Graphical Methods Of Data Analysis Research Articles

Multiple and multilevel graphical models

AbstractGraphical models have played an important role in inferring dependence structures, discovering multivariate interactions among high‐dimensional data associated with classes of interest such as disease status, and visualizing their association. When data are modeled with Gaussian Markov random fields, the graphical model is called a Gaussian graphical model. It has been used to investigate the conditional dependency structure between random variables by estimating sparse precision matrices. Although the Gaussian model has been widely applied, the normality assumption is rather restrictive. Hence, several methods have been proposed under assumptions weaker than the Gaussian assumptions to handle continuous, discrete, and mixed data. However, modeling data of heterogeneous classes and multilevel networks still poses challenges. Addressing these challenges stresses open problems and points out new directions for research. In this article, we review various undirected graphical models for multiple, joint, and multilevel graphs.This article is categorized under:Statistical Models > Graphical ModelsStatistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

Analyzing Markov chain Monte Carlo output

AbstractMarkov chain Monte Carlo (MCMC) is a sampling‐based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be difficult to assess when the MCMC method is producing reliable results. We present some fundamental methods for ensuring a reliable simulation experiment. In particular, we present a workflow for output analysis in MCMC providing estimators, approximate sampling distributions, stopping rules, and visualization tools.This article is categorized under: Statistical Models > Bayesian Models Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods

Individualized inference through fusion learning

AbstractFusion learning methods, developed for the purpose of analyzing datasets from many different sources, have become a popular research topic in recent years. Individualized inference approaches through fusion learning extend fusion learning approaches to individualized inference problems over a heterogeneous population, where similar individuals are fused together to enhance the inference over the target individual. Both classical fusion learning and individualized inference approaches through fusion learning are established based on weighted aggregation of individual information, but the weight used in the latter is localized to the target individual. This article provides a review on two individualized inference methods through fusion learning, iFusion and iGroup, that are developed under different asymptotic settings. Both procedures guarantee optimal asymptotic theoretical performance and computational scalability.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Data: Types and Structure > Massive Data

Nonparametric volatility prediction

AbstractVolatility can be defined as the conditional expectation of the squared return of a financial asset. Many of the classical nonparametric regression estimators can be applied in volatility prediction. Examples of nonparametric estimators include moving averages and kernel estimators. However, it has been difficult to beat some parametric estimators from the generalized autoregressive conditionally heteroscedastic family using nonparametric estimators. We review some promising suggestions for nonparametric volatility prediction.This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical Models > Time Series Models

Filtering‐based approaches for functional data classification

AbstractBecause of its many practical applications, classifying functional data has received considerable attention over the last decades. Most classification approaches for functional data are extended from those for multivariate data. During the extension, two strategies, namely filtering and regularization, have commonly been employed to tackle the issues raised by the fact that functional data are intrinsically infinite‐dimensional. Because of space limitations, we focus on the filtering methods in this review.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification

Tweedie regression models and its geometric sums for (semi‐)continuous data

AbstractTweedie regression models (TRMs) are flexible tools to deal with non‐negative right‐skewed data and can handle semi‐continuous data, that is, continuous data with probability mass at zero. The geometric sums of Tweedie random variables lead to the geometric Tweedie distributions. Their corresponding regression models (GTRMs) provide not only additional flexibility to deal with continuous, semi‐continuous, heavily right‐skewed data but also a possibility of under‐variation than TRMs. Estimation and inference based on the likelihood approach for TRMs and GTRMs are challenging owing to the presence of an infinity sum and an intractable integral in the probability function along with non‐trivial restrictions on the Tweedie power parameter space. Thus, methods based on quasi‐likelihood have been proposed and successfully applied for estimation and inference in these classes of regression models. In this paper, our central focus is upon characterizing as well as comparing TRMs and GTRMs taking into consideration their variation and zero‐mass indices. Besides, we attempt to illustrate their application through some data analyses. Furthermore, we discuss the challenges for the computational implementation of such probability distributions and corresponding regression models referring to some available implementations in R.This article is categorized under: Statistical Models > Fitting Models Statistical Models > Generalized Linear Models Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms

On nonparametric conditional independence tests for continuous variables

AbstractTesting conditional independence (CI) for continuous variables is a fundamental but challenging task in statistics. Many tests for this task are developed and used increasingly widely by data analysts. This article reviews the current status of the nonparametric part of these tests, which assumes no parametric form for the joint continuous density function. The different ways to approach the CI are summarized. Tests are also grouped according to their data assumptions and method types. A numerical comparison is also conducted for representative tests.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

Multiple testing approaches for hypotheses in integrative genomics

AbstractWith the explosion in available technologies for measuring many biological phenomena on a large scale, there have been concerted efforts in a variety of biological and medical settings to perform systems biology analyses. A crucial question then becomes how to combine data across the various large‐scale data types. This article reviews the data types that can be considered and treats so‐called horizontal and vertical integration analyses. This article focuses on the use of multiple testing approaches in order to perform integrative analyses. Two questions help to clarify the class of procedures that should be used. The first deals with whether a horizontal or vertical integration is being performed. The second is if there is a priority for a given platform. Based on the answers to these questions, we review various methodologies that could be applied.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Applications of Computational Statistics > Genomics/Proteomics/Genetics

