scholarly journals Thinning a Triangulation of a Bayesian Network or Undirected Graph to Create a Minimal Triangulation

2017 ◽  
Vol 25 (03) ◽  
pp. 1750014
Author(s):  
Edmund Jones ◽  
Vanessa Didelez
Keyword(s):  
Bayesian Network ◽  
Graphical Model ◽  
Undirected Graph ◽  
Computer Experiment ◽  
R Package ◽  
The Other ◽  
Prime Decomposition ◽  
Original Graph ◽  
Minimal Triangulation

In one procedure for finding the maximal prime decomposition of a Bayesian network or undirected graphical model, the first step is to create a minimal triangulation of the network, and a common and straightforward way to do this is to create a triangulation that is not necessarily minimal and then thin this triangulation by removing excess edges. We show that the algorithm for thinning proposed in several previous publications is incorrect. A different version of this algorithm is available in the R package gRbase, but its correctness has not previously been proved. We prove that this version is correct and provide a simpler version, also with a proof. We compare the speed of the two corrected algorithms in three ways and find that asymptotically their speeds are the same, neither algorithm is consistently faster than the other, and in a computer experiment the algorithm used by gRbase is faster when the original graph is large, dense, and undirected, but usually slightly slower when it is directed.

scholarly journals AIS-BN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks

2000 ◽  
Vol 13 ◽  
pp. 155-188 ◽  
Author(s):  
J. Cheng ◽  
M. J. Druzdzel
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Importance Sampling ◽  
Network Models ◽  
Evidential Reasoning ◽  
The Other ◽  
Sampling Algorithm ◽  
Importance Function ◽  
Sampling Algorithms ◽  
Bayesian Network Models

Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in finite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from different stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, likelihood weighting (Fung & Chang, 1989; Shachter & Peot, 1989) and self-importance sampling (Shachter & Peot, 1989). We used in our tests three large real Bayesian network models available to the scientific community: the CPCS network (Pradhan et al., 1994), the PathFinder network (Heckerman, Horvitz, & Nathwani, 1990), and the ANDES network (Conati, Gertner, VanLehn, & Druzdzel, 1997), with evidence as unlikely as 10^-41. While the AIS-BN algorithm always performed better than the other two algorithms, in the majority of the test cases it achieved orders of magnitude improvement in precision of the results. Improvement in speed given a desired precision is even more dramatic, although we are unable to report numerical results here, as the other algorithms almost never achieved the precision reached even by the first few iterations of the AIS-BN algorithm.

scholarly journals Disentangling microbial associations from hidden environmental and technical factors via latent graphical models

2019 ◽  
Author(s):  
Zachary D. Kurtz ◽  
Richard Bonneau ◽  
Christian L. Müller
Keyword(s):  
Graphical Models ◽  
Graphical Model ◽  
R Package ◽  
Comprehensive Collection ◽  
Performance Guarantees ◽  
Ecological Association ◽  
Microbial Associations ◽  
Sparse Inverse Covariance Estimation ◽  
Statistical Relationships ◽  
And Function

AbstractDetecting community-wide statistical relationships from targeted amplicon-based and metagenomic profiling of microbes in their natural environment is an important step toward understanding the organization and function of these communities. We present a robust and computationally tractable latent graphical model inference scheme that allows simultaneous identification of parsimonious statistical relationships among microbial species and unobserved factors that influence the prevalence and variability of the abundance measurements. Our method comes with theoretical performance guarantees and is available within the SParse InversE Covariance estimation for Ecological ASsociation Inference (SPIEC-EASI) framework (‘SpiecEasi’ R-package). Using simulations, as well as a comprehensive collection of amplicon-based gut microbiome datasets, we illustrate the method’s ability to jointly identify compositional biases, latent factors that correlate with observed technical covariates, and robust statistical microbial associations that replicate across different gut microbial data sets.

Proper connection of power graphs of finite groups

2020 ◽  
pp. 2150033
Author(s):  
Xuanlong Ma
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Undirected Graph ◽  
The Other ◽  
Connection Number ◽  
Power Graph ◽  
Vertex Set ◽  
Proper Connection Number ◽  
A Finite Group

Let [Formula: see text] be a finite group. The power graph of [Formula: see text] is the undirected graph whose vertex set is [Formula: see text], and two distinct vertices are adjacent if one is a power of the other. The reduced power graph of [Formula: see text] is the subgraph of the power graph of [Formula: see text] obtained by deleting all edges [Formula: see text] with [Formula: see text], where [Formula: see text] and [Formula: see text] are two distinct elements of [Formula: see text]. In this paper, we determine the proper connection number of the reduced power graph of [Formula: see text]. As an application, we also determine the proper connection number of the power graph of [Formula: see text].

