Deep neural networks excel in supervised learning tasks but are constrained by the need for extensive labeled data. Self-supervised learning emerges as a promising alternative, allowing models to learn without explicit labels. Information theory has shaped deep neural networks, particularly the information bottleneck principle. This principle optimizes the trade-off between compression and preserving relevant information, providing a foundation for efficient network design in supervised contexts. However, its precise role and adaptation in self-supervised learning remain unclear. In this work, we scrutinize various self-supervised learning approaches from an information-theoretic perspective, introducing a unified framework that encapsulates the self-supervised information-theoretic learning problem. This framework includes multiple encoders and decoders, suggesting that all existing work on self-supervised learning can be seen as specific instances. We aim to unify these approaches to understand their underlying principles better and address the main challenge: many works present different frameworks with differing theories that may seem contradictory. By weaving existing research into a cohesive narrative, we delve into contemporary self-supervised methodologies, spotlight potential research areas, and highlight inherent challenges. Moreover, we discuss how to estimate information-theoretic quantities and their associated empirical problems. Overall, this paper provides a comprehensive review of the intersection of information theory, self-supervised learning, and deep neural networks, aiming for a better understanding through our proposed unified approach.

Medical time series are sequential data collected over time that measures health-related signals, such as electroencephalography (EEG), electrocardiography (ECG), and intensive care unit (ICU) readings. Analyzing medical time series and identifying the latent patterns and trends that lead to uncovering highly valuable insights for enhancing diagnosis, treatment, risk assessment, and disease progression. However, data mining in medical time series is heavily limited by the sample annotation which is time-consuming and labor-intensive, and expert-depending. To mitigate this challenge, the emerging self-supervised contrastive learning, which has shown great success since 2020, is a promising solution. Contrastive learning aims to learn representative embeddings by contrasting positive and negative samples without the requirement for explicit labels. Here, we conducted a systematic review of how contrastive learning alleviates the label scarcity in medical time series based on PRISMA standards. We searched the studies in five scientific databases (IEEE, ACM, Scopus, Google Scholar, and PubMed) and retrieved 1908 papers based on the inclusion criteria. After applying excluding criteria, and screening at title, abstract, and full text levels, we carefully reviewed 43 papers in this area. Specifically, this paper outlines the pipeline of contrastive learning, including pre-training, fine-tuning, and testing. We provide a comprehensive summary of the various augmentations applied to medical time series data, the architectures of pre-training encoders, the types of fine-tuning classifiers and clusters, and the popular contrastive loss functions. Moreover, we present an overview of the different data types used in medical time series, highlight the medical applications of interest, and provide a comprehensive table of 51 public datasets that have been utilized in this field. In addition, this paper will provide a discussion on the promising future scopes such as providing guidance for effective augmentation design, developing a unified framework for analyzing hierarchical time series, and investigating methods for processing multimodal data. Despite being in its early stages, self-supervised contrastive learning has shown great potential in overcoming the need for expert-created annotations in the research of medical time series.