Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically distributed (i.i.d.) samples. In this work, we focus on stable Gaussian processes and investigate the theoretical properties of $\ell _1$-regularized estimates in two important statistical problems in the context of high-dimensional time series: (a) stochastic regression with serially correlated errors and (b) transition matrix estimation in vector autoregressive (VAR) models. We derive nonasymptotic upper bounds on the estimation errors of the regularized estimates and establish that consistent estimation under high-dimensional scaling is possible via $\ell_1$-regularization for a large class of stable processes under sparsity constraints. A key technical contribution of the work is to introduce a measure of stability for stationary processes using their spectral properties that provides insight into the effect of dependence on the accuracy of the regularized estimates. With this proposed stability measure, we establish some useful deviation bounds for dependent data, which can be used to study several important regularized estimates in a time series setting.Comment: Published at http://dx.doi.org/10.1214/15-AOS1315 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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.

Transforming growth factor-beta (TGF-beta) induces epithelial-mesenchymal transition (EMT) of epithelial cells in both normal embryonic development and certain pathological contexts. Here, we show that TGF-beta induced-EMT in human lung cancer cells (A549; adenocarcinoma cells) mediates tumor cell migration and invasion phenotypes. To gain insights into molecular events during EMT, we employed a global stable isotope labeled profiling strategy using iTRAQ reagents, followed by 2DLC-MS/MS, which identified a total of 51 differentially expressed proteins during EMT; 29 proteins were up-regulated and 22 proteins were down-regulated. Down-regulated proteins were predominantly enzymes involved in regulating nutrient or drug metabolism. The majority of the TGF-beta-induced proteins (such as tropomyosins, filamin A, B, & C, integrin-beta1, heat shock protein27, transglutaminase2, cofilin, 14-3-3 zeta, ezrin-radixin-moesin) are involved in the regulation of cell migration, adhesion and invasion, suggesting the acquisition of a invasive phenotype.

Consensus clustering (CC) has been adopted for unsupervised class discovery in many genomic studies. It calculates how frequently two samples are grouped together in repeated clustering runs, and uses the resulting pairwise "consensus rates" for visual demonstration that clusters exist, for comparing cluster stability, and for estimating the optimal cluster number (K). However, the sensitivity and specificity of CC have not been systemically assessed. Through simulations we find that CC is able to divide randomly generated unimodal data into apparently stable clusters for a range of K, essentially reporting chance partitions of cluster-less data. For data with known structure, the common implementations of CC perform poorly in identifying the true K. These results suggest that CC should be applied and interpreted with caution. We found that a new metric based on CC, the proportion of ambiguously clustered pairs (PAC), infers K equally or more reliably than similar methods in simulated data with known K. Our overall approach involves the use of realistic null distributions based on the observed gene-gene correlation structure in a given study, and the implementation of PAC to more accurately estimate K. We discuss the strength of our approach in the context of other ensemble-based methods.