196 research outputs found
Gene expression network reconstruction by convex feature selection when incorporating genetic perturbations.
No full textCellular gene expression measurements contain regulatory information that can be used to discover novel network relationships. Here, we present a new algorithm for network reconstruction powered by the adaptive lasso, a theoretically and empirically well-behaved method for selecting the regulatory features of a network. Any algorithms designed for network discovery that make use of directed probabilistic graphs require perturbations, produced by either experiments or naturally occurring genetic variation, to successfully infer unique regulatory relationships from gene expression data. Our approach makes use of appropriately selected cis-expression Quantitative Trait Loci (cis-eQTL), which provide a sufficient set of independent perturbations for maximum network resolution. We compare the performance of our network reconstruction algorithm to four other approaches: the PC-algorithm, QTLnet, the QDG algorithm, and the NEO algorithm, all of which have been used to reconstruct directed networks among phenotypes leveraging QTL. We show that the adaptive lasso can outperform these algorithms for networks of ten genes and ten cis-eQTL, and is competitive with the QDG algorithm for networks with thirty genes and thirty cis-eQTL, with rich topologies and hundreds of samples. Using this novel approach, we identify unique sets of directed relationships in Saccharomyces cerevisiae when analyzing genome-wide gene expression data for an intercross between a wild strain and a lab strain. We recover novel putative network relationships between a tyrosine biosynthesis gene (TYR1), and genes involved in endocytosis (RCY1), the spindle checkpoint (BUB2), sulfonate catabolism (JLP1), and cell-cell communication (PRM7). Our algorithm provides a synthesis of feature selection methods and graphical model theory that has the potential to reveal new directed regulatory relationships from the analysis of population level genetic and gene expression data
A Realizability Approach to Constructing Higher Types via Classifiers
No full textWe construct an interpretation of higher types into Peano arithmetic, showing in particular that every model of PA is a model of higher types. This is a reversal of Gödel’s Dialectica construction. We also define the classifier degrees, a degree structure which subsumes the Turing degrees, the enumeration degrees, and the many-one degrees. The classifier degrees boast a rich structure and many well-behaved operations
Sparse Model Building From Genome-Wide Variation With Graphical Models
No full textHigh throughput sequencing and expression characterization have lead to an explosion of phenotypic and genotypic molecular data underlying both experimental studies and outbred populations. We develop a novel class of algorithms to reconstruct sparse models among these molecular phenotypes (e.g. expression products) and genotypes (e.g. single nucleotide polymorphisms), via both a Bayesian hierarchical model, when the sample size is much smaller than the model dimension (i.e. p n) and the well characterized adaptive lasso algo- rithm. Specifically, we propose novel approaches to the problems of increasing power to detect additional loci in genome-wide association studies using our variational algorithm, efficiently learning directed cyclic graphs from expression and genotype data using the adaptive lasso, and constructing genomewide undirected graphs among genotype, expression and downstream phenotype data using an extension of the variational feature selection algorithm. The Bayesian hierarchical model is derived for a parametric multiple regression model with a mixture prior of a point mass and normal distribution for each regression coefficient, and appropriate priors for the set of hyperparameters. When combined with a probabilistic consistency bound on the model dimension, this approach leads to very sparse solutions without the need for cross validation. We use a variational Bayes approximate inference approach in our algorithm, where we impose a complete factorization across all parameters for the approximate posterior distribution, and then minimize the KullbackLeibler divergence between the approximate and true posterior distributions. Since the prior distribution is non-convex, we restart the algorithm many times to find multiple posterior modes, and combine information across all discovered modes in an approximate Bayesian model averaging framework, to reduce the variance of the posterior probability estimates. We perform analysis of three major publicly available data-sets: the HapMap 2 genotype and expression data collected on immortalized lymphoblastoid cell lines, the genome-wide gene expression and genetic marker data collected for a yeast intercross, and genomewide gene expression, genetic marker, and downstream phenotypes related to weight in a mouse F2 intercross. Based on both simulations and data analysis we show that our algorithms can outperform other state of the art model selection procedures when including thousands to hundreds of thousands of genotypes and expression traits, in terms of aggressively controlling false discovery rate, and generating rich simultaneous statistical models
Coal: Black Death for Red Culture
No full textThis is a Red Paper about coal mining in American Indian lands and its impact on water, soil, air quality, economy, natural environment, cultures, and development of tribes. The author makes an analysis of the damaging impact of strip mining, coal fired electricity, and coal gasification on the soil, underground water reserves, air, and the natural environment of Native American communities. The author also includes a critical analysis of the role of the U.S. Interior Department, the BIA, and the leasing treaties in tribal development programs to call for more participation of the Indian communities for protecting and managing natural resources in Indian lands.https://digitalrepository.unm.edu/lhnac/1006/thumbnail.jp
Gene Expression Network Reconstruction by Convex Feature Selection when Incorporating Genetic Perturbations
No full text[Photograph 2012.201.B0362.0795]
No full textPhotograph used for a story in the Daily Oklahoman newspaper. Caption: "Oklahoma author and historian Guy Logsdon of Tulsa autographs a copy of his book on Wednesday for Stan Paregien of Snyder, Texas, during the 1991 meeting of Western Writers of America Inc.
Example of a graphical model equivalence class when determining regulatory relationships among four genes ().
No full text<p>Edges represent the direction of regulation. In this case, the true regulatory network connecting the four genes (blue) has the same sampling distribution as the other three incorrect models (red). Without perturbations (i.e. eQTL), each of these models will equivalently describe the pattern of expression observed among these genes for any data-set.</p
Example of biological relationships that can be reconstructed by the algorithm.
No full text<p>An expression Quantitative Trait Locus (eQTL) directly alters the expression level of Gene A, a relationship that we represent in our network model with the parameter . This gene in turn has an effect on Gene B through an unobserved pathway represented by the ‘Factors’ node. While these factors are unobserved we can still infer that there is a regulatory effect of Gene A on the downstream Gene B, which is represented in our network model by the parameter .</p
Performance of our algorithm using the adaptive lasso for directed cyclic graphs compared to other algorithms.
No full text<p>These other algorithms include the PC-algorithm, the QDG algorithm, and the QTLnet algorithm for reconstructing different cyclic topologies of 10 genes (a) and (b) or 30 genes (c) and (d). For a dense directed cyclic topology (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1001014#pcbi-1001014-g004" target="_blank">Figure 4c</a>), the power (a) and false discovery rate (b) are plotted as a function of the sample size for five replicate simulations. Similarly, for an intermediately dense directed cyclic topology of 30 genes (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1001014#pcbi-1001014-g004" target="_blank">Figure 4d</a>), the power (c) and false discovery rate (d) are plotted.</p
Outline of the structure of Step 2 of the algorithm.
No full text<p>(a) After selection of phenotypes in Step 1, we produce a covariance matrix between observed gene expression products, and their associated unique <i>cis</i>-eQTL. (b) A convex feature selection method (the adaptive lasso) is used to learn the structure of the inverse covariance matrix, which is also the conditional independence or interaction network among gene expression products and <i>cis</i>-eQTL genotypes. (c) The directed cyclic network among expression products can then be recovered directly from the conditional independence network, using the “Recovery” Theorem. For Step 3, each of the induced edges between expression phenotypes and <i>cis</i>-eQTL, shown in (b), are tested to ensure marginal independence using a permutation test.</p
- …
