Robust High-Dimensional Linear Regression

Abstract

The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the most important factors in predicting outcomes. However, the economic importance of learning has made it a natural target for adversarial manipulation of training data, which we term poisoning attacks. Prior approaches to dealing with robust supervised learning rely on strong assumptions about the nature of the feature matrix, such as feature independence and sub-Gaussian noise with low variance. We propose an integrated method for robust regression that relaxes these assumptions, assuming only that the feature matrix can be well approximated by a low-rank matrix. Our techniques integrate improved robust low-rank matrix approximation and robust principle component regression, and yield strong performance guarantees. Moreover, we experimentally show that our methods significantly outperform state of the art both in running time and prediction error.

Targeted Backdoor Attacks on Deep Learning Systems Using Data Poisoning

“…Highlights of differences to previous work on poisoning attacks. After presenting the details of the threat model above, we emphasize again the differences between this work and a long line of existing work studying poisoning attacks and defenses [10], [38], [12], [11], [68], [44], [9], [35], [70], [39], [61]. For example, the latest results from Liu et al [39] demonstrate effective defense strategies against training data poisoning when a large portion of poisoning samples are injected.…”