Internet of Medical Things (IoMT) is igniting many emerging smart health applications, by continuously streaming the big data for data-driven innovations. One critical obstacle in IoMT big data is the power hungriness of long-term data transmission. Targeting this challenge, we propose a novel framework called, IoMT big-data Bayesian-backward deep-encoder learning (IBBD), which mines deep autoencoder (AE) configurations for data sparsification and determines optimal tradeoffs between information loss and power overhead. More specifically, the IBBD framework leverages an additional external Bayesian-backward loop that recommends AE configurations, on top of a traditional deep learning loop that executes and evaluate the AE quality. The IBBD recommendation is based on confidence to further minimize the regularized metrics that quantify the quality of AE configurations, and it further leverages regularization techniques to allow adjusting error–power tradeoffs in the mining process. We have conducted thorough experiments on a cardiac data streaming application and demonstrated the superiority of IBBD over the common practices such as discrete wavelet transform, and we have further generalized IBBD through validating the optimal AE configurations determined on one user to other users. This study is expected to greatly advance IoMT big data streaming practices toward precision medicine.