Search results for "Gaussian Graphical Model"
showing 10 items of 17 documents
Genetic Network construction in CML gene expression profile data analysis
2009
Aim of this paper is to define a new statistical framework to identify central modules in Gaussian Graphical Models (GGMs) estimated by gene expression data measured on a sample of patients with negative molecular response to imatinib. A central module is defined as a module of a GGM which contains genes that are defined differentially expressed.
Model selection for penalized Gaussian Graphical Models
2013
High-dimensional data refers to the case in which the number of parameters is of one or more order greater than the sample size. Penalized Gaussian graphical models can be used to estimate the conditional independence graph in high-dimensional setting. In this setting, the crucial issue is to select the tuning parameter which regulates the sparsity of the graph. In this paper, we focus on estimating the "best" tuning parameter. We propose to select this tuning parameter by minimizing an information criterion based on the generalized information criterion and to use a stability selection approach in order to obtain a more stable graph. The performance of our method is compared with the state…
Operational and financial performance of Italian airport companies: A dynamic graphical model
2016
Abstract This paper provides evidence on the relationship within a set of financial and operational indicators for Italian airports over 2008–2014. The limited sample size of national and regional airports suggests to apply the penalised RCON ( V , E ) model, which falls within the class of Gaussian graphical models. It provides both estimate and easy way to visualise conditional independence structures of the variables. Moreover, it is particularly suitable for handling longitudinal data where small number of units and huge number of variables have been collected. Findings highlight that a qualified concept of size matters in determining good financial performance. Specifically, increasing…
Dynamic factorial graphical models for dynamic networks
2014
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molec- ular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. H…
cglasso: An R Package for Conditional Graphical Lasso Inference with Censored and Missing Values
2023
Sparse graphical models have revolutionized multivariate inference. With the advent of high-dimensional multivariate data in many applied fields, these methods are able to detect a much lower-dimensional structure, often represented via a sparse conditional independence graph. There have been numerous extensions of such methods in the past decade. Many practical applications have additional covariates or suffer from missing or censored data. Despite the development of these extensions of sparse inference methods for graphical models, there have been so far no implementations for, e.g., conditional graphical models. Here we present the general-purpose package cglasso for estimating sparse co…
Dynamic Gaussian Graphical Models for Modelling Genomic Networks
2014
After sequencing the entire DNA for various organisms, the challenge has become understanding the functional interrelatedness of the genome. Only by understanding the pathways for various complex diseases can we begin to make sense of any type of treatment. Unfortunately, decyphering the genomic network structure is an enormous task. Even with a small number of genes the number of possible networks is very large. This problem becomes even more difficult, when we consider dynamical networks. We consider the problem of estimating a sparse dynamic Gaussian graphical model with \(L_1\) penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynami…
Sparse model-based network inference using Gaussian graphical models
2010
We consider the problem of estimating a sparse dynamic Gaussian graphical model with L1 penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynamics, known presence or absence of links in the graphical model or equality constraints on the parameters. The model is defined on the basis of partial correlations, which results in a specific class precision matrices. A priori L1 penalized maximum likelihood estimation in this class is extremely difficult, because of the above mentioned constraints, the computational complexity of the L1 constraint on the side of the usual positive-definite constraint. The implementation is non-trivial, but we sh…
L1-Penalized Censored Gaussian Graphical Model
2018
Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this article, we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithm…
Cyclic coordinate for penalized Gaussian graphical models with symmetry restriction
2014
In this paper we propose two efficient cyclic coordinate algorithms to estimate structured concentration matrix in penalized Gaussian graphical models. Symmetry restrictions on the concentration matrix are particularly useful to reduce the number of parameters to be estimated and to create specific structured graphs. The penalized Gaussian graphical models are suitable for high-dimensional data.
A computationally fast alternative to cross-validation in penalized Gaussian graphical models
2015
We study the problem of selection of regularization parameter in penalized Gaussian graphical models. When the goal is to obtain the model with good predicting power, cross validation is the gold standard. We present a new estimator of Kullback-Leibler loss in Gaussian Graphical model which provides a computationally fast alternative to cross-validation. The estimator is obtained by approximating leave-one-out-cross validation. Our approach is demonstrated on simulated data sets for various types of graphs. The proposed formula exhibits superior performance, especially in the typical small sample size scenario, compared to other available alternatives to cross validation, such as Akaike's i…