In this paper we introduce the DMR -- a prototype-based method and network
architecture for deep learning which is using a decision tree (DT)-based
inference and synthetic data to balance the classes. It builds upon the
recently introduced xDNN method addressing more complex multi-class problems,
specifically when classes are highly imbalanced. DMR moves away from a direct
decision based on all classes towards a layered DT of pair-wise class
comparisons. In addition, it forces the prototypes to be balanced between
classes regardless of possible class imbalances of the training data. It has
two novel mechanisms, namely i) using a DT to determine the winning class
label, and ii) balancing the classes by synthesizing data around the prototypes
determined from the available training data. As a result, we improved
significantly the performance of the resulting fully explainable DNN as
evidenced by the best reported result on the well know benchmark problem
Caltech-101 surpassing our own recently published "world record". Furthermore,
we also achieved another "world record" for another very hard benchmark
problem, namely Caltech-256 as well as surpassed the results of other
approaches on Faces-1999 problem. In summary, we propose a new approach
specifically advantageous for imbalanced multi-class problems that achieved two
world records on well known hard benchmark problems and the best result on
another problem in terms of accuracy. Moreover, DMR offers full explainability,
does not require GPUs and can continue to learn from new data by adding new
prototypes preserving the previous ones but not requiring full retraining.

提出使用基于决策树的推理和合成数据来平衡分类，具有可完整解释且不需要使用 GPU 的 DMR 原型方法和网络架构，可以有效解决多类别问题中类别不平衡的问题，并在多个基准测试问题的测试中获得最佳表现和两个世界纪录。

朝向深度机器推理：基于原型的深度神经网络与决策树推理

Towards Deep Machine Reasoning: a Prototype-based Deep Neural Network  with Decision Tree Inference

In the last few years, many different performance measures have been
introduced to overcome the weakness of the most natural metric, the Accuracy.
Among them, Matthews Correlation Coefficient has recently gained popularity
among researchers not only in machine learning but also in several application
fields such as bioinformatics. Nonetheless, further novel functions are