Robust nonparametric regression: A review

AbstractNonparametric regression methods provide an alternative approach to parametric estimation that requires only weak identification assumptions and thus minimizes the risk of model misspecification. In this article, we survey some nonparametric regression techniques, with an emphasis on kernel‐based estimation, that are additionally robust to atypical and outlying observations. While the main focus lies on robust regression estimation, robust bandwidth selection and conditional scale estimation are discussed as well. Robust estimation in popular nonparametric models such as additive and varying‐coefficient models is summarized too. The performance of the main methods is demonstrated on a real dataset.This article is categorized under:Statistical and Graphical Methods of Data Analysis > Robust MethodsStatistical and Graphical Methods of Data Analysis > Nonparametric Methods

A review of approximate Bayesian computation methods via density estimation: Inference for simulator‐models

AbstractThis paper provides a review of approximate Bayesian computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional approaches. We show advantages and limitations of models based on parametric approaches and we then draw attention to developments in machine learning, which we believe have the potential to make ABC scalable to higher dimensions and may be the future direction for research in this area.This article is categorized under: Algorithms and Computational Methods < Algorithms Statistical and Graphical Methods of Data Analysis < Bayesian Methods and Theory Statistical Models < Simulation Models

Nonparametric curve estimation and bootstrap bandwidth selection

AbstractOver the last four decades, the bootstrap method has been considered so as to define data‐driven bandwidth selectors for nonparametric curve estimation. An extensive and updated review of bootstrap methods used to select the smoothing parameter for the nonparametric estimation of several curves has been carried out. Different data generating processes have been profoundly reviewed, such as the classical independent and identically distributed setup as well as dependent, censored, length‐biased, grouped, missing or directional data, among others. Several curves have also been considered, such as the density, regression, hazard rate, intensity, latency, incidence, or distribution functions, among many others. It is worth mentioning that there exist situations where Monte Carlo methods are not needed when using the bootstrap for bandwidth selections. This idea has also been exploited to find closed expressions for the bootstrap version of criterion functions for some proxy of the real curve estimator.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Density Estimation

High‐dimensional covariance matrix estimation

AbstractCovariance matrix estimation plays an important role in statistical analysis in many fields, including (but not limited to) portfolio allocation and risk management in finance, graphical modeling, and clustering for genes discovery in bioinformatics, Kalman filtering and factor analysis in economics. In this paper, we give a selective review of covariance and precision matrix estimation when the matrix dimension can be diverging with, or even larger than the sample size. Two broad categories of regularization methods are presented. The first category exploits an assumed structure of the covariance or precision matrix for consistent estimation. The second category shrinks the eigenvalues of a sample covariance matrix, knowing from random matrix theory that such eigenvalues are biased from the population counterparts when the matrix dimension grows at the same rate as the sample size.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

Envelope methods

AbstractAn envelope is a relatively new construct for decreasing estimative and predictive variation relative to standard methods in multivariate statistics, sometimes by amounts equivalent to increasing the sample size many times over. Essentially a form of targeted dimension reduction that is descendent from sufficient dimension reduction, an envelope inherits its underlying philosophy from Fisher's notion of sufficient statistics. The initial development of envelope methods took place largely in the context of the multivariate linear model, resulting in response envelopes for response reduction, predictor envelopes for predictor reduction, simultaneous envelopes for response and predictor reduction and partial envelopes for specialized considerations, each demonstrating a potential for substantial reduction in estimative variation. These advances demonstrated that there are close connections between envelopes and some standard multivariate methods like partial least squares regression and canonical correlations. Subsequently, envelope methodology has been adapted and extended to diverse areas, including envelopes for regressions with matrix and tensor‐valued responses, envelopes for spatial statistics, quantile envelopes for quantile regression, Bayesian response envelopes. Sparse versions of response and predictor envelopes have also been developed. More generally, there is also envelope methodology for reducing the variation in any asymptotically normal vector‐valued estimator. These advances have opened a new chapter in multivariate statistics, allowing variation that is material to the goals of an analysis to be separated effectively from immaterial variation that serves only to confound estimation and prediction.This article is categorized under: Statistical Models > Multivariate Models Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Dimension Reduction

Analysis of ranking data

AbstractRanking is one of the simple and efficient data collection techniques to understand individuals' perception and preferences for some items such as products, people, and species. Ranking data are frequently collected when individuals are asked to rank a set of items according to a certain preference criterion. Over the years, many statistical models and methods have been developed for analyzing ranking data. This paper will give a literature review of these models and methods and present the recent advances of the analysis of ranking data.This article is categorized under:Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

Tensor decomposition for dimension reduction

AbstractTensor data are data with multiway array structure. They are often very high dimensional and are routinely encountered in many scientific fields. Dimension reduction is the technique of reducing the number of underlying variables for compressed data representation and for model parsimony. Tensor dimension reduction aims for reducing the tensor data dimension while keeping data's tensor structure.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data

Computation of exact probabilities associated with overlapping pattern occurrences

