Parameter estimation in generalized linear models, such as linear and logistic regression problems, is among the most fundamental and well-studied statistical optimization problems. It serves as the primary workhorse in statistical studies arising from a variety of disciplines, ranging from economics [Smi12], biology [VGSM05], and the social sciences [Gor10].

We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line of research were based on the robust gradient descent framework of [PSBR20], a firstorder method using biased gradient queries, or the Sever framework of [DKK+19], an iterative outlier-removal method calling a stationary point finder. We present nearly-linear time algorithms for robust regression problems with improved runtime or estimation guarantees compared to the state-of-the-art.

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.

Neural networks have shown great predictive power when applied to unstructured data such as images and natural languages.

Semi-Supervised Video Salient Object Detection (SS-VSOD) is challenging because of the lack of temporal information caused by sparse annotations in video sequences. Most works address this problem by generating pseudo labels for unlabeled data. However, error-prone pseudo labels negatively affect the VOSD model. Therefore, a deeper insight into pseudo labels should be developed. In this work, we aim to explore 1) how to utilize the incorrect predictions in pseudo labels to guide the network to generate more robust pseudo labels and 2) how to further screen out the noise that still exists in the improved pseudo labels. To this end, we propose an Uncertainty-Guided Pseudo Label Generator (UGPLG), which makes full use of inter-frame information to ensure the temporal consistency of the pseudo-labels and improves the robustness of the pseudo labels by strengthening the learning of difficult scenarios. Furthermore, we also introduce adversarial learning to address the noise problems in pseudo labels, guaranteeing the positive guidance of pseudo labels during model training. Experimental results demonstrate that our methods outperform existing semi-supervised method and partial fully-supervised methods across five public benchmarks of DAVIS, FBMS, MCL, ViSal, and SegTrack-V2. Code and dataset are available at https://github.com/Lanezzz/UGPL.