Tyrus Berry, Assistant Professor, Mathematical Sciences, will soon begin a project developing semiparametric modeling techniques that optimally leverage the strengths of parametric and nonparametric methods, while negating their weaknesses.
Parametric modeling uses a model with a finite, fixed number of unknowns that are typically fit using training data.
Semiparametric modeling is when there is a regression model with both a finite- and an infinite-dimensional component.
Parametric modeling is the most powerful paradigm in terms of ability to fit a large model from a reasonable amount of data. This power comes at the expense of inflexibility, and even a small mismatch between the parametric form and the truth can dramatically degrade the model's usefulness.
Via this project, Berry will propose a framework that allows the flexible nonparametric models to fill in gaps and correct the low-dimensional model error in a parametric model. The natural framework he is proposing uses an ensemble of states in the parametric model to represent the uncertainty in the current forecast or state estimate. His framework also estimates a full probability distribution for the nonparametric model.
This project is important because there is increasing demand across scientific disciplines for efficient tools to learn state variables and make optimal predictions for limited noisy observations. For these predictions to be actionable, they must also have quantifiable uncertainty, and be robust to model misspecification. The semiparametric framework will help address the growing problem of identifying parameters that exhibit strong nonlinearity, such as network structure parameters.
Berry will receive $233,747 from the National Science Foundation for this project. Funding will begin in September 2020 and will end in late August 2023.