scholarly journals Replicates in high dimensions, with applications to latent variable graphical models

Biometrika ◽  
2016 ◽  
Vol 103 (4) ◽  
pp. 761-777 ◽  
Author(s):  
Kean Ming Tan ◽  
Yang Ning ◽  
Daniela M. Witten ◽  
Han Liu
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
High Dimensions

scholarly journals Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity

Biometrika ◽  
2020 ◽  
Author(s):  
S Na ◽  
M Kolar ◽  
O Koyejo
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
Graphical Model ◽  
Brain Connectivity ◽  
Statistical Error ◽  
Real Data ◽  
Low Rank ◽  
Conditional Dependence ◽  
Gradient Descent Algorithm ◽  
The Difference

Abstract Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

A network psychometric approach to neurocognitive functioning in Alzheimer's disease

2020 ◽  
Author(s):  
Cameron Ferguson
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Network Analysis ◽  
Psychometric Properties ◽  
Graphical Models ◽  
Network Structure ◽  
Latent Variable ◽  
Network Models ◽  
Information Criterion ◽  
Graphical Lasso

Introduction: descriptions of the typical pattern of neurocognitive impairment in Alzheimer’s disease (AD) refer to relationships between neurocognitive domains as well as deficits within domains. However, the former of these relationships have not been statistically modelled. Accordingly, this study aimed to model the unique variance between neurocognitive variables in AD, amnestic mild cognitive impairment (aMCI), and cognitive normality (CN) using network analysis. Methods: Gaussian Graphical Models with Extended Bayesian Information Criterion model selection and graphical lasso regularisation were used to estimate network models of neurocognitive variables in AD (n = 229), aMCI (n = 397) and CN (n = 193) groups. The psychometric properties of the models were investigated using simulation and bootstrapping procedures. Exploratory analyses of network structure invariance across groups were conducted. Results: neurocognitive network models were estimated for each group and found to have good psychometric properties. Exploratory investigations suggested that network structure was not invariant across CN and aMCI (p = 0.03), CN and AD (p < 0.01), and aMCI and AD neurocognitive networks (p < 0.01).Conclusions: network analysis can be used to robustly model the relationships between neurocognitive variables in AD, aMCI and CN. Network structure was not invariant, suggesting that relationships between neurocognitive variables differ across groups along the AD spectrum. Points of convergence and contrast with latent-variable models are explored.

scholarly journals GP-Select: Accelerating EM Using Adaptive Subspace Preselection

2017 ◽  
Vol 29 (8) ◽  
pp. 2177-2202 ◽  
Author(s):  
Jacquelyn A. Shelton ◽  
Jan Gasthaus ◽  
Zhenwen Dai ◽  
Jörg Lücke ◽  
Arthur Gretton
Keyword(s):  
Graphical Models ◽  
Latent Variables ◽  
Latent Variable ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Object Localization ◽  
Selection Function ◽  
Inference Problems ◽  
Compact Approximation ◽  
Nonparametric Procedure

We propose a nonparametric procedure to achieve fast inference in generative graphical models when the number of latent states is very large. The approach is based on iterative latent variable preselection, where we alternate between learning a selection function to reveal the relevant latent variables and using this to obtain a compact approximation of the posterior distribution for EM. This can make inference possible where the number of possible latent states is, for example, exponential in the number of latent variables, whereas an exact approach would be computationally infeasible. We learn the selection function entirely from the observed data and current expectation-maximization state via gaussian process regression. This is in contrast to earlier approaches, where selection functions were manually designed for each problem setting. We show that our approach performs as well as these bespoke selection functions on a wide variety of inference problems. In particular, for the challenging case of a hierarchical model for object localization with occlusion, we achieve results that match a customized state-of-the-art selection method at a far lower computational cost.

