Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is flawed given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes as it does not represent the adjacency matrix. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence and thus, agrees with the experimenter's intuition on the average behavior of nodes under treatment. The solution to our model is sparse via Bayesian LASSO. In addition, we propose an adaptive extension so that different shrinkage can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting and compositional responses via appropriate hierarchical structure. We apply our model to a human gut and a soil microbial compositional datasets and we highlight that CG-LASSO can estimate biologically meaningful network structures in the data. The CG-LASSO software is available as an R package at https://github.com/YunyiShen/CAR-LASSO.
Understanding how microbes interact with each other is key to revealing the underlying role that microorganisms play in the host or environment and to identifying microorganisms as an agent that can potentially alter the host or environment. For example, understanding how the microbial interactions associate with parasitic infection can help resolve potential drug or diagnostic test for parasitic infection. To unravel the microbial interactions, existing tools often rely on graphical models to infer the conditional dependence of microbial abundances to represent their interactions. However, cu…
The interactions between microbial taxa in microbiome data has been under great research interest in the science community. In particular, several methods such as SPIEC-EASI, gCoda, and CD-trace have been proposed to model the conditional dependency between microbial taxa, in order to eliminate the detection of spurious correlations. However, all those methods are built upon the central log-ratio (CLR) transformation, which results in a degenerate covariance matrix and thus an undefined inverse covariance matrix as the estimation of the underlying network. Jiang et al. (2021) and Tian et al. (…
Microbiome data analyses require statistical tools that can simultaneously decode microbes' reactions to the environment and interactions among microbes. We introduce CARlasso, the first user-friendly open-source and publicly available R package to fit a chain graph model for the inference of sparse microbial networks that represent both interactions among nodes and effects of a set of predictors. Unlike in standard regression approaches, the edges represent the correct conditional structure among responses and predictors that allows the incorporation of prior knowledge from controlled experim…
High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands of genes that are active (expressed) in certain tissue cells. To this end, we wish to fit regression and classification models with a large number of features (also called variables, predictors). In the past decade, penalized likelihood methods for fitting regression models based on hyper-LASSO penalization have received increasing attention in the literatur…
LIT-LVM: Structured Regularization for Interaction Terms in Linear Predictors using Latent Variable Models
Department of Computer and Data Sciences（计算机与数据科学系）；Case Western Reserve University（凯斯西储大学）；Department of Mathematics and Computer Science（数学与计算机科学系）；Suffolk University（索尔福德大学）
In response to the challenges of data mining, discriminant analysis continues to evolve as a vital branch of statistics. Our recently introduced method of vertex discriminant analysis (VDA) is ideally suited to handle multiple categories and an excess of predictors over training cases. The current paper explores an elaboration of VDA that conducts classification and variable selection simultaneously. Adding lasso ($\ell_1$-norm) and Euclidean penalties to the VDA loss function eliminates unnecessary predictors. Lasso penalties apply to each predictor coefficient separately; Euclidean penalties…
Motivated by a challenging problem in financial trading we are presented with a mixture of regressions with variable selection problem. In this regard, one is faced with data which possess outliers, skewness and, simultaneously, due to the nature of financial trading, one would like to be able to construct clusters with specific predictors that are fairly sparse. We develop a Bayesian mixture of lasso regressions with $t-$errors to reflect these specific demands. The resulting model is necessarily complex and to fit the model to real data, we develop a state-of-the-art Particle Markov chain Mo…
Bayesian networks can represent directed gene regulations and therefore are favored over co-expression networks. However, hardly any Bayesian network study concerns the false discovery control (FDC) of network edges, leading to low accuracies due to systematic biases from inconsistent false discovery levels in the same study. We design four empirical tests to examine the FDC of Bayesian networks from three p-value based lasso regression variable selections --- two existing and one we originate. Our method, lassopv, computes p-values for the critical regularization strength at which a predictor…
Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks in such applications that poses a challenge for statistical inference is the presence of a small number of strongly interconnected nodes in a network which are called hubs. For example, in microbiome research hubs or microbial taxa play a significant role in maintaining stability of the microbial community structure. In this paper, we investigate the problem …
Medical imaging involves high-dimensional data, yet their acquisition is obtained for limited samples. Multivariate predictive models have become popular in the last decades to fit some external variables from imaging data, and standard algorithms yield point estimates of the model parameters. It is however challenging to attribute confidence to these parameter estimates, which makes solutions hardly trustworthy. In this paper we present a new algorithm that assesses parameters statistical significance and that can scale even when the number of predictors p $\ge$ 10^5 is much higher than the n…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while effectively detect local features. The sparse group lasso penalty is imposed to select important functional predictors while capture shared information among them. The estimation problem can be reformulated into a standard second-order cone program and then solved by an interior point method. We also give a novel algorithm by using alternating direction met…
The analysis of human microbiome data is often based on dimension-reduced graphical displays and clustering derived from vectors of microbial abundances in each sample. Common to these ordination methods is the use of biologically motivated definitions of similarity. Principal coordinate analysis, in particular, is often performed using ecologically defined distances, allowing analyses to incorporate context-dependent, non-Euclidean structure. Here we describe how to take a step beyond ordination plots and incorporate this structure into high-dimensional penalized regression models. Within thi…
Although genome-wide association studies (GWAS) have proven powerful for comprehending the genetic architecture of complex traits, they are challenged by a high dimension of single-nucleotide polymorphisms (SNPs) as predictors, the presence of complex environmental factors, and longitudinal or functional natures of many complex traits or diseases. To address these challenges, we propose a high-dimensional varying-coefficient model for incorporating functional aspects of phenotypic traits into GWAS to formulate a so-called functional GWAS or fGWAS. The Bayesian group lasso and the associated MC…
Tropical cyclones (TCs) rank among the most costly natural disasters in the United States, and accurate forecasts of track and intensity are critical for emergency response. Intensity guidance has improved steadily but slowly, as processes which drive intensity change are not fully understood. Because most TCs develop far from land-based observing networks, geostationary satellite imagery is critical to monitor these storms. However, these complex data can be challenging to analyze in real time, and off-the-shelf machine learning algorithms have limited applicability on this front due to their…
Statistical inference after variable selection in Cox models: A simulation study
Mathematical Statistics and Artificial Intelligence in Medicine, University of Augsburg（医学中的数学统计与人工智能，乌尔姆大学）；Center for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg（高级分析与预测科学中心（CAAPS），乌尔姆大学）
