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The vision of pervasive machine learning (ML) services can be realized by training an ML model on time using real-time data collected by internet of things (IoT) devices. To this end, IoT devices require offloading their data to an edge server in proximity. On the other hand, high dimensional data with a heavy volume causes a significant burden to an IoT device with a limited energy budget. To cope with the limitation, we propose a novel offloading architecture, called joint data deepening and prefetching (JD2P), which is feature-by-feature offloading comprising two key techniques. The first one is data deepening, where each data sample's features are sequentially offloaded in the order of importance determined by the data embedding technique such as principle component analysis (PCA). No more features are offloaded when the features offloaded so far are enough to classify the data, resulting in reducing the amount of offloaded data. The second one is data prefetching, where some features potentially required in the future are offloaded in advance, thus achieving high efficiency via precise prediction and parameter optimization. To verify the effectiveness of JD2P, we conduct experiments using the MNIST and fashion-MNIST dataset. Experimental results demonstrate that the JD2P can significantly reduce the expected energy consumption compared with several benchmarks without degrading learning accuracy.