COLLOQUIUM: Jing Liu, "Robust Linear Regression, Robust PCA, and High-dimensional Robust Mean Estimation via Sparsity Regularization"

Being robust to outliers or malicious agents is of paramount importance when we fuel the AI by big data. In this talk I will first introduce a novel L0-regularization framework for outlier-robust data analysis. In the context of robust linear regression and robust PCA problems, I will show that the proposed framework can recover the underlying signal/subspace exactly in the noiseless setting, and stably in the noisy setting. Furthermore, we will see that this framework can tolerate more outliers and has smaller error bound than the L1-relaxation approach. In the second part of this talk, I will introduce our recent work on high-dimensional robust mean estimation problem, which has applications in distributed learning with malicious agents. We formulate this problem as an L0-minimizatoin objective, which is shown to have near-optimal breakdown point and order-optimal estimation error bound. Then we propose a computationally tractable iterative Lp-minimization and hard thresholding algorithm that outputs an order-optimal robust estimate of the population mean.

Jing Liu is an 'Illinois Future Faculty Fellow' in CS department of UIUC working with Prof. Sanmi Koyejo and Prof. Bo Li. Before that, he is a postdoctoral research associate in Coordinated Science Lab (CSL) of UIUC hosted by Prof. Venu Veeravalli. He obtained his Ph.D. degree from UCSD and Master degree from Tsinghua University. His research interests include data science, Internet of Things (IoT), distributed learning, and trustworthy machine learning.

Part of the Illinois Computer Science Speakers Series. Faculty Host: Sanmi Koyejo