A theory for the risk bound of myoelectric control with adaptive learning

In order to overcome the performance degradation of long-term myoelectric pattern recognition, many studies introduced adaptive learning methods, which track the concept drift to reduce the potential misclassification risk (MR). Different from phenomenological analysis, for the first time, this paper intends to analytically model the learning process of adaptive learners with delayed and incomplete supervised information (noted as realistic adaptive learners, RAL). With theoretical analysis, we (1) proved that the MR upper bound of the RAL increases but converges to its limitation along with the time; (2) proved that for continuous concept drift, we can lower down the expected MR by improving the updating frequency; (3) predicted on what time the adaptive learner would exceed a given warning value of the expected risk; (4) designed a measure p, which determines the shape of the change curve and the limitation of the risk bound, to compare different adaptive learners. We also designed a method to estimate p without cumbersome long-term data. Based on realistic myoelectric data, we evaluated the performance of various learners with different p values and the inversely estimated results of p from the performance. The results showed the existence of the MR bound limitation of the RAL, as well as the great linearity (R-squared value of 0.941) of the estimation for p.