Internet-enabled physical devices with “smart” processing capabilities are becoming the tools for understanding the complexity of the global inter-connected world we inhabit. The Internet of Things (IoT) churns tremendous amounts of data flooding from devices scattered across multiple locations to the processing engines of almost all industry sectors. However, as the number of “things” surpasses the population of the technology-enabled world, real-time processing and energy-efficiency are great challenges of the big data era transitioning to IoT. In this article, we introduce a lightweight adaptive monitoring framework suitable for smart IoT devices with limited processing capabilities. Our framework, inexpensively and in place dynamically adjusts the monitoring intensity and the amount of data disseminated through the network based on a low-cost adaptive and probabilistic learning model capable of capturing at runtime the current evolution and variability of the data stream. By accomplishing this, energy consumption and data volume are reduced, allowing IoT devices to preserve battery and ease processing on cloud computing and streaming services. Experiments on real-world data from cloud services, internet security services, wearables and intelligent transportation services, show that our framework achieves a balance between efficiency and accuracy. Specifically, our framework reduces data volume by 74 percent, energy consumption by at least 71 percent, while maintaining accuracy always above 89 percent.