Rethinking Weak Supervision in Helping Contrastive Learning

Contrastive learning has shown outstanding performances in both supervised and unsupervised learning, and has recently been introduced to solve weakly supervised learning problems such as semi-supervised learning and noisy label learning. Despite the empirical evidence showing that semi-supervised labels improve the representations of contrastive learning, it remains unknown if noisy supervised information can be directly used in training instead of after manual denoising. Therefore, to explore the mechanical differences between semi-supervised and noisy-labeled information in helping contrastive learning, we establish a unified theoretical framework of contrastive learning under weak supervision. Specifically, we investigate the most intuitive paradigm of jointly training supervised and unsupervised contrastive losses. By translating the weakly supervised information into a similarity graph under the framework of spectral clustering based on the posterior probability of weak labels, we establish the downstream classification error bound. We prove that semi-supervised labels improve the downstream error bound whereas noisy labels have limited effects under such a paradigm. Our theoretical findings here provide new insights for the community to rethink the role of weak supervision in helping contrastive learning.

GBHT: Gradient Boosting Histogram Transform for Density Estimation

In this paper, we propose a density estimation algorithm called \textit{Gradient Boosting Histogram Transform} (GBHT), where we adopt the \textit{Negative Log Likelihood} as the loss function to make the boosting procedure available for the unsupervised tasks. From a learning theory viewpoint, we first prove fast convergence rates for GBHT with the smoothness assumption that the underlying density function lies in the space $C^{0,\alpha}$. Then when the target density function lies in spaces $C^{1,\alpha}$, we present an upper bound for GBHT which is smaller than the lower bound of its corresponding base learner, in the sense of convergence rates. To the best of our knowledge, we make the first attempt to theoretically explain why boosting can enhance the performance of its base learners for density estimation problems. In experiments, we not only conduct performance comparisons with the widely used KDE, but also apply GBHT to anomaly detection to showcase a further application of GBHT.

Leveraged Weighted Loss for Partial Label Learning

As an important branch of weakly supervised learning, partial label learning deals with data where each instance is assigned with a set of candidate labels, whereas only one of them is true. Despite many methodology studies on learning from partial labels, there still lacks theoretical understandings of their risk consistent properties under relatively weak assumptions, especially on the link between theoretical results and the empirical choice of parameters. In this paper, we propose a family of loss functions named \textit{Leveraged Weighted} (LW) loss, which for the first time introduces the leverage parameter $\beta$ to consider the trade-off between losses on partial labels and non-partial ones. From the theoretical side, we derive a generalized result of risk consistency for the LW loss in learning from partial labels, based on which we provide guidance to the choice of the leverage parameter $\beta$. In experiments, we verify the theoretical guidance, and show the high effectiveness of our proposed LW loss on both benchmark and real datasets compared with other state-of-the-art partial label learning algorithms.