Create Presentation
Download Presentation

Download Presentation
## Recovering Temporally Rewiring Networks: A Model-based Approach

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Recovering Temporally Rewiring Networks: A Model-based**Approach Fan Guo, Steve Hanneke, Wenjie Fu, Eric P. Xing School of Computer Science, Carnegie Mellon University ICML 2007 Presentation**Social Networks**Physicist Collaborations High School Dating The Internet All the images are from http://www-personal.umich.edu/~mejn/networks/. That page includes original citations.**Biological Networks**Model for the Yeast cell cycle transcriptional regulatory networkFig. 4 from (T.I. Lee et al., Science 298, 799-804, 25 Oct 2002) Protein-Protein Interaction Network in S. cerevisiaeFig. 1 from (H. Jeong et al., Nature 411, 41-42, 3 May 2001) The small image is from http://www.raiks.de/img/dyna_title_zoom.jpg**When interactions are hidden…**• Infer the hiddennetwork topology from node attribute observations. • Methods: Optimizing a score function; Information-theoretic approaches; Model-based approach … • Most of them pool the data together to infer a static network topology. ICML 2007 Presentation**And changing over time**• Network topologies and functions are not static: • Social networks can grow as we know more friends • Biological networks rewire under different conditions Fig. 1b fromGenomic analysis of regulatory network dynamics reveals large topological changes N. M. Luscombe, et al. Nature 431, 308-312, 16 September 2004 ICML 2007 Presentation**Overview**• Network topologies and functions are not always static. • We propose probabilistic models and algorithms for recovering latent network topologies that are changing over time from node attribute observations. ICML 2007 Presentation**Rewiring Networks of Genes**• Networks rewire over discrete timesteps Part of the image is modified from Fig. 3b (E. Segal et al., Nature Genetics 34, 166-176, June 2003).**The Graphical Model**Transition Model Emission Model ICML 2007 Presentation**Technical Challenges**• Latent network structures are of higher dimensions than observed node attributes • How to place constraints on the latent space? • Limited evidence per timestep • How to share the information across time? ICML 2007 Presentation**Energy Based Conditional Probablities**• Energy-based conditional probability model (recall Markov random fields…) • Energy-based model is easier to analysis, but even the design of approximate inference algorithm can be hard. 10/23/2014 ICML 2007 Presentation ICML 2007 Presentation 10**Transition Model**• Based on our previous work on discrete temporal network models in the ICML’06 SNA-Workshop. • Model network rewiring as a Markov process. • An expressive framework using energy-based local probabilities (based on ERGM): • Features of choice: (Density) (Edge Stability) (Transitivity) 10/23/2014 ICML 2007 Presentation ICML 2007 Presentation 11**Emission Model in General**• Given the network topology, how to generate the binary node attributes? • Another energy-based conditional model: • All features are pairwise which induces an undirected graph corresponding to the time-specific network topology; • Additional information shared over time is represented by a matrix of parameters Λ; • The design of feature functionΦ is application-specific. 10/23/2014 ICML 2007 Presentation ICML 2007 Presentation 12**Design of Features for Gene Expression**• The feature function • If no edge between i and j, Φequals 0; • Otherwise the sign of Φ depends on Λijand the empirical correlation of xi, xj at time t. ICML 2007 Presentation**Graphical Structure Revisit**Hidden rewiring networks Initial network to define the prior on A1 Time-invariant parameters dictating the direction of pairwise correlation in the example ICML 2007 Presentation**Inference**• A natural approach to infer the hidden networks A1:T is Gibbs sampling: • To evaluate the log-odds • Conditional probabilities in a Markov blanket Tractable transition model; the partition function is the product of per edge terms Computation is straightforward Given the graphical structure, run variable elimination algorithms, works well for small graphs ICML 2007 Presentation**Parameter Estimation**• Grid search is very helpful, although Monte Carlo EM can be implemented. • Trade-off between the transition model and emission model: • Larger θ : better fit of the rewiring processes; • Larger η : better fit of the observations. ICML 2007 Presentation**Results from Simulation**• Data generated from the proposed model. • Starting from a network (A0) of 10 nodes and 14 edges. • The length of the time series T = 50. • Compare three approaches using F1 score: • avg: averaged network from “ground truth”(approx. upper bounds the performance of any static network inference algorithm) • htERG: infer timestep-specific networks • sERG: the static counterpart of the proposed algorithm • Study the “edge-switching events” ICML 2007 Presentation**Varying Parameter Values**• F1 scores on different parameter settings (varying ) ICML 2007 Presentation**Varying the Amount of Data**• F1 scores on different number of examples ICML 2007 Presentation**Capturing Edge Switching**• Summary on capturing edge switching in networks • Three cases studied: offset, false positive, missing(false negative) • mean and rms of offset timesteps ICML 2007 Presentation**Results on Drosophila Data**• The proposed model was applied to infer the muscle development sub-network (Zhao et al., 2006) on Drosophila lifecycle gene expression data (Arbeitman et al., 2002). • 11 genes, 66timesteps over 4 development stages • Further biological experiments are necessary for verification. Network in (Zhao et al. 2006) Embryonic Larval Pupal & Adult ICML 2007 Presentation**Summary**• A new class of probabilistic models to address the problem of recoving hidden, time-dependent network topologies and an example in a biological context. • An example of employing energy-based model to define meaningful features and simplify parameterization. • Future work • Larger-scale network analysis (100+?) • Developing emission models for richer context ICML 2007 Presentation**Acknowledgement**• Yanxin Shi CMU • Wentao Zhao Texas A&M University • Hetunandan Kamisetty CMU ICML 2007 Presentation**Thank You!**ICML 2007 Presentation