This paper presents the R package gRapHD for efficient selection of high-dimensional undirected graphical models. The package provides tools for selecting trees, forests and decomposable models minimizing information criteria such as AIC or BIC, and for displaying the independence graphs of the models. It has also some useful tools for analysing graphical structures. It supports the use of discrete, continuous, or both types of variables simultaneously.
We introduce GGLasso, a Python package for solving General Graphical Lasso problems. The Graphical Lasso scheme, introduced by (Friedman 2007) (see also (Yuan 2007; Banerjee 2008)), estimates a sparse inverse covariance matrix $Θ$ from multivariate Gaussian data $\mathcal{X} \sim \mathcal{N}(μ, Σ) \in \mathbb{R}^p$. Originally proposed by (Dempster 1972) under the name Covariance Selection, this estimation framework has been extended to include latent variables in (Chandrasekaran 2012). Recent extensions also include the joint estimation of multiple inverse covariance matrices, see, e.g., in (…
A tutorial-style introduction to the R-package robFitConGraph is given. The latter provides a robust goodness-of-fit test for Gaussian graphical models. Its use is demonstrated at a data example on music performance anxiety, which also illustrates why one would want to fit a Gaussian graphical model - and why one should do so robustly. The underlying statistical theory is briefly explained. The paper describes package version 0.4.1, available on CRAN from December 1, 2022. See https://CRAN.R-project.org/package=robFitConGraph
Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decomposable) with continuous, discrete, and mixed variables. The package efficiently implements recent improvements in the Bayesian literature, including that of Mohammadi and Wit (2015) and Dobra and Mohammadi (2018). To speed up computations, the computationally intensive tasks hav…
A graphical model is a multivariate (potentially very high dimensional) probabilistic model, which is formed by combining lower dimensional components. Inference (computation of conditional probabilities) is based on message passing algorithms that utilize conditional independence structures. In graphical models for discrete variables with finite state spaces, there is a fundamental problem in high dimensions: A discrete distribution is represented by a table of values, and in high dimensions such tables can become prohibitively large. In inference, such tables must be multiplied which can lea…
Longitudinal (panel) data provide the opportunity to examine temporal patterns of individuals, because measurements are collected on the same person at different, and often irregular, time points. The data is typically visualised using a "spaghetti plot", where a line plot is drawn for each individual. When overlaid in one plot, it can have the appearance of a bowl of spaghetti. With even a small number of subjects, these plots are too overloaded to be read easily. The interesting aspects of individual differences are lost in the noise. Longitudinal data is often modelled with a hierarchical l…
We present the R-package mgm for the estimation of k-order Mixed Graphical Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow t…
Graphical models are a powerful tool in modelling and analysing complex biological associations in high-dimensional data. The R-package netgwas implements the recent methodological development on copula graphical models to (i) construct linkage maps, (ii) infer linkage disequilibrium networks from genotype data, and (iii) detect high-dimensional genotype-phenotype networks. The netgwas learns the structure of networks from ordinal data and mixed ordinal-and-continuous data. Here, we apply the functionality in netgwas to various multivariate example datasets taken from the literature to demonst…
The numerical availability of statistical inference methods for a modern and robust analysis of longitudinal- and multivariate data in factorial experiments is an essential element in research and education. While existing approaches that rely on specific distributional assumptions of the data (multivariate normality and/or characteristic covariance matrices) are implemented in statistical software packages, there is a need for user-friendly software that can be used for the analysis of data that do not fulfill the aforementioned assumptions and provide accurate p-value and confidence interval…
High Dimensional Semiparametric Gaussian Copula Graphical Models
在本文中，我们提出了一个半参数的方法，命名为nonparanormal怀疑，有效和鲁棒的估计高维无向图模型。为了实现建模的灵活性，我们考虑了Liu等人（2009）提出的高斯Copula图形模型（或非超自然模型）。为了实现估计的鲁棒性，我们利用非参数基于秩的相关系数估计，包括斯皮尔曼的ρ和肯德尔的τ。在高维情况下，我们证明了非超常怀疑论者在图和参数估计中都达到了最优的参数收敛速度。这一令人欣喜的结果表明，高斯copula图形模型可以作为流行的高斯图形模型的安全替代品，即使数据是真正的高斯。除了理论分析，我们还进行了彻底的数值模拟，比较不同的估计，他们的图恢复性能在理想和嘈杂的设置。所提出的方法，然后应用于一个大规模的基因组数据集，以说明其经验的有用性。实现所提出的方法的R语言软件包可以在Comprehensive R Archive Network上获得：http：//cran。r-project.org/.
