Gene regulatory network inference based on modified adaptive lasso.

Genes regulate each other and form a gene regulatory network (GRN) to realise biological functions. Elucidating GRN from experimental data remains a challenging problem in systems biology. Numerous techniques have been developed and sparse linear regression methods become a promising approach to infer accurate GRNs. However, most linear methods are either based on steady-state gene expression data or their statistical properties are not analysed. Here, two sparse penalties, adaptive least absolute shrinkage and selection operator and smoothly clipped absolute deviation, are proposed to infer GRNs from time-course gene expression data based on an auto-regressive model and their Oracle properties are proved under mild conditions. The effectiveness of those methods is demonstrated by applications to in silico and real biological data.

Agencies that regulate electricity providers often apply nonparametric data envelopment analysis (DEA) to assess the relative efficiency of each firm. The reliability and validity of DEA are contingent upon selecting relevant input variables. In the era of big (wide) data, the assumptions of traditional variable selection techniques are often violated due to challenges related to high-dimensional data and their standard empirical properties. Currently, regulators have access to a large number of potential input variables. Therefore, our aim is to introduce new machine learning methods for regulators of the energy market. We also propose a new two-step analytical approach where, in the first step, the machine learning-based adaptive least absolute shrinkage and selection operator (ALASSO) is used to select variables and, in the second step, selected variables are used in a DEA model. In contrast to previous research, we find, by using a more realistic data-generating process common for production functions (i.e., Cobb–Douglas and Translog), that the performance of different machine learning techniques differs substantially in different empirically relevant situations. Simulations also reveal that the ALASSO is superior to other machine learning and regression-based methods when the collinearity is low or moderate. However, in situations of multicollinearity, the LASSO approach exhibits the best performance. We also use real data from the Swedish electricity distribution market to illustrate the empirical relevance of selecting the most appropriate variable selection method.

The problem of detecting multiple undocumented change-points in a historical temperature sequence with simple linear trend is formulated by a linear model. We apply adaptive least absolute shrinkage and selection operator (Lasso) to estimate the number and locations of change-points. Model selection criteria are used to choose the Lasso smoothing parameter. As adaptive Lasso may overestimate the number of change-points, we perform post-selection on change-points detected by adaptive Lasso using multivariate t simultaneous confidence intervals. Our method is demonstrated on the annual temperature data (year: 1902–2000) from Tuscaloosa, Alabama.

ABSTRACTIn this paper, we show the validity of the adaptive least absolute shrinkage and selection operator (LASSO) procedure in estimating stationary autoregressive distributed lag(p,q) models with innovations in a broad class of conditionally heteroskedastic models. We show that the adaptive LASSO selects the relevant variables with probability converging to one and that the estimator is oracle efficient, meaning that its distribution converges to the same distribution of the oracle-assisted least squares, i.e., the least square estimator calculated as if we knew the set of relevant variables beforehand. Finally, we show that the LASSO estimator can be used to construct the initial weights. The performance of the method in finite samples is illustrated using Monte Carlo simulation.

BackgroundA considerable portion of the HIV pandemic is composed of people under antiretroviral therapy, many of whom get a late diagnosis. Patients starting antiretroviral therapy (ART) at a very advanced stage of HIV disease attain a low recovery of CD4 T cells. Factors associated with poor recovery are incompletely described. This study aimed at finding variables associated with CD4 T cell recovery in late-presenting HIV patients.MethodsWe studied a cohort of HIV+ patients initiating ART with very low basal CD4 T cell counts. We defined immune recovery as the net increase in circulating CD4 T cell counts after one year on ART. We analyzed diverse routine laboratory determinations at different times using Least Absolute Shrinkage and Selection Operator (LASSO), adaptive LASSO and Conditional Inference Random Forest.ResultsCD4/CD8 ratio, % CD4 T cells and CD8 T cell counts at different times were the main recovery correlates, validated by all approaches. Unexpectedly, basal hematocrit was a consistent predictor. Additionally, week 24 creatinine had a high lasso coefficient, and alkaline phosphatase had a high conditional inference random forest coefficients, although neither was verified by other tests.ConclusionsCD4 T cell proportions are associated with CD4 T cell recovery, independently of cell counts. Inflammation-related variables could also affect reconstitution. These accessible variables may reflect underlying mechanisms and could improve the follow up of patients starting ART with an advanced HIV infection.

