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Low-power sensing technologies have emerged for acquiring physiologically indicative patient signals. However, to enable devices with high clinical value, a critical requirement is the ability to analyze the signals to extract specific medical information. Yet given the complexities of the underlying processes, signal analysis poses numerous challenges. Data-driven methods based on machine learning offer distinct solutions, but unfortunately the computations are not well supported by traditional DSP. This paper presents a custom processor that integrates a CPU with configurable accelerators for discriminative machine-learning functions. A support-vector-machine accelerator realizes various classification algorithms as well as various kernel functions and kernel formulations, enabling range of points within an accuracy-versus-energy and -memory trade space. An accelerator for embedded active learning enables prospective adaptation of the signal models by utilizing sensed data for patient-specific customization, while minimizing the effort from human experts. The prototype is implemented in 130-nm CMOS and operates from 1.2 V-0.55 V (0.7 V for SRAMs). Medical applications for EEG-based seizure detection and ECG-based cardiac-arrhythmia detection are demonstrated using clinical data, while consuming 273 μJ and 124 μJ per detection, respectively; this represents 62.4× and 144.7× energy reduction compared to an implementation based on the CPU. A patient-adaptive cardiac-arrhythmia detector is also demonstrated, reducing the analysis-effort required for model customization by 20 ×.