Bayesian Networks

2011 ◽  
pp. 89-93 ◽  
Author(s):  
Ahmad Bashir ◽  
Latifur Khan ◽  
Mamoun Awad
Keyword(s):  
Neural Networks ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Decision Trees ◽  
Graphical Model ◽  
Conditional Probabilities ◽  
Rule Bases

A Bayesian network is a graphical model that finds probabilistic relationships among variables of a system. The basic components of a Bayesian network include a set of nodes, each representing a unique variable in the system, their inter-relations, as indicated graphically by edges, and associated probability values. By using these probabilities, termed conditional probabilities, and their interrelations, we can reason and calculate unknown probabilities. Furthermore, Bayesian networks have distinct advantages compared to other methods, such as neural networks, decision trees, and rule bases, which we shall discuss in this paper.

A network-based algorithm for the identification of moonlighting noncoding RNAs and its application in sepsis

2020 ◽  
Author(s):  
Xueyan Liu ◽  
Yong Xu ◽  
Ran Wang ◽  
Sheng Liu ◽  
Jun Wang ◽  
...  
Keyword(s):  
Functional Annotation ◽  
Expression Patterns ◽  
Noncoding Rnas ◽  
R Package ◽  
The Other ◽  
Great Promise ◽  
Multiple Functions ◽  
Moonlighting Proteins ◽  
Genome Level ◽  
Protein Modules

Abstract Moonlighting proteins provide more options for cells to execute multiple functions without increasing the genome and transcriptome complexity. Although there have long been calls for computational methods for the prediction of moonlighting proteins, no method has been designed for determining moonlighting long noncoding ribonucleicacidz (RNAs) (mlncRNAs). Previously, we developed an algorithm MoonFinder for the identification of mlncRNAs at the genome level based on the functional annotation and interactome data of lncRNAs and proteins. Here, we update MoonFinder to MoonFinder v2.0 by providing an extensive framework for the detection of protein modules and the establishment of RNA–module associations in human. A novel measure, moonlighting coefficient, was also proposed to assess the confidence of an ncRNA acting in a moonlighting manner. Moreover, we explored the expression characteristics of mlncRNAs in sepsis, in which we found that mlncRNAs tend to be upregulated and differentially expressed. Interestingly, the mlncRNAs are mutually exclusive in terms of coexpression when compared to the other lncRNAs. Overall, MoonFinder v2.0 is dedicated to the prediction of human mlncRNAs and thus bears great promise to serve as a valuable R package for worldwide research communities (https://cran.r-project.org/web/packages/MoonFinder/index.html). Also, our analyses provide the first attempt to characterize mlncRNA expression and coexpression properties in adult sepsis patients, which will facilitate the understanding of the interaction and expression patterns of mlncRNAs.

Development of a Bayesian Network for the Prognosis of Head Injuries using Graphical Model Selection Techniques

1999 ◽  
Vol 38 (01) ◽  
pp. 37-42 ◽  
Author(s):  
G. C. Sakellaropoulos ◽  
G. C. Nikiforidis
Keyword(s):  
Model Selection ◽  
Bayesian Network ◽  
Analytical Approach ◽  
Graphical Model ◽  
Head Injuries ◽  
Sources Of Information ◽  
Laboratory Findings ◽  
Learning Techniques ◽  
Head Injured ◽  
Injured Patients

Abstract:The assessment of a head-injured patient’s prognosis is a task that involves the evaluation of diverse sources of information. In this study we propose an analytical approach, using a Bayesian Network (BN), of combining the available evidence. The BN’s structure and parameters are derived by learning techniques applied to a database (600 records) of seven clinical and laboratory findings. The BN produces quantitative estimations of the prognosis after 24 hours for head-injured patients in the outpatients department. Alternative models are compared and their performance is tested against the success rate of an expert neurosurgeon.

Understanding Harmful Algal Bloom Dynamics in a Mediterranean Hypereutrophic Reservoir insights from a Bayesian Network and a Structural Equation Model

2020 ◽  
Author(s):  
Ibrahim Alameddine ◽  
Eliza Deutsch
Keyword(s):  
Bayesian Network ◽  
Structural Equation Model ◽  
Temperature Effects ◽  
Structural Equation ◽  
Nutrient Loading ◽  
Harmful Algal Bloom ◽  
Equation Model ◽  
The Other ◽  
Nutrient Loads ◽  
Bloom Formation

