Nonlinear models in machine learning

Most modern methods in sparse and low-rank representations of data in machine learning are inherently linear: features combine linearly to predict outcomes, or high-dimensional observations lie along a subspace or hyperplane. However, this linear assumption is overly restrictive in many practical problems. My lab is developing novel methods for nonlinear matrix completion – i.e., for estimating missing elements of high-dimensional data without the linear constraint. We are considering both single index models (which assume an unknown nonlinear corruption of the data must be inferred to accurately estimate missing data) and union of subspace models (which assume data lie along one among several candidate subspaces or hyperplanes).

• D. Pimentel-Alarcon, L. Balzano, R. Marcia, R. Nowak, and R. Willett, “Group-sparse subspace clustering with missing data.” IEEE Statistical Signal Processing Workshop, 2016.
• R. Ganti, L. Balzano, and R. Willett, “Matrix Completion Under Monotonic Single Index Models,” in Proc. Neural Information Processing Systems, 2015.