学术报告报告题目：Large-scale Network Reconstruction Based on Ordinary Differential Equation Systems
报告人：邱兴 教授
报告时间：2017年8月28日上午9:00-10:30
报告地点：4号楼4318室
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短期讲学内容及时间安排如下：
讲学标题：Statistical Methods for Differential Equation Modeling
| 时间 | 地点 | 讲学内容 | 报告人 |
| 8月29日（周二）9：00－12：00 | 4318 | Introduction to functional data analysis | 邱兴教授 |
| 8月30日（周三）9：00－12：00 | 4318 | Introduction to functional data analysis | 邱兴教授 |
| 8月31日（周四）9：00－12：00 | 4318 | Introduction to ordinary differential equations | 邱兴教授 |
| 9月1日（周五） 9：00－12：00 | 4318 | Statistical methods for inverse problem | 邱兴教授 |
| 9月4日（周一） 9：00－12：00 | 4318 | Statistical methods for inverse problem | 邱兴教授 |
| 9月5日（周二） 9：00－12：00 | 4318 | Sparcity, stability, and controllability | 邱兴教授 |
| 9月6日（周三） 9：00－12：00 | 4318 | Partial differential equations and other future research opportunities； | 邱兴教授 |
| 9月7日（周四） 9：00－12：00 | 4318 | Partial differential equations and other future research opportunities； | 邱兴教授 |
Title: Large-scale Network Reconstruction Based on Ordinary Differential Equation Systems
Abstract:
Many complex biological systems can be represented as quantitative networks. Most popular examples include protein-protein interaction network and gene regulatory network. Typically, these systems consist of thousands of nodes (i.e., proteins and genes) and potentially millions of edges (the interactions between nodes). When time-course data are available, researchers can use ordinary differential equation (ODE) systems to model the dynamic behavior of these systems. In these ODE-based networks, each node is modeled as a function of time, and a directed edge is considered as a linear or nonlinear term in the ODE system that relates the measure of the head node to the tail node. The value of an edge reflects the strength of the connection between the head and tail nodes.
Two distinct but related questions are often asked in these applications: How many edges have nonzero values? For those nonzero edges, what are the best estimates of these edges? In statistical language, the first question is model selection and the second one is parameter estimation. For large-scale networks, these two questions are very difficult because even for linear ODE systems, their solutions are not linear functions thus we must rely on nonlinear optimization methods in ultra-high dimensional parameter spaces.
To answer this challenge, we develop a parameter estimation and variable selection method based on the ideas of similarity transformation and separable least squares (SLS). Simulation studies demonstrate that our method outperforms the direct least squares (LS) method and the vector-based two-stage method that are currently available both in terms of estimation accuracy and computational costs. We applied this new method to two real data sets: a yeast cell cycle gene expression data set with 30 dimensions and 930 unknown parameters and the Standard & Poor 1500 index stock price data with 1250 dimensions and 1,563,750 unknown parameters, to illustrate the utility and numerical performance of the proposed method for large-scale systems in practice.