The accelerated failure time (AFT) model is a linear model under the log-transformation of survival time that has been introduced as a useful alternative to the proportional hazards (PH) model. In this paper we propose variable-selection procedures of fixed effects in a parametric AFT model using penalized likelihood approaches. We use three popular penalty functions, least absolute shrinkage and selection operator (LASSO), adaptive LASSO and smoothly clipped absolute deviation (SCAD). With these procedures we can select important variables and estimate the fixed effects at the same time. The performance of the proposed method is evaluated using simulation studies, including the investigation of impact of misspecifying the assumed distribution. The proposed method is illustrated with a primary biliary cirrhosis (PBC) data set.

Recurrent neural network based hybrid model for reconstructing gene regulatory network

Reconstruction of gene regulatory networks (GRNs), which explicitly represent the causality of developmental or regulatory process, is of utmost interest and has become a challenging computational problem for understanding the complex regulatory mechanisms in cellular systems. However, all existing methods of inferring GRNs from gene expression profiles have their strengths and weaknesses. In particular, many properties of GRNs, such as topology sparseness and non-linear dependence, are generally in regulation mechanism but seldom are taken into account simultaneously in one computational method. In this work, we present a novel method for inferring GRNs from gene expression data considering the non-linear dependence and topological structure of GRNs by employing path consistency algorithm (PCA) based on conditional mutual information (CMI). In this algorithm, the conditional dependence between a pair of genes is represented by the CMI between them. With the general hypothesis of Gaussian distribution underlying gene expression data, CMI between a pair of genes is computed by a concise formula involving the covariance matrices of the related gene expression profiles. The method is validated on the benchmark GRNs from the DREAM challenge and the widely used SOS DNA repair network in Escherichia coli. The cross-validation results confirmed the effectiveness of our method (PCA-CMI), which outperforms significantly other previous methods. Besides its high accuracy, our method is able to distinguish direct (or causal) interactions from indirect associations. All the source data and code are available at: http://csb.shu.edu.cn/subweb/grn.htm. lnchen@sibs.ac.cn; zpliu@sibs.ac.cn Supplementary data are available at Bioinformatics online.

A (conservative) test is applied to investigate the optimal lag structure for modelingrealized volatility dynamics. The testing procedure relies on the recent theoretical results that showthe ability of the adaptive least absolute shrinkage and selection operator (adaptive lasso) to combinee cient parameter estimation, variable selection, and valid inference for time series processes. In anapplication to several constituents of the SP (ii) in many cases the relevant information for prediction is included in the first 22lags, corroborating previous results concerning the accuracy and the diffculty of outperforming outof-sample the heterogeneous autoregressive (HAR) model; and (iii) some common features of theoptimal lag structure can be identified across assets belonging to the same market segment or showinga similar beta with respect to the market index.

Mean-variance portfolio optimization is widely used by financial professionals as a fundamental strategy for constructing portfolios that achieve the highest returns for a given degree of risk tolerance. This traditional approach suffers from computational instability issues, which are often solved by integrating regularization-based methods. However, regularized mean-variance models overlook sector considerations, emphasizing a need for market-informed portfolio optimization. In this paper, we propose an extended mean-variance portfolio selection framework that incorporates a new adaptive sparse-group least absolute shrinkage and selection operator (LASSO) regularization as a penalty parameter. In the proposed model, the sparse optimal portfolio is selected considering both sectors and assets simultaneously. Moreover, the inclusion of adaptive weights in the regularization, estimated based on chosen criteria, enables the use of more market data in a Markowitz portfolio model. We also develop an efficient alternating direction method of multipliers (ADMM) algorithm that guarantees convergence, for finding the optimal sparse portfolio. The effectiveness of the suggested portfolio selection model is validated by numerical results derived from the constituents of the Standard and Poor’s 500. These results demonstrate superior performance over our selected benchmark models across various evaluation measurements.

