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Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to assume piecewise stationarity, where the model can change at potentially many change points. We propose a three-stage procedure for simultaneous estimation of change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and solve it using a penalized least square estimator with a total variation penalty. We show that the penalized estimation method over-estimates the number of change points, and propose a selection criterion to identify the change points. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We prove that the proposed procedure consistently detects the number and location of change points, and provides consistent estimates of VAR parameters. The performance of the method is illustrated through several simulated and real data examples. for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractFueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work has primarily addressed estimation. To bridge this gap, we develop a new statistical inference procedure for high-dimensional Hawkes processes. The key ingredient for the inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarize the entire history of the process. Combining recent martingale central limit theorem with the new concentration inequality, we then characterize the convergence rate of the test statistics in a continuous time domain. Finally, to account for potential non-stationarity of the process in practice, we extend our statistical inference procedure to a flexible class of Hawkes processes with time-varying background intensities and unknown transition functions. The finite sample validity of the inferential tools is illustrated via extensive simulations and further applied to a neuron spike train data set. [ABSTRACT FROM AUTHOR]

Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and in response to external stimuli. In biology and medicine, these changes have been found to be predictive of complex diseases. They have also been used to gain insight into mechanisms of disease initiation and progression. Primarily motivated by biological applications, this article provides a review of recent statistical machine learning methods for inferring networks and identifying changes in their structures. This article is categorized under:Data: Types and Structure > Graph and Network DataStatistical Models > Graphical Models [ABSTRACT FROM AUTHOR]

For multiple testing problems, Benjamini and Hochberg (1995) proposed the false discovery rate (FDR) as an alternative to the family-wise error rate (FWER). Since then, researchers have provided many proofs to control the FDR under different assumptions. Storey et al. (2004) showed that the rejection threshold of a BH step-up procedure is a stopping time with respect to the reverse filtration generated by the pvalues and proposed a new proof based on the martingale theory. Following this work, martingale methods have been widely used to establish FDR control in various settings, but have been primarily applied to reverse filtration only. However, forward filtration can be more amenable for generalized and adaptive FDR controlling procedures. In this paper, we present a new proof, based on forward filtration, for step-down FDR controlling procedures that start from small p-values and update the rejection regions as larger p-values are observed. [ABSTRACT FROM AUTHOR]

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new algorithm that requires conditioning only on small sets of variables. The proposed algorithm, which is essentially a modified version of the PC-Algorithm, offers significant gains in both computational complexity and estimation accuracy. In particular, it results in more efficient and accurate estimation in large networks containing hub nodes, which are common in biological systems. We prove the consistency of the proposed algorithm, and show that it also requires a less stringent faithfulness assumption than the PC-Algorithm. Simulations in low and high-dimensional settings are used to illustrate these findings. An application to gene expression data suggests that the proposed algorithm can identify a greater number of clinically relevant genes than current methods. [ABSTRACT FROM AUTHOR]

We consider the problem of nonparametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well suited to high-dimensional sparse additive models and combines the appealing features of finite basis representation and smoothing penalties. In the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when component functions possess different levels of complexity. In contrast, a smoothing spline-type penalty on the component functions is adaptive but does not provide a parsimonious representation. Our proposal simultaneously achieves parsimony and adaptivity in a computationally efficient way. We demonstrate these properties through empirical studies and show that our estimator converges at the minimax rate for functions within a hierarchical class. We further establish minimax rates for a large class of sparse additive models. We also develop an efficient algorithm that scales similarly to the lasso with the number of covariates and sample size. [ABSTRACT FROM AUTHOR]

Despite recent and growing interest in using Twitter to examine human behavior and attitudes, there is still significant room for growth regarding the ability to leverage Twitter data for social science research. In particular, gleaning demographic information about Twitter users—a key component of much social science research—remains a challenge. This article develops an accurate and reliable data processing approach for social science researchers interested in using Twitter data to examine behaviors and attitudes, as well as the demographic characteristics of the populations expressing or engaging in them. Using information gathered from Twitter users who state an intention to not vote in the 2012 presidential election, we describe and evaluate a method for processing data to retrieve demographic information reported by users that is not encoded as text (e.g., details of images) and evaluate the reliability of these techniques. We end by assessing the challenges of this data collection strategy and discussing how large-scale social media data may benefit demographic researchers. [ABSTRACT FROM AUTHOR]

Rationale: Understanding mechanisms of resistance to M. tuberculosis (M.tb) infection in humans could identify novel therapeutic strategies as it has for other infectious diseases, such as HIV. Objectives: To compare the early transcriptional response of M.tb-infected monocytes between Ugandan household contacts of tuberculosis patients who demonstrate clinical resistance to M.tb infection (cases) and matched controls with latent tuberculosis infection. Methods: Cases (n = 10) and controls (n = 18) were selected from a long-term household contact study in which cases did not convert their tuberculin skin test (TST) or develop tuberculosis over two years of follow up. We obtained genome-wide transcriptional profiles of M.tb-infected peripheral blood monocytes and used Gene Set Enrichment Analysis and interaction networks to identify cellular processes associated with resistance to clinical M.tb infection. Measurements and main results: We discovered gene sets associated with histone deacetylases that were differentially expressed when comparing resistant and susceptible subjects. We used small molecule inhibitors to demonstrate that histone deacetylase function is important for the pro-inflammatory response to in-vitro M.tb infection in human monocytes. Conclusions: Monocytes from individuals who appear to resist clinical M.tb infection differentially activate pathways controlled by histone deacetylase in response to in-vitro M.tb infection when compared to those who are susceptible and develop latent tuberculosis. These data identify a potential cellular mechanism underlying the clinical phenomenon of resistance to M.tb infection despite known exposure to an infectious contact. [ABSTRACT FROM AUTHOR]

Motivation: Pathway enrichment analysis has become a key tool for biomedical researchers to gain insight into the underlying biology of differentially expressed genes, proteins and metabolites. It reduces complexity and provides a system-level view of changes in cellular activity in response to treatments and/or in disease states. Methods that use existing pathway network information have been shown to outperform simpler methods that only take into account pathway membership. However, despite significant progress in understanding the association amongst members of biological pathways, and expansion of data bases containing information about interactions of biomolecules, the existing network information may be incomplete or inaccurate and is not cell-type or disease condition-specific. Results: We propose a constrained network estimation framework that combines network estimation based on cell- and condition-specific high-dimensional Omics data with interaction information from existing data bases. The resulting pathway topology information is subsequently used to provide a framework for simultaneous testing of differences in expression levels of pathway members, as well as their interactions. We study the asymptotic properties of the proposed network estimator and the test for pathway enrichment, and investigate its small sample performance in simulated and real data settings. [ABSTRACT FROM AUTHOR]