arXiv subjects

Hongzhe Li

Publications and source records attributed to Hongzhe Li.

60 records · Page 4Linked to original sources

arXiv2013

Learning local directed acyclic graphs based on multivariate time series data

Multivariate time series (MTS) data such as time course gene expression data in genomics are often collected to study the dynamic nature of the systems. These data provide important information about the causal dependency among a set of random variables. In this paper, we introduce a computationally efficient algorithm to learn directed acyclic graphs (DAGs) based on MTS data, focusing on learning the local structure of a given target variable. Our algorithm is based on learning all parents (P), all children (C) and some descendants (D) (PCD) iteratively, utilizing the time order of the variables to orient the edges. This time series PCD-PCD algorithm (tsPCD-PCD) extends the previous PCD-PCD algorithm to dependent observations and utilizes composite likelihood ratio tests (CLRTs) for testing the conditional independence. We present the asymptotic distribution of the CLRT statistic and show that the tsPCD-PCD is guaranteed to recover the true DAG structure when the faithfulness condition holds and the tests correctly reject the null hypotheses. Simulation studies show that the CLRTs are valid and perform well even when the sample sizes are small. In addition, the tsPCD-PCD algorithm outperforms the PCD-PCD algorithm in recovering the local graph structures. We illustrate the algorithm by analyzing a time course gene expression data related to mouse T-cell activation.

stat.AP↗

arXiv2013

Variable selection for sparse Dirichlet-multinomial regression with an application to microbiome data analysis

With the development of next generation sequencing technology, researchers have now been able to study the microbiome composition using direct sequencing, whose output are bacterial taxa counts for each microbiome sample. One goal of microbiome study is to associate the microbiome composition with environmental covariates. We propose to model the taxa counts using a Dirichlet-multinomial (DM) regression model in order to account for overdispersion of observed counts. The DM regression model can be used for testing the association between taxa composition and covariates using the likelihood ratio test. However, when the number of covariates is large, multiple testing can lead to loss of power. To address the high dimensionality of the problem, we develop a penalized likelihood approach to estimate the regression parameters and to select the variables by imposing a sparse group $\ell_1$ penalty to encourage both group-level and within-group sparsity. Such a variable selection procedure can lead to selection of the relevant covariates and their associated bacterial taxa. An efficient block-coordinate descent algorithm is developed to solve the optimization problem. We present extensive simulations to demonstrate that the sparse DM regression can result in better identification of the microbiome-associated covariates than models that ignore overdispersion or only consider the proportions. We demonstrate the power of our method in an analysis of a data set evaluating the effects of nutrient intake on human gut microbiome composition. Our results have clearly shown that the nutrient intake is strongly associated with the human gut microbiome.

stat.AP↗

arXiv2012

A sparse conditional Gaussian graphical model for analysis of genetical genomics data

Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to standard genetic analysis in order to identify the gene expression quantitative loci (eQTL). However, the genetic architecture for many gene expressions may be complex, and poorly estimated genetic architecture may compromise the inferences of the dependency structures of the genes at the transcriptional level. In this paper we introduce a sparse conditional Gaussian graphical model for studying the conditional independent relationships among a set of gene expressions adjusting for possible genetic effects where the gene expressions are modeled with seemingly unrelated regressions. We present an efficient coordinate descent algorithm to obtain the penalized estimation of both the regression coefficients and the sparse concentration matrix. The corresponding graph can be used to determine the conditional independence among a group of genes while adjusting for shared genetic effects. Simulation experiments and asymptotic convergence rates and sparsistency are used to justify our proposed methods. By sparsistency, we mean the property that all parameters that are zero are actually estimated as zero with probability tending to one. We apply our methods to the analysis of a yeast eQTL data set and demonstrate that the conditional Gaussian graphical model leads to a more interpretable gene network than a standard Gaussian graphical model based on gene expression data alone.

stat.AP↗

arXiv2011

The sparse Laplacian shrinkage estimator for high-dimensional regression

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic associated with a graph as the penalty function. We call it the sparse Laplacian shrinkage (SLS) method. The SLS uses the minimax concave penalty for encouraging sparsity and Laplacian quadratic penalty for promoting smoothness among coefficients associated with the correlated predictors. The SLS has a generalized grouping property with respect to the graph represented by the Laplacian quadratic. We show that the SLS possesses an oracle property in the sense that it is selection consistent and equal to the oracle Laplacian shrinkage estimator with high probability. This result holds in sparse, high-dimensional settings with p >> n under reasonable conditions. We derive a coordinate descent algorithm for computing the SLS estimates. Simulation studies are conducted to evaluate the performance of the SLS method and a real data example is used to illustrate its application.

math.ST↗

arXiv2010

Variable selection and regression analysis for graph-structured covariates with an application to genomics

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks. This kind of a priori use of graphs is a useful supplement to the standard numerical data such as microarray gene expression data. In this paper we consider the problem of regression analysis and variable selection when the covariates are linked on a graph. We study a graph-constrained regularization procedure and its theoretical properties for regression analysis to take into account the neighborhood information of the variables measured on a graph. This procedure involves a smoothness penalty on the coefficients that is defined as a quadratic form of the Laplacian matrix associated with the graph. We establish estimation and model selection consistency results and provide estimation bounds for both fixed and diverging numbers of parameters in regression models. We demonstrate by simulations and a real data set that the proposed procedure can lead to better variable selection and prediction than existing methods that ignore the graph information associated with the covariates.

stat.AP↗

arXiv2008

A hidden spatial-temporal Markov random field model for network-based analysis of time course gene expression data

Microarray time course (MTC) gene expression data are commonly collected to study the dynamic nature of biological processes. One important problem is to identify genes that show different expression profiles over time and pathways that are perturbed during a given biological process. While methods are available to identify the genes with differential expression levels over time, there is a lack of methods that can incorporate the pathway information in identifying the pathways being modified/activated during a biological process. In this paper we develop a hidden spatial-temporal Markov random field (hstMRF)-based method for identifying genes and subnetworks that are related to biological processes, where the dependency of the differential expression patterns of genes on the networks are modeled over time and over the network of pathways. Simulation studies indicated that the method is quite effective in identifying genes and modified subnetworks and has higher sensitivity than the commonly used procedures that do not use the pathway structure or time dependency information, with similar false discovery rates. Application to a microarray gene expression study of systemic inflammation in humans identified a core set of genes on the KEGG pathways that show clear differential expression patterns over time. In addition, the method confirmed that the TOLL-like signaling pathway plays an important role in immune response to endotoxins.

stat.AP↗