By combining robust regression and prior information, we develop an effective robust regression method that can resist adaptive adversarial attacks. Due to the widespread existence of noise and data corruption, it is necessary to recover the true regression parameters when a certain proportion of the response variables have been corrupted. Methods to overcome this problem often involve robust least-squares regression. However, few methods achieve good performance when dealing with severe adaptive adversarial attacks. Based on the combination of prior information and robust regression via hard thresholding from [ 1 ], this paper proposes an algorithm that improves the breakdown point when facing adaptive adversarial attacks. Furthermore, to improve the robustness and reduce the estimation error caused by the inclusion of a prior, the idea of Bayesian reweighting is used to construct a more robust algorithm. We prove the theoretical convergence of proposed algorithms under mild conditions. Extensive experiments show that, under different dataset attacks, our algorithms achieve state-of-the-art results compared with other benchmark algorithms, demonstrating the robustness of the proposed approach.

Identifying interpretable patterns in multi-electrode recordings is a longstanding and increasingly pressing challenge in neuroscience.

Despite relaxed assumptions, the proposed method possesses proven theoretical guarantees for both detection and localization.

In this paper, we show that distri-butionally robust logistic regression with mixed ( i.e., numerical and categorical) features, despite amounting to an optimization problem of exponential size, admits a polynomial-time solution scheme.

We extend Algorithm 1 to stochastic gradient descent (SGD). Algorithm 3 here modifies Algorithm 1 to allow transformations on both parameters and data. In this section, we derive the group actions for the test functions and multi-layer neural networks. More details about group theory can be found in textbooks such as Lang (2002). B.1 Continuous symmetry in test functions B.1.1 Ellipse Consider the following loss function with a 2 R However, we will only use the 2 variable version in the experiments.

One major concern of AM is the heavier memory overhead compared with the fixed-point iteration.

Language is an important tool for humans to share knowledge.

However, environments are nonstationary in many real-world applications.