The primary challenge of multi-label active learning, differing it from multi-class active learning, lies in assessing the informativeness of an indefinite number of labels while also accounting for the inherited label correlation. Existing studies either require substantial computational resources to leverage correlations or fail to fully explore label dependencies. Additionally, real-world scenarios often require addressing intrinsic biases stemming from imbalanced data distributions. In this paper, we propose a new multi-label active learning strategy to address both challenges. Our method incorporates progressively updated positive and negative correlation matrices to capture co-occurrence and disjoint relationships within the label space of annotated samples, enabling a holistic assessment of uncertainty rather than treating labels as isolated elements. Furthermore, alongside diversity, our model employs ensemble pseudo labeling and beta scoring rules to address data imbalances. Extensive experiments on four realistic datasets demonstrate that our strategy consistently achieves more reliable and superior performance, compared to several established methods.