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Abstract:
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Mathematical/computational biologists often use differential equations to describe the dynamics of genetic networks---the interacting systems of DNA, mRNA, proteins, and various molecules that regulate life at the cellular level. Quantitative molecular abundance data is increasingly available, creating a strong demand for sound techniques for fitting differential equation models. Yet, little attention has been paid to this problem in statistics, probabilistic modeling, or machine learning communities. I will discuss statistical and computational challenges in fitting differential equations to noisy, incomplete biological data and my work on combining optimization and regression approaches that address these issues. I will present results on modeling spatio-temporal expression data from the gap gene network of Drosophila melanogaster.
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