This project aims to develop algorithms and analysis techniques for large scale optimization and sampling problems that arise in machine learning. Some of the main treads are:
- Stochastic greedy methods for convex optimization
- Generalizations of Nesterov's celebrated acceleration approach for smooth convex optimization in continuous time
- Developing parameter estimation methods for deep neural networks based on analysis of their representation and generalization properties.
- Development of efficient sampling methods and for their analysis via an optimization approach.
- Alternating minimization approaches to non-convex optimization problems, such as dictionary learning and neural network parameter estimation.
- Developing effective uncertainty estimates for machine learning methods, based on the design of appropriate loss functions.
- Developing methodology, based on fast Laplacian solvers, that is suitable for large scale graph data.