information criterion (BIC) can be used to efficiently determine the number of iterations in S-OMP. We further provide empirical evidence on the benefit of variable selection using multiple regression outputs jointly, as opposed to performing variable selection for each output separately. The finite sample performance of S-OMP is demonstrated on extensive simulation studies, and on a genetic association mapping problem. $Keywords$ Adaptive Lasso; Greedy forward regression; Orthogonal matching pursuit; Multi-output regression; Multi-task learning; Simultaneous orthogonal matching pursuit; Sure screening; Variable selectio

Extracellular volume regulation and growth

We have formalized extracellular and intracellular volume interaction with each other and the influence of these processes on the type of cell growth. The linearized model was verified by stereo metric solution and the results were compared with experimental data. Two theoretical solutions were found: Solution 1, extracellular volume (ECV) was calculated to be about 23% of total body volume (TV). Stereo metric solution suggested the cubic cell cluster formed by 8-cells. This hypothesis (Solution l) explains the ECV to be compatible with the widely accepted value (about 23% of TV). In addition, the 8-cell cluster hypothesis explains the existence of ECV oscillation with the period of about seven days. This hypothesis probably describes the dominant type of growth in humans. Solution 2, in this type of growth, ECV fills about 77% per cent of TV. Instead of the 8-cell cube, in this type of proliferation 4-cells could form a tetrahedron. This type of growth could be beneficial in processes where free space in tissue or organ must be filled for example in peptic ulcer healing and namely in repopulating of free space in a bone after high dose chemotherapy

Graph Estimation From Multi-attribute Data

Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating graphs from multi-attribute data. Instead of estimating the partial correlation as in current literature, our method estimates the partial canonical correlations that naturally accommodate complex nodal features. Computationally, we provide an efficient algorithm which utilizes the multi-attribute structure. Theoretically, we provide sufficient conditions which guarantee consistent graph recovery. Extensive simulation studies demonstrate performance of our method under various conditions. Furthermore, we provide illustrative applications to uncovering gene regulatory networks from gene and protein profiles, and uncovering brain connectivity graph from functional magnetic resonance imaging data.Comment: Extended simulation study. Added an application to a new data se

Optical Coherence Tomography for Examination of Parchment Degradation

A novel application of Optical Coherence Tomography utilizing infrared light of 830 nm central wavelength for non invasive examination of the structure of parchment, some covered with iron gall ink, is presented. It is shown that both the parchment and the ink applied are sufficiently transparent to light of this wavelength. In the study, Spectral OCT (SOCT) as well as Polarisation Sensitive OCT (PS-OCT) techniques were used to obtain cross-sectional images of samples of parchment based on scattering properties. The second technique was additionally employed to recover the birefringence properties and the optical axis orientations of the sample. It was shown that freshly produced parchment exhibits a degree of birefringence. However, this property declines with ageing, and samples of old parchment completely depolarise the incident light

TREX1 is expressed by microglia in normal human brain and increases in regions affected by ischemia

BACKGROUND: Mutations in the three-prime repair exonuclease 1 (TREX1) gene have been associated with neurological diseases, including Retinal Vasculopathy with Cerebral Leukoencephalopathy (RVCL). However, the endogenous expression of TREX1 in human brain has not been studied. METHODS: We produced a rabbit polyclonal antibody (pAb) to TREX1 to characterize TREX1 by Western blotting (WB) of cell lysates from normal controls and subjects carrying an RVCL frame-shift mutation. Dual staining was performed to determine cell types expressing TREX1 in human brain tissue. TREX1 distribution in human brain was further evaluated by immunohistochemical analyses of formalin-fixed, paraffin-embedded samples from normal controls and patients with RVCL and ischemic stroke. RESULTS: After validating the specificity of our anti-TREX1 rabbit pAb, WB analysis was utilized to detect the endogenous wild-type and frame-shift mutant of TREX1 in cell lysates. Dual staining in human brain tissues from patients with RVCL and normal controls localized TREX1 to a subset of microglia and macrophages. Quantification of immunohistochemical staining of the cerebral cortex revealed that TREX1 CONCLUSIONS: TREX1 is expressed by a subset of microglia in normal human brain, often in close proximity to the microvasculature, and increases in the setting of ischemic lesions. These findings suggest a role for TREX

Estimating time-varying networks

Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant network from observation data, little has been done toward estimating time-varying networks from time series of entity attributes. In this paper we present two new machine learning methods for estimating time-varying networks, which both build on a temporally smoothed $l_1$-regularized logistic regression formalism that can be cast as a standard convex-optimization problem and solved efficiently using generic solvers scalable to large networks. We report promising results on recovering simulated time-varying networks. For real data sets, we reverse engineer the latent sequence of temporally rewiring political networks between Senators from the US Senate voting records and the latent evolving regulatory networks underlying 588 genes across the life cycle of Drosophila melanogaster from the microarray time course.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS308 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org