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This paper proposes PickNet, a neural network model for real-time channel selection for an ad hoc microphone array consisting of multiple recording devices like cell phones. Assuming at most one person to be vocally active at each time point, PickNet identifies the device that is spatially closest to the active person for each time frame by using a short spectral patch of just hundreds of milliseconds. The model is applied to every time frame, and the short time frame signals from the selected microphones are concatenated across the frames to produce an output signal. As the personal devices are usually held close to their owners, the output signal is expected to have higher signal-to-noise and direct-to-reverberation ratios on average than the input signals. Since PickNet utilizes only limited acoustic context at each time frame, the system using the proposed model works in real time and is robust to changes in acoustic conditions. Speech recognition-based evaluation was carried out by using real conversational recordings obtained with various smartphones. The proposed model yielded significant gains in word error rate with limited computational cost over systems using a block-online beamformer and a single distant microphone.