Online and Distributed Robust Regressions under Adversarial Data Corruption
This work solves robust regression for big data applications where traditional methods fail due to scalability and corruption issues, though it is incremental as it builds on existing robust methods.
The paper tackles robust least-squares regression in large datasets with adversarial corruption by proposing online and distributed algorithms that address computational infeasibility, heterogeneous corruption, and corruption estimation challenges, achieving strong robustness guarantees with constant error bounds and superior effectiveness in experiments.
In today's era of big data, robust least-squares regression becomes a more challenging problem when considering the adversarial corruption along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer from several challenges when applied in huge dataset including 1) computational infeasibility of handling an entire dataset at once, 2) existence of heterogeneously distributed corruption, and 3) difficulty in corruption estimation when data cannot be entirely loaded. This paper proposes online and distributed robust regression approaches, both of which can concurrently address all the above challenges. Specifically, the distributed algorithm optimizes the regression coefficients of each data block via heuristic hard thresholding and combines all the estimates in a distributed robust consolidation. Furthermore, an online version of the distributed algorithm is proposed to incrementally update the existing estimates with new incoming data. We also prove that our algorithms benefit from strong robustness guarantees in terms of regression coefficient recovery with a constant upper bound on the error of state-of-the-art batch methods. Extensive experiments on synthetic and real datasets demonstrate that our approaches are superior to those of existing methods in effectiveness, with competitive efficiency.