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。

FI-CBL：一种基于专家规则的概率概念学习方法

FI-CBL: A Probabilistic Method for Concept-Based Learning with Expert  Rules

Concept Bottleneck Model (CBM) is a methods for explaining neural networks.
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 relationship between the output and concept similar to linear
regression. However, this interpretation requires observing all concepts and
decreases the generalization performance of neural networks. Partial CBM
(PCBM), which uses partially observed concepts, has been devised to resolve
these difficulties. Although some numerical experiments suggest that the
generalization performance of PCBMs is almost as high as that of the original
neural networks, the 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 with a three-layered and
linear architecture. The result indcates that the structure of partially
observed concepts decreases the Bayesian generalization error compared with
that of CBM (full-observed concepts).

Concept Bottleneck Model (CBM) methods for explaining neural networks have been improved upon with the introduction of Partial CBM (PCBM), which uses partially observed concepts and shows promising generalization performance, as revealed in this study through Bayesian analysis.

贝叶斯泛化误差的上界在局部概念瓶颈模型中：局部瓶颈模型胜过朴素瓶颈模型

Upper Bound of Bayesian Generalization Error in Partial Concept  Bottleneck Model (CBM): Partial CBM outperforms naive CBM

With the increasing demands for accountability, interpretability is becoming
an essential capability for real-world AI applications. However, most methods
utilize post-hoc approaches rather than training the interpretable model. In
this article, we propose a novel interpretable model based on the concept
bottleneck model (CBM). CBM uses concept labels to train an intermediate layer
as the additional visible layer. However, because the number of concept labels
restricts the dimension of this layer, it is difficult to obtain high accuracy
with a small number of labels. To address this issue, we integrate supervised
concepts with unsupervised ones trained with self-explaining neural networks
(SENNs). By seamlessly training these two types of concepts while reducing the
amount of computation, we can obtain both supervised and unsupervised concepts
simultaneously, even for large-sized images. We refer to the proposed model as
the concept bottleneck model with additional unsupervised concepts (CBM-AUC).
We experimentally confirmed that the proposed model outperformed CBM and SENN.
We also visualized the saliency map of each concept and confirmed that it was
consistent with the semantic meanings.

本文提出了一种基于概念瓶颈模型的新型可解释模型，集成了监督和无监督概念，减少了计算量，同时取得了比 CBM 和 SENN 更优异的实验效果，并可视化每个概念的显著性图，符合语义意义。