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June 2016 - Zuogong

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Statistical inference of regulatory networks fro circadian regulation
Dirk, H., & Marco, G. (2014). Statistical inference of regulatory networks for circadian regulation. Statistical Applications in Genetics and Molecular Biology. http://dx.doi.org/10.1515/sagmb-2013-0051

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June 2016 - Zuogong

  1. 1. Statistical inference of regulatory networks for circadian regulation — Methodology Part Zuogong Yue Pizzaclub, 15th June 2016 Authors: Andrej Aderhold, Dirk Huskier, Marco Grzegorczyk
  2. 2. o Mathematical formulation of transcriptional regulation1 Problem Formulation 2 1 Barenco, M., Tomescu, D., Brewer, D., Callard, R., Stark, J., & Hubank, M. (2006). Ranked prediction of p53 targets using hidden variable dynamic modeling. Genome Biology, 7(3), R25. o Regulatory networks (bipartite structure) yg1 yg2 yg3 xg1 xg2 xg3 xg4 xg5
  3. 3. Methods 3 o Graphical Gaussian Models (GGM) The components corresponding to two genes are stochastically independent conditional on the remaining system if and only if the corresponding element in the inverse covariance matrix is zero.
  4. 4. Methods 4 o Sparse Regression (LASSO and Elastic Net) (LASSO) (Elastic Net)
  5. 5. Methods 5 o Time-varying Sparse Regression (Tesla)
  6. 6. Methods 6 o Hierarchical Bayesian Regression Model (HBR) linear regression model: prior: then getting the posterior: and the marginal likelihood:
  7. 7. Methods 7 o Hierarchical Bayesian Regression Model (HBR) (cont.) Finally we get the marginal posterior distribution on Maximizing the above posterior by Markov chain Monte Carlo (MCMC) and
  8. 8. Methods 8 o Non-homogeneous Hierarchical Bayesian Model Applying HBR on a multiple change-point process: Divide the target variable into sub vectors
  9. 9. Methods 9 o Automatic Relevance Determination (ARD) - Sparse Bayesian Regression (SBR) Using the prior distribution: (choosing appropriate hyper parameters can lead to sparse solutions): The marginal likelihood: Maximize the marginal likelihood by Expectation Maximization (EM) method
  10. 10. Methods 10 o Bayesian Spline Autoregression (BSA) The original covariates are augmented with B-spline basis functions. To encourage network sparsity, a slab-and-stick-like Bayesian variable selection scheme2 is used. 2 Smith, M., & Kohn, R. (1996). Nonparametric regression using Bayesian variable selection. Journal of Econometrics, 75(2), 317–343.
  11. 11. Methods 11 o Gaussian Processes (GP) where is the well-known kernel function. Calculate the posterior: Marginalize and perform maximization:
  12. 12. Methods 12 o Mutual Information Methods (ARACNE) The mutual information (MI) is given by A pruning mechanism by Margolin (2006):
  13. 13. Methods 13 o Mixture Bayesian Network Models (MBN) Representing as a Gaussian mixture model (GMM): Maximize the likelihood of the conditional GMM:
  14. 14. Methods 14 o Gaussian Bayesian Network (BGe) Calculate the posterior distribution of and perform maximization Assume that Impose a normal-Wishart prior:
  15. 15. 15 Thank you!

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