BackgroundInferring a gene regulatory network (GRN) from high throughput biological data is often an under-determined problem and is a challenging task due to the following reasons: (1) thousands of genes are involved in one living cell; (2) complex dynamic and nonlinear relationships exist among genes; (3) a substantial amount of noise is involved in the data, and (4) the typical small sample size is very small compared to the number of genes. We hypothesize we can enhance our understanding of gene interactions in important biological processes (differentiation, cell cycle, and development, etc) and improve the inference accuracy of a GRN by (1) incorporating prior biological knowledge into the inference scheme, (2) integrating multiple biological data sources, and (3) decomposing the inference problem into smaller network modules.ResultsThis study presents a novel GRN inference method by integrating gene expression data and gene functional category information. The inference is based on module network model that consists of two parts: the module selection part and the network inference part. The former determines the optimal modules through fuzzy c-mean (FCM) clustering and by incorporating gene functional category information, while the latter uses a hybrid of particle swarm optimization and recurrent neural network (PSO-RNN) methods to infer the underlying network between modules. Our method is tested on real data from two studies: the development of rat central nervous system (CNS) and the yeast cell cycle process. The results are evaluated by comparing them to previously published results and gene ontology annotation information.ConclusionThe reverse engineering of GRNs in time course gene expression data is a major obstacle in system biology due to the limited number of time points. Our experiments demonstrate that the proposed method can address this challenge by: (1) preprocessing gene expression data (e.g. normalization and missing value imputation) to reduce the data noise; (2) clustering genes based on gene expression data and gene functional category information to identify biologically meaningful modules, thereby reducing the dimensionality of the data; (3) modeling GRNs with the PSO-RNN method between the modules to capture their nonlinear and dynamic relationships. The method is shown to lead to biologically meaningful modules and networks among the modules.

In the field of quantitative remote sensing of forest biomass, a prominent phenomenon is the increasing number of explanatory variables. Then how to effectively select explanatory variables has become an important issue. Linear regression model is one of the commonly used remote sensing models. In the process of establishing the linear regression model, a vital step is to select explanatory variables. Focusing on variable selection and model stability, this paper conducts a comparative study on the performance of eight linear regression parameter estimation methods (Stepwise Regression Method (SR), Criterions Based on The Bayes Method (BIC), Criterions Based on The Bayes Method (AIC), Criterions Based on Prediction Error (Cp), Least Absolute Shrinkage and Selection Operator (Lasso), Adaptive Lasso, Smoothly Clipped Absolute Deviation (SCAD), Non-negative garrote (NNG)) in the subtropical forest biomass remote sensing model development. For the purpose of comparison, OLS and RR, are commonly used as methods with no variable selection ability, and are also compared and discussed. The performance of five aspects are evaluated in this paper: (i) Determination coefficient, prediction error, model error, etc., (ii) significance test about the difference between determination coefficients, (iii) parameter stability, (iv) variable selection stability and (v) variable selection ability of the methods. All the results are obtained through a five ten-fold CV. Some evaluation indexes are calculated with or without degrees of freedom. The results show that BIC performs best in comprehensive evaluation, while NNG, Cp and AIC perform poorly as a whole. Other methods show a great difference in the performance on each index. SR has a strong capability in variable selection, although it is poor in commonly used indexes. The short-wave infrared band and the texture features derived from it are selected most frequently by various methods, indicating that these variables play an important role in forest biomass estimation. Some of the conclusions in this paper are likely to change as the study object changes. The ultimate goal of this paper is to introduce various model establishment methods with variable selection capability, so that we can have more choices when establishing similar models, and we can know how to select the most appropriate and effective method for specific problems.

