Performance Evaluation of Few-shot Learning-based System Identification

This paper proposes a performance evaluation method for few-shot learning-based system identification. The basic idea behind the proposed approach is to use ``probably approximately correct (PAC)'' to assess the obtained boundary of identification errors. The study demonstrates effectiveness of the proposed solution when the noise is not white and there are only limited data samples for the identification in practical applications. The contributions of this study include: 1) modeling errors are quantified via the $L_\infty$ norm; 2) the bounded noises are considered; 3) it is shown that both the modeling and prediction errors can be reduced by increasing the size of training data. Rigorous mathematical analysis and a case study demonstrate the effectiveness of the proposed performance evaluation strategy.