In several applied fields, multimodality assessment is a crucial task as a previous exploratory tool or for determining the suitability of certain distributions. The goal of this paper is to present the utilities of the R package multimode, which collects different exploratory and testing nonparametric approaches for determining the number of modes and their estimated location. Specifically, some graphical tools, allowing for the identification of mode patterns, based on the kernel density estimation are provided (SiZer map, mode tree or mode forest). Several formal testing procedures for dete…
Data visualization and interaction with large data sets is known to be essential and critical in many businesses today, and the same applies to research and teaching, in this case, when exploring large and complex mathematical objects. GAP is a computer algebra system for computational discrete algebra with an emphasis on computational group theory. The existing XGAP package for GAP works exclusively on the X Window System. It lacks abstraction between its mathematical and graphical cores, making it difficult to extend, maintain, or port. In this paper, we present Francy, a graphical semantics…
Mixed data arise when observations are described by a mixture of numerical and categorical variables. The R package PCAmixdata extends to this type of data standard multivariate analysis methods which allow description, exploration and visualization of the data. The key techniques/methods included in the package are principal component analysis for mixed data (PCAmix), varimax-like orthogonal rotation for PCAmix, and multiple factor analysis for mixed multi-table data. This paper proposes a unified mathematical presentation of the different methods with common notations, as well as providing a…
Increased application of multivariate data in many scientific areas has considerably raised the complexity of analysis and interpretation. Although quite a few approaches have been put forward to address this issue, there is still a gap between the most efficient proposed methods and available software. muvis is an R package (core team (2017)) which is a toolkit for analyzing multivariate datasets. Several tools are implemented for common analyses of multivariate datasets, including preprocessing, dimensionality reduction, statistical analysis, Probabilistic Graphical Modeling, hypothesis test…
The prediction interval is gaining prominence in meta-analysis as it enables the assessment of uncertainties in treatment effects and heterogeneity between studies. However, coverage probabilities of the current standard method for constructing prediction intervals cannot retain their nominal levels in general, particularly when the number of synthesized studies is moderate or small, because their validities depend on large sample approximations. Recently, several methods have developed been to address this issue. This paper briefly summarizes the recent developments in methods of prediction i…
It is critical to accurately simulate data when employing Monte Carlo techniques and evaluating statistical methodology. Measurements are often correlated and high dimensional in this era of big data, such as data obtained in high-throughput biomedical experiments. Due to the computational complexity and a lack of user-friendly software available to simulate these massive multivariate constructions, researchers resort to simulation designs that posit independence or perform arbitrary data transformations. To close this gap, we developed the Bigsimr Julia package with R and Python interfaces. T…
Glovo（Glovo公司）；Universidad Torcuato Di Tella（托尔夸托迪特利亚大学）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）
We study the selection of adjustment sets for estimating the interventional mean under an individualized treatment rule. We assume a non-parametric causal graphical model with, possibly, hidden variables and at least one adjustment set comprised of observable variables. Moreover, we assume that observable variables have positive costs associated with them. We define the cost of an observable adjustment set as the sum of the costs of the variables that comprise it. We show that in this setting there exist adjustment sets that are minimum cost optimal, in the sense that they yield non-parametric…
In this report we describe a tool for comparing the performance of graphical causal structure learning algorithms implemented in the TETRAD freeware suite of causal analysis methods. Currently the tool is available as package in the TETRAD source code (written in Java). Simulations can be done varying the number of runs, sample sizes, and data modalities. Performance on this simulated data can then be compared for a number of algorithms, with parameters varied and with performance statistics as selected, producing a publishable report. The package presented here may also be used to compare str…
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…
