Embodied AI strives to create agents capable of learning and tackling complex tasks involving physical interactions, with potential applications in many areas, such as housekeeping, caregiving, and logistics. Such agents must be able to perceive their environment, construct scene representations, and carry out reasoning and actions to accomplish task-specific goals. However, existing learning approaches rely on human annotations or unrealistic simulations, leading to generalization problems in the real world. Thus, it is crucial to equip embodied agents with the ability to autonomously learn from real-world data, minimizing reliance on human supervision and enabling adaptability to new tasks. We propose that the key to autonomous learning of embodied agents is the mutual correlations in the unlabeled data. In this presentation, we will talk about how we can efficiently compute mutual correlations of data by developing novel neural estimators. We will also show how these freely available mutual correlations can help reduce human annotation effort in learning label-efficient perception, scene representation, and grounded concepts for generalizable interaction policies. We hope leveraging mutual correlations in the unlabeled data will empower embodied agents to learn in unseen environments and automatically acquire novel interaction skills.