CAREER: New methods for multivariate analysis in high dimensions

Datasets from imaging, gene microarray experiments, and many other fields often have more measured characteristics than subjects. Analyzing these data with standard statistical methods is either impossible or inadequate. The investigator addresses this problem by developing new statistical methods that are appropriate for such datasets. The investigator develops theoretical justifications for these new methods and fast computational algorithms for their application. Software that implements these algorithms will be made available to the public. These new products will help practitioners in industry create better predictive models and will also help advance research in many other fields. The investigator will also develop new curricula, including the creation of an undergraduate statistical computing course, an undergraduate statistical machine learning course, a Ph.D.-level topics course, and a new track within the undergraduate statistics major.

Building statistical models when the number of explanatory variables exceeds the sample size is an exciting area at the forefront of multivariate analysis. Fitting these models with classical techniques is typically impossible and some constraints or penalties must be imposed. Penalties that encourage zeros in parameter estimates have received substantial attention. These penalties are useful because they lead to interpretable parameter estimates, but assuming that these zeros exist may be inappropriate in some applications. The investigator develops and analyzes new methods to fit models in high dimensions that do not require that zeros are present in the parameters of interest, but still allow the practitioner to make simple interpretations of the fit in terms of the measured variables. This includes the development of new methods to fit multiple response regression models and multinomial logistic regression models, as well as the development of new methods to shrink characteristics of inverse covariance estimates that are needed to fit predictive models. The investigator will develop new curricula and involve Ph.D. students in the research.