Low-Order Conditional Independence Graphs for Inferring Genetic Networks
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As a powerful tool for analyzing full conditional (in-)dependencies between random variables, graphical models have become increasingly popular to infer genetic networks based on gene expression data. However, full (unconstrained) conditional relationships between random variables can be only estimated accurately if the number of observations is relatively large in comparison to the number of variables, which is usually not fulfilled for high-throughput genomic data.Recently, simplified graphical modeling approaches have been proposed to determine dependencies between gene expression profiles. For sparse graphical models such as genetic networks, it is assumed that the zero- and first-order conditional independencies still reflect reasonably well the full conditional independence structure between variables. Moreover, low-order conditional independencies have the advantage that they can be accurately estimated even when having only a small number of observations. Therefore, using only zero- and first-order conditional dependencies to infer the complete graphical model can be very useful. Here, we analyze the statistical and probabilistic properties of these low-order conditional independence graphs (called 0-1 graphs). We find that for faithful graphical models, the 0-1 graph contains at least all edges of the full conditional independence graph (concentration graph). For simple structures such as Markov trees, the 0-1 graph even coincides with the concentration graph. Furthermore, we present some asymptotic results and we demonstrate in a simulation study that despite their simplicity, 0-1 graphs are generally good estimators of sparse graphical models. Finally, the biological relevance of some applications is summarized.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Articles in the same Issue
- Article
- Low-Order Conditional Independence Graphs for Inferring Genetic Networks
- A Generalized Clustering Problem, with Application to DNA Microarrays
- A Bayes Regression Approach to Array-CGH Data
- Statistical Selection of Maintenance Genes for Normalization of Gene Expressions
- Predicting the Strongest Domain-Domain Contact in Interacting Protein Pairs
- Dimension Reduction for Classification with Gene Expression Microarray Data
- A New Type of Stochastic Dependence Revealed in Gene Expression Data
- A New Order Estimator for Fixed and Variable Length Markov Models with Applications to DNA Sequence Similarity
- Quality Optimised Analysis of General Paired Microarray Experiments
- Issues of Processing and Multiple Testing of SELDI-TOF MS Proteomic Data
- Cross-Validated Bagged Prediction of Survival
- Treatment of Uninformative Families in Mean Allele Sharing Tests for Linkage
- Quantile-Function Based Null Distribution in Resampling Based Multiple Testing
- Combining Results of Microarray Experiments: A Rank Aggregation Approach
- Model Selection for Mixtures of Mutagenetic Trees
- Pseudo-likelihood for Non-reversible Nucleotide Substitution Models with Neighbour Dependent Rates
- A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting
- Bayesian Hierarchical Model for Correcting Signal Saturation in Microarrays Using Pixel Intensities
- Using Complexity for the Estimation of Bayesian Networks
- Detecting Local High-Scoring Segments: a First-Stage Approach for Genome-Wide Association Studies
- Examining Protein Structure and Similarities by Spectral Analysis Technique
- Parameter Estimation for the Exponential-Normal Convolution Model for Background Correction of Affymetrix GeneChip Data
- Approximate Sample Size Calculations with Microarray Data: An Illustration
- Numerical Solutions for Patterns Statistics on Markov Chains
- A Heuristic Bayesian Method for Segmenting DNA Sequence Alignments and Detecting Evidence for Recombination and Gene Conversion
- A Two-Step Multiple Comparison Procedure for a Large Number of Tests and Multiple Treatments
- Validation in Genomics: CpG Island Methylation Revisited
- An Improved Nonparametric Approach for Detecting Differentially Expressed Genes with Replicated Microarray Data
- Letter to the Editor
- Treating Expression Levels of Different Genes as a Sample in Microarray Data Analysis: Is it Worth a Risk?
- Reader's Reaction
- Reader's Reaction to "Dimension Reduction for Classification with Gene Expression Microarray Data" by Dai et al (2006)
Articles in the same Issue
- Article
- Low-Order Conditional Independence Graphs for Inferring Genetic Networks
- A Generalized Clustering Problem, with Application to DNA Microarrays
- A Bayes Regression Approach to Array-CGH Data
- Statistical Selection of Maintenance Genes for Normalization of Gene Expressions
- Predicting the Strongest Domain-Domain Contact in Interacting Protein Pairs
- Dimension Reduction for Classification with Gene Expression Microarray Data
- A New Type of Stochastic Dependence Revealed in Gene Expression Data
- A New Order Estimator for Fixed and Variable Length Markov Models with Applications to DNA Sequence Similarity
- Quality Optimised Analysis of General Paired Microarray Experiments
- Issues of Processing and Multiple Testing of SELDI-TOF MS Proteomic Data
- Cross-Validated Bagged Prediction of Survival
- Treatment of Uninformative Families in Mean Allele Sharing Tests for Linkage
- Quantile-Function Based Null Distribution in Resampling Based Multiple Testing
- Combining Results of Microarray Experiments: A Rank Aggregation Approach
- Model Selection for Mixtures of Mutagenetic Trees
- Pseudo-likelihood for Non-reversible Nucleotide Substitution Models with Neighbour Dependent Rates
- A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting
- Bayesian Hierarchical Model for Correcting Signal Saturation in Microarrays Using Pixel Intensities
- Using Complexity for the Estimation of Bayesian Networks
- Detecting Local High-Scoring Segments: a First-Stage Approach for Genome-Wide Association Studies
- Examining Protein Structure and Similarities by Spectral Analysis Technique
- Parameter Estimation for the Exponential-Normal Convolution Model for Background Correction of Affymetrix GeneChip Data
- Approximate Sample Size Calculations with Microarray Data: An Illustration
- Numerical Solutions for Patterns Statistics on Markov Chains
- A Heuristic Bayesian Method for Segmenting DNA Sequence Alignments and Detecting Evidence for Recombination and Gene Conversion
- A Two-Step Multiple Comparison Procedure for a Large Number of Tests and Multiple Treatments
- Validation in Genomics: CpG Island Methylation Revisited
- An Improved Nonparametric Approach for Detecting Differentially Expressed Genes with Replicated Microarray Data
- Letter to the Editor
- Treating Expression Levels of Different Genes as a Sample in Microarray Data Analysis: Is it Worth a Risk?
- Reader's Reaction
- Reader's Reaction to "Dimension Reduction for Classification with Gene Expression Microarray Data" by Dai et al (2006)