The receiver operating characteristic (ROC) curve is the most popular tool used to evaluate the discriminatory capability of diagnostic tests/biomarkers measured on a continuous scale when distinguishing between two alternative disease states (e.g, diseased and nondiseased). In some circumstances, the test's performance and its discriminatory ability may vary according to subject-specific characteristics or different test settings. In such cases, information-specific accuracy measures, such as the covariate-specific and the covariate-adjusted ROC curve are needed, as ignoring covariate informa…
The Neyman-Scott point process is a widely used point process model which is easily interpretable and easily extendable to include various types of inhomogeneity. The inference for such complex models is then complicated and fast methods, such as minimum contrast method or composite likelihood approach do not provide accurate estimates or fail completely. Therefore, we introduce Bayesian MCMC approach for the inference of Neymann-Scott point process models with inhomogeneity in any or all of the following model components: process of cluster centers, mean number of points in a cluster, spread …
The cgam package contains routines to fit the generalized additive model where the components may be modeled with shape and smoothness assumptions. The main routine is cgam and nineteen symbolic routines are provided to indicate the relationship between the response and each predictor, which satisfies constraints such as monotonicity, convexity, their combinations, tree, and umbrella orderings. The user may specify constrained splines to fit the components for continuous predictors, and various types of orderings for the ordinal predictors. In addition, the user may specify parametrically mode…
BCAM - Basque Center for Applied Mathematics（BCAM - 巴斯克应用数学中心）；University of the Basque Country UPV/EHU（巴斯克大学 UPV/EHU）；Télécom Paris（巴黎电信学院）
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which unpredictable outcomes are common. These measures can be modeled as random variables and compared among each other via their expected values or more sophisticated tools such as null hypothesis statistical tests. In this paper, we propose an alternative framework to visually compare two samples according to their estimated cumulative distribution functions. First, we…
Learning graphical models from data is an important problem with wide applications, ranging from genomics to the social sciences. Nowadays datasets often have upwards of thousands---sometimes tens or hundreds of thousands---of variables and far fewer samples. To meet this challenge, we have developed a new R package called sparsebn for learning the structure of large, sparse graphical models with a focus on Bayesian networks. While there are many existing software packages for this task, this package focuses on the unique setting of learning large networks from high-dimensional data, possibly …
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art workflows suffer from the need for heuristic or subjective manual choices, high computational complexity, or strong parametric assumptions. We address these problems by establishing a theoretical link between multivariate/conditional independence testing, and model comparison in the multivariate predictive modelling aka supervised learning task. This link all…
We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data. This package implements recent results in the literature, including Friedman et al. (2007), Liu et al. (2009, 2012) and Liu et al. (2010). Compared with the existing graph estimation package glasso, the huge package provides extra features: (1) instead of using Fortan, it is written in C, which makes the code more portable and easier to modify; (2) besides fitting Gaussian graphical models, it also provides functions for fitting high dimensional semiparametric G…
DeepMind（深度思维）；Massachusetts Institute of Technology（麻省理工学院）
PGMax is an open-source Python package for (a) easily specifying discrete Probabilistic Graphical Models (PGMs) as factor graphs; and (b) automatically running efficient and scalable loopy belief propagation (LBP) in JAX. PGMax supports general factor graphs with tractable factors, and leverages modern accelerators like GPUs for inference. Compared with existing alternatives, PGMax obtains higher-quality inference results with up to three orders-of-magnitude inference time speedups. PGMax additionally interacts seamlessly with the rapidly growing JAX ecosystem, opening up new research possibil…
We propose estimation methods for change points in high-dimensional covariance structures with an emphasis on challenging scenarios with missing values. We advocate three imputation like methods and investigate their implications on common losses used for change point detection. We also discuss how model selection methods have to be adapted to the setting of incomplete data. The methods are compared in a simulation study and applied to a time series from an environmental monitoring system. An implementation of our proposals within the R-package hdcd is available via the Supplementary materials…
Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart. With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart. In moderate to high-dimensions, this ratio is often approximated using sampling-based methods as computationally expensiv…