AbstractSearching for patterns in data is important because it can lead to the discovery of sequence segments that play a functional role. The complexity of pattern statistics that are used in data analysis and the need of the sampling distribution of those statistics for inference renders efficient computation methods as paramount. This article gives an overview of the main methods used to compute distributions of statistics of overlapping pattern occurrences, specifically, generating functions, correlation functions, the Goulden‐Jackson cluster method, recursive equations, and Markov chain embedding. The underlying data sequence will be assumed to be higher‐order Markovian, which includes sparse Markov models and variable length Markov chains as special cases. Also considered will be recent developments for extending the computational capabilities of the Markov chain‐based method through an algorithm for minimizing the size of the chain's state space, as well as improved data modeling capabilities through sparse Markov models. An application to compute a distribution used as a test statistic in sequence alignment will serve to illustrate the usefulness of the methodology.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Pattern Recognition Data: Types and Structure > Categorical Data Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms

Multiscalar genetic pathway modeling with hybrid Bayesian networks

AbstractBayesian network modeling of real world datasets is often complicated by the fact that they are hybrid datasets that contain both discrete and continuous variables. For example, recent advances in high throughput biotechnologies have made it possible to generate large‐scale data across multiple biological scales—from discrete variables such as DNA variations to continuous variables such as omics traits and disease phenotypes. Such large heterogeneous and multiscalar datasets present a great challenge for biological knowledge discovery. Here we discuss the Bayesian Network Webserver (http://compbio.uthsc.edu/BNW), a web‐based platform for creating hybrid Bayesian network models, and its use in discovering causal relationships from heterogeneous and multiscalar system genetics datasets.This article is categorized under:Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional DataStatistical Models > Bayesian ModelsStatistical Models > Graphical ModelsApplications of Computational Statistics > Computational and Molecular Biology

Soft clustering

AbstractClustering is one of the most used tools in data analysis. In the last decades, due to the increasing complexity of data, soft clustering has received a great deal of attention. There exist different approaches that can be considered as soft. The most known is the fuzzy approach that consists in assigning objects to clusters with membership degrees, depending on the dissimilarities between each object and all the prototypes, ranging in the unit interval. Closely related to the fuzzy approach, there is the possibilistic one that, differently from the previous one, relaxes some constraints on the membership degrees. In particular, the objects are assigned to clusters with degrees of typicalities, depending just on the dissimilarities between each object and the closest prototype. A further soft approach is the rough one. In this case, there are not degrees ranging between 0 and 1 but objects with intermediate features belong to the boundary region and are assigned to more than one cluster. Even if it is not universally recognized in the scientific community as an approach of soft clustering, from our point of view, the model‐based approach can also be considered as such. Model‐based clustering methods also produce a soft partition of the objects and the posterior probability of a component membership may play a role similar to the membership degree. The four approaches are critically described from a theoretical point of view and an empirical comparative analysis is carried out.This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and ClassificationStatistical and Graphical Methods of Data Analysis > Multivariate AnalysisStatistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis

Matrix completion from a computational statistics perspective

AbstractIn the matrix completion problem, we seek to estimate the missing entries of a matrix from a small sample of the total number of entries in a matrix. While this task is hopeless in general, structured matrices that are appropriately sampled can be completed with surprising accuracy. In this review, we examine the success behind low‐rank matrix completion, one of the most studied and employed versions of matrix completion. Formulating the matrix completion problem as a low‐rank matrix estimation problem admits several strengths: good empirical performance on real data, statistical guarantees, and practical algorithms with convergence guarantees. We also examine how matrix completion relates to the classical study of missing data analysis (MDA) in statistics. By drawing on the MDA perspective, we see opportunities to weaken the commonly enforced assumption of missing completely at random in matrix completion.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

Goodness‐of‐fit testing in sparse contingency tables when the number of variables is large

AbstractThe Pearson and likelihood ratio statistics are commonly used to test goodness of fit for models applied to data from a multinomial distribution. When data are from a table formed by the cross‐classification of a large number of variables, the common statistics may have low power and inaccurate Type I error level due to sparseness. One approach to finding a valid approximation to the achieved significance level (ASL) is to use a bootstrap distribution for the test statistic. For a composite null hypothesis with unknown parameters, the parametric bootstrap has been employed. The parametric bootstrap can be computationally demanding, but a recent development provides a method for computationally efficient calculation of the Pearson–Fisher statistic for very large sparse tables. Another approach employs orthogonal components of the Pearson–Fisher statistic obtained from lower‐order marginal distributions of a large cross‐classified table rather than the joint distribution. These statistics are used essentially for focused tests and have mostly been applied to latent variable models. They have very good performance for Type I error rate and power, even when applied to a sparse table. However, there are limitations when the number of variables becomes larger than 20. Some related statistics also employ lower‐order marginals, but they are not components of the Pearson–Fisher statistic. The performance of these approaches is compared for obtaining a valid ASL for a goodness‐of‐fit test applied to a very large multi‐way contingency table. The approaches are compared with a small simulation study.This article is categorized under: Types and Structure > Categorical Data Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling Statistical Models > Fitting Models