Many tree algorithms have been developed for regression problems. Although they are regarded as good algorithms, most of them suffer from loss of prediction accuracy when there are many irrelevant variables and the number of predictors exceeds the number of observations. We propose the multistep regression tree with adaptive variable selection to handle this problem. The variable selection step and the fitting step comprise the multistep method. The multistep generalized unbiased interaction detection and estimation (GUIDE) with adaptive forward selection (fg) algorithm, as a variable selection tool, performs better than some of the well-known variable selection algorithms such as efficacy adaptive regression tube hunting (EARTH), FSR (false selection rate), LSCV (least squares cross-validation), and LASSO (least absolute shrinkage and selection operator) for the regression problem. The results based on simulation study show that fg outperforms other algorithms in terms of selection result and computation time. It generally selects the important variables correctly with relatively few irrelevant variables, which gives good prediction accuracy with less computation time.

BackgroundWe propose a novel Markov Blanket-based repeated-fishing strategy (MBRFS) in attempt to increase the power of existing Markov Blanket method (DASSO-MB) and maintain its advantages in omic data analysis.ResultsBoth simulation and real data analysis were conducted to assess its performances by comparing with other methods including χ2 test with Bonferroni and B-H adjustment, least absolute shrinkage and selection operator (LASSO) and DASSO-MB. A serious of simulation studies showed that the true discovery rate (TDR) of proposed MBRFS was always close to zero under null hypothesis (odds ratio = 1 for each SNPs) with excellent stability in all three scenarios of independent phenotype-related SNPs without linkage disequilibrium (LD) around them, correlated phenotype-related SNPs without LD around them, and phenotype-related SNPs with strong LD around them. As expected, under different odds ratio and minor allel frequency (MAFs), MBRFS always had the best performances in capturing the true phenotype-related biomarkers with higher matthews correlation coefficience (MCC) for all three scenarios above. More importantly, since proposed MBRFS using the repeated fishing strategy, it still captures more phenotype-related SNPs with minor effects when non-significant phenotype-related SNPs emerged under χ2 test after Bonferroni multiple correction. The various real omics data analysis, including GWAS data, DNA methylation data, gene expression data and metabolites data, indicated that the proposed MBRFS always detected relatively reasonable biomarkers.ConclusionsOur proposed MBRFS can exactly capture the true phenotype-related biomarkers with the reduction of false negative rate when the phenotype-related biomarkers are independent or correlated, as well as the circumstance that phenotype-related biomarkers are associated with non-phenotype-related ones.Electronic supplementary materialThe online version of this article (doi:10.1186/s12863-016-0358-5) contains supplementary material, which is available to authorized users.

PurposeTo better identify the physiology of triple-negative breast neoplasm (TNBN), we analyzed the TNBN gene regulatory network using gene expression data.MethodsWe collected TNBN gene expression data from The Cancer Genome Atlas to construct a TNBN gene regulatory network using least absolute shrinkage and selection operator regression. In addition, we constructed a triple-positive breast neoplasm (TPBN) network for comparison. Furthermore, survival analysis based on gene expression levels and differentially expressed gene (DEG) analysis were carried out to support and compare the network analysis results, respectively.ResultsThe TNBN gene regulatory network, which followed a power-law distribution, had 10,237 vertices and 17,773 edges, with an average vertex-to-vertex distance of 8.6. The genes ZDHHC20 and RAPGEF6 were identified by centrality analysis to be important vertices. However, in the DEG analysis, we could not find meaningful fold changes in ZDHHC20 and RAPGEF6 between the TPBN and TNBN gene expression data. In the multivariate survival analysis, the hazard ratio for ZDHHC20 and RAPGEF6 was 1.677 (1.192–2.357) and 1.676 (1.222–2.299), respectively.ConclusionOur TNBN gene regulatory network was a scale-free one, which means that the network would be easily destroyed if the hub vertices were attacked. Thus, it is important to identify the hub vertices in the network analysis. In the TNBN gene regulatory network, ZDHHC20 and RAPGEF6 were found to be oncogenes. Further study of these genes could help to reveal a novel method for treating TNBN in the future.