Kiryung Lee

The max-affine function has been utilized to model multivariate polynomials and a class of deep neural networks. We consider two variations of max-affine regression in practical scenarios. First, we consider robust max-affine regression resilient to adversarial corruption on a subset of training data. Second, we consider sparse max-affine regression to describe the nonlinear relationship between a dependent variable and an unknown subset of independent variables. We present an iterative algorithm for each problem with the local convergence guarantee. For robust max-affine regression, we propose an alternating minimization algorithm derived from the Gauss-Newton method for the least absolute deviation. To implement variable selection for max-affine regression, projected gradient descent with an adaptive step size rule has been studied. The sample complexity and tolerable ratio of outliers are quantified in the non-asymptotic analysis. Due to the non-convexity of the optimization underlying parameter estimation, starting these iterative algorithms from a suitable initialization is important. We propose and analyze an improved spectral initialization leveraging sparse principal components for sparse max-affine regression. A robust initialization scheme has been shown empirically successful in the presence of outliers. Finally, we demonstrate a set of comprehensive numerical experiments that corroborate our theoretical results. This is the joint work with Seonho Kim and Haitham Kanj.

Biography:

Kiryung Lee is an Assistant Professor with the Electrical and Computer Engineering Department at the Ohio State University. He received the B.S. and M.S. degrees in electrical engineering from Seoul National University and the Ph.D. in electrical and computer engineering from the University of Illinois at Urbana-Champaign. His research focuses on developing mathematical theory and optimization algorithms for inverse problems in signal processing, imaging, machine learning, statistics, and data science. He is a recipient of the NSF CAREER Award.