Tabu Search-Enhanced Graphical Models for Classification in High Dimensions

2008 ◽  
Vol 20 (3) ◽  
pp. 423-437 ◽  
Author(s):  
Xue Bai ◽  
Rema Padman ◽  
Joseph Ramsey ◽  
Peter Spirtes
Keyword(s):  
Tabu Search ◽  
Graphical Models ◽  
High Dimensions

scholarly journals Recent Integrations of Latent Variable Network Modeling With Psychometric Models

2021 ◽  
Vol 12 ◽  
Author(s):  
Selena Wang
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
Network Modeling ◽  
Network Models ◽  
Latent Variable Models ◽  
Independent Learning ◽  
Psychometric Models ◽  
R Packages

The combination of network modeling and psychometric models has opened up exciting directions of research. However, there has been confusion surrounding differences among network models, graphic models, latent variable models and their applications in psychology. In this paper, I attempt to remedy this gap by briefly introducing latent variable network models and their recent integrations with psychometric models to psychometricians and applied psychologists. Following this introduction, I summarize developments under network psychometrics and show how graphical models under this framework can be distinguished from other network models. Every model is introduced using unified notations, and all methods are accompanied by available R packages inducive to further independent learning.

Structural Equation Models

2009 ◽  
Author(s):  
Kenneth A. Bollen ◽  
Sophia Rabe‐Hesketh ◽  
Anders Skrondal
Keyword(s):  
Factor Analysis ◽  
Graphical Models ◽  
Latent Variable ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Model Fit ◽  
Model Specification ◽  
Estimation Model ◽  
Recent Developments ◽  
Multilevel Structural Equation

This article explains the use of factor analysis types of models to develop measures of latent concepts which were then combined with causal models of the underlying latent concepts. In particular, it offers an overview of the classic structural equation models (SEMs) when the latent and observed variables are continuous. Then it looks at more recent developments that include categorical, count, and other noncontinuous variables as well as multilevel structural equation models. The model specification, assumptions, and notation are covered. This is followed by addressing implied moments, identification, estimation, model fit, and respecification. The penetration of SEMs has been high in disciplines such as sociology, psychology, educational testing, and marketing, but lower in economics and political science despite the large potential number of applications. Today, SEMs have begun to enter the statistical literature and to re-enter biostatistics, though often under the name ‘latent variable models’ or ‘graphical models’.

scholarly journals Efficient Regularization Parameter Selection for Latent Variable Graphical Models via Bi-Level Optimization

2019 ◽  
Author(s):  
Joachim Giesen ◽  
Frank Nussbaum ◽  
Christopher Schneider
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
Graphical Model ◽  
Regularization Parameter ◽  
Relative Weight ◽  
Low Rank ◽  
Semidefinite Program ◽  
Wide Range ◽  
Regularization Parameters ◽  
Feasible Solutions

Latent variable graphical models are an extension of Gaussian graphical models that decompose the precision matrix into a sparse and a low-rank component. These models can be learned with theoretical guarantees from data via a semidefinite program. This program features two regularization terms, one for promoting sparsity and one for promoting a low rank. In practice, however, it is not straightforward to learn a good model since the model highly depends on the regularization parameters that control the relative weight of the loss function and the two regularization terms. Selecting good regularization parameters can be modeled as a bi-level optimization problem, where the upper level optimizes some form of generalization error and the lower level provides a description of the solution gamut. The solution gamut is the set of feasible solutions for all possible values of the regularization parameters. In practice, it is often not feasible to describe the solution gamut efficiently. Hence, algorithmic schemes for approximating solution gamuts have been devised. One such scheme is Benson's generic vector optimization algorithm that comes with approximation guarantees. So far Benson's algorithm has not been used in conjunction with semidefinite programs like the latent variable graphical Lasso. Here, we develop an adaptive variant of Benson's algorithm for the semidefinite case and show that it keeps the known approximation and run time guarantees. Furthermore, Benson's algorithm turns out to be practically more efficient for the latent variable graphical model than the existing solution gamut approximation scheme on a wide range of data sets.

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