<p>Cyanobacteria blooms, especially those involving Microcystis, are an increasing problem facing many freshwater systems worldwide. In this study, a Bayesian Network (BN) along with a Structural Equation Model (SEM) were concurrently developed through data-driven learning and expert elicitation in order to better delineate the main pathways responsible for the Microcystis dominance in a Mediterranean semi-arid hypereutrophic reservoir. The resulting two model structures were then compared with regards to the pathways they identified between the physical lake conditions and the nutrient loads on one hand and Microcystis dominance on the other. The two models were also used to predict the probability of bloom formation under different scenarios of climate change and nutrient loading. Both models showed that, given the eutrophic status of the study reservoir, direct temperature effects appear to be the primary driving force behind the Microcystis growth and dominance. Indirect temperature effects, which modulated water column stratification and internal nutrient release, were also found to play an important role in bloom formation. On the other hand, both models revealed that the direct nutrient pathways were less important as compared to the temperature effects, with internal nutrient loads dominating over external loads due to the seasonal variability in river flows, typical of Mediterranean rivers. Nevertheless, the BN model was unable to capture the recursive relationships between Microcystis and its forcings.</p>

scholarly journals csdR, an R package for differential co-expression analysis

2021 ◽  
Author(s):  
Jakob P. Pettersen ◽  
Eivind Almaas
Keyword(s):  
Data Analysis ◽  
Expression Analysis ◽  
R Package ◽  
Ease Of Use ◽  
The Other ◽  
Gene Pairs ◽  
Computational Performance ◽  
Parallel Speedup ◽  
Multiple Processing ◽  
Number Of Iterations

AbstractBackgroundDifferential co-expression network analysis has become an important tool to gain understanding of biological phenotypes and diseases. The CSD algorithm is a method to generate differential co-expression networks by comparing gene co-expressions from two different conditions. Each of the gene pairs is assigned conserved (C), specific (S) and differentiated (D) scores based on the co-expression of the gene pair between the two conditions. The result of the procedure is a network where the nodes are genes and the links are the gene pairs with the highest C-, S-, and D-scores. However, the existing CSD-implementations suffer from poor computational performance, difficult user procedures and lack of documentation.ResultsWe created the R-package csdR aimed at reaching good performance together with ease of use, sufficient documentation, and with the ability to play well with other tools for data analysis. csdR was benchmarked on a realistic dataset with 20, 645 genes. After verifying that the chosen number of iterations gave sufficient robustness, we tested the performance against the two existing CSD implementations. csdR was superior in performance to one of the implementations, whereas the other did not run. Our implementation can utilize multiple processing cores. However, we were unable to achieve more than ∼ 2.7 parallel speedup with saturation reached at about 10 cores.ConclusionsThe results suggest that csdR is a useful tool for differential co-expression analysis and is able to generate robust results within a workday on datasets of realistic sizes when run on a workstation or compute server.

scholarly journals Probabilistic Graphical Model using Bayesian Networks for Predicting Clinical Outcome after Posterior Decompression in Patients with Cervical Spondylotic Myelopathy

2020 ◽  
Author(s):  
Sung Bae Park ◽  
Sohee Oh ◽  
Changwon Yoo ◽  
Dong Ah Shin ◽  
Sun-Ho Lee ◽  
...  
Keyword(s):  
Clinical Outcome ◽  
Bayesian Network ◽  
Cervical Spondylotic Myelopathy ◽  
Graphical Model ◽  
Probabilistic Graphical Model ◽  
Symptom Duration ◽  
Posterior Decompression ◽  
Causal Factors ◽  
Gait Impairment ◽  
Network Analyses

Abstract BackgroundThe objective of this study was to develop a probabilistic graphical model (PGM) to show the personalized prediction of clinical outcome in patients with cervical spondylotic myelopathy (CSM) with different clinical conditions after posterior decompression and to use the PGM to identify causal predictors of the outcome.MethodsWe included data from 59 patients who had undergone cervical posterior decompression for CSM. The candidate predictive parameters were age, sex, body mass index, trauma history, symptom duration, preoperative and last Japanese Orthopaedic Association (JOA) scores, gait impairment, claudication, bladder dysfunction, Nurick grade, American Spinal Injury Association (ASIA) grade, smoking, diabetes mellitus, cardiopulmonary disorders, hypertension, stroke, Parkinson disease, dementia, psychiatric disorders, arthritis, ossification of the posterior longitudinal ligament, cord signal change in T1-weighted images, postoperative kyphosis, and cord compression ratio. Statistical and Bayesian network analyses were used to create the PGM and identify predictive factors.ResultsIn multiple linear regression analysis, preoperative JOA score, presence of a psychiatric disorder, and ASIA grade were identified as significant factors associated with the last JOA score. Dementia, sex, preoperative JOA score, and gait impairment were causal factors in the PGM with 93.2% accuracy. Sex, dementia, and preoperative JOA score were direct causal factors related to the last JOA score. Being female, having dementia, and a low preoperative JOA score were significantly related to having a low last JOA score. The PGM showed that preoperative JOA score and sex did not affect the last JOA score in patients with dementia. The probability of having a high last JOA score was higher in men with a high preoperative JOA score than in women with the same preoperative state (74% vs. 2%, respectively).ConclusionsThe causal predictors of surgical outcome for CSM were sex, dementia, and preoperative JOA score. Use of the PGM with the Bayesian network may be useful personalized medicine tool for predicting the outcome for each patient with CSM.

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