A method for solving concept-based learning (CBL) problem is proposed. The
main idea behind the method is to divide each concept-annotated image into
patches, to transform the patches into embeddings by using an autoencoder, and
to cluster the embeddings assuming that each cluster will mainly contain
embeddings of patches with certain concepts. To find concepts of a new image,
the method implements the frequentist inference by computing prior and
posterior probabilities of concepts based on rates of patches from images with
certain values of the concepts. Therefore, the proposed method is called the
Frequentist Inference CBL (FI-CBL). FI-CBL allows us to incorporate the expert
rules in the form of logic functions into the inference procedure. An idea
behind the incorporation is to update prior and conditional probabilities of
concepts to satisfy the rules. The method is transparent because it has an
explicit sequence of probabilistic calculations and a clear frequency
interpretation. Numerical experiments show that FI-CBL outperforms the concept
bottleneck model in cases when the number of training data is small. The code
of proposed algorithms is publicly available.

提出一种解决基于概念学习（CBL）问题的方法，该方法通过将每个概念标注图像划分为补丁，并使用自编码器将这些补丁转换为嵌入向量，然后假设每个聚类主要包含具有特定概念的补丁的嵌入向量，通过计算具有特定概念的图像的补丁比率，计算先验概率和后验概率以推断新图像的概念，从而结合专家规则以适应先验和条件概率，并且该方法透明，具有明确的概率计算序列和清晰的频率解释，数值实验表明在训练数据较少时，FI-CBL 的性能优于概念瓶颈模型。