Event cameras are neuromorphic vision sensors that asynchronously capture pixellevel intensity changes with high temporal resolution and dynamic range. These make them well suited for monocular depth estimation under challenging lighting conditions. However, progress in event-based monocular depth estimation remains constrained by the quality of supervision: LiDAR-based depth labels are inherently sparse, spatially incomplete, and prone to artifacts. Consequently, these signals are suboptimal for learning dense depth from sparse events. To address this problem, we propose Distil-E2D, a framework that distills depth priors from the image domain into the event domain by generating dense synthetic pseudolabels from co-recorded APS or RGB frames using foundational depth models. These pseudolabels complement sparse LiDAR depths with dense semantically rich supervision informed by large-scale image-depth datasets. To reconcile discrepancies between synthetic and real depths, we introduce a Confidence-Guided Calibrated Depth Loss that learns nonlinear depth alignment and adaptively weights supervision by alignment confidence. Additionally, our architecture integrates past predictions via a Context Transformer and employs a Dual-Decoder Training scheme that enhances encoder representations by jointly learning metric and relative depth abstractions. Experiments on benchmark datasets show that Distil-E2D achieves state-of-the-art performance in event-based monocular depth estimation across both event-only and event+APS settings.

In the adversarial training framework of Carmon et al. (2019); Gowal et al. (2021), people use generated/real unlabeled data with pseudolabels to improve adversarial robustness. We provide statistical insights to explain why the artificially generated data improve adversarial training. In particular, we study how the attack strength and the quality of the unlabeled data affect adversarial robustness in this framework. Our results show that with a high-quality unlabeled data generator, adversarial training can benefit greatly from this framework under large attack strength, while a poor generator can still help to some extent. To make adaptions concerning the quality of generated data, we propose an algorithm that performs online adjustment to the weight between the labeled real data and the generated data, aiming to optimize the adversarial risk. Numerical studies are conducted to verify our theories and show the effectiveness of the proposed algorithm.

For labels taking values in a finite metric space, we introduce techniques new to weak supervision based on pseudo-Euclidean embeddings andtensor decompositions, providing anearly-consistent noise rate estimator.

For labels taking values in a finite metric space, we introduce techniques new to weak supervision based on pseudo-Euclidean embeddings andtensor decompositions, providing anearly-consistent noise rate estimator.

Weak supervision (WS) is a rich set of techniques that produce pseudolabels by aggregating easily obtained but potentially noisy label estimates from various sources. WS is theoretically well-understood for binary classification, where simple approaches enable consistent estimation of pseudolabel noise rates. Using this result, it has been shown that downstream models trained on the pseudolabels have generalization guarantees nearly identical to those trained on clean labels. While this is exciting, users often wish to use WS for \emph{structured prediction}, where the output space consists of more than a binary or multi-class label set: e.g.