Finding and explaining structural hierarchies in models of complex systems

Sloppy models form a universality class of complex, nonlinear models in which outcomes are significantly affected by only a small subset of parameter combinations, arising in disparate fields from systems biology to accelerator physics. By unifying information geometric interpretations of sloppiness with Chebyshev approximation theory, I will derive a formal and systematic explanation of why sloppiness occurs. I will then extend this framework to general probabilistic models and data, to derive a widely-applicable manifold-learning method called InPCA that ameliorates a canonical problem in machine learning: the "curse of dimensionality".