Abstract
For human centered future society, artificial intelligence (AI) has been desired in many fields.Since we need responsibility of information systems using AI, in particular, car driving or medical systems,explanation methods have been proposed for machine learning models.Concept Bottleneck Model (CBM) is one of methods to make neural networks explainable.In CBM, concepts which correspond to reasons of outputs are inserted in the last intermediate layer as observed values.It is expected that we can interpret the relation between the output and the concept like linear regression.However, it requires observation for all concepts and decrease generalization performance of neural networks.Partial CBM (PCBM) has been devised for resolving these difficulty.It uses partially-observed concepts.While some numerical experiments demonstrate that the generalization performance of PCBMs is almost as high as that of original neural networks,theoretical behavior of its generalization error has not been yet clarified since PCBM is singular statistical model.In this paper, we reveal the Bayesian generalization error in PCBM whose architecture is three-layered and linear.The result shows that the structure of partially-observed concepts makes decrease the Bayesian generalization error compared with CBM (full-obsereved concepts).
