Oksana Chernova

Project

Our project is concerned with a problem in shape-constrained density estimation in the area of statistics. Density estimates help to visualize data, reveal its features, and make inferences. In this setting, there are two main reasons for imposing shape constraints, e.g., monotonicity and convexity. First, such shape constraints may be directly motivated by the problem under investigation. Second, methods built around shape constraints often allow one to derive an estimator that does not depend on a tuning parameter.
The class of log-concave functions can be considered as a natural infinite-dimensional generalization of Gaussian densities and lies at the heart of modern nonparametric inference, due to both the modeling flexibility and its attractive statistical properties. However, the inefficiency of existing computational algorithms remains an obstacle to more widespread adoption of this approach by practitioners.
We develop methodology for efficient log-­concave density estimation, creating tools to be used by practitioners to solve modern data challenges. Our approach for higher-dimensional cases is to apply an exponential ­series method combined with a score matching ­procedure.