Before revision:  Existing approaches mostly focus on constructing calibration maps with low calibration errors . Contrary to these methods, we study post-hoc calibration for multi-class classification under constraints, as a calibrator with a low calibration error does not necessarily mean it is usefulin practice .
After revision:  Existing approaches mostly focus on constructing calibration maps with low calibration errors , however, this quality is inadequate for a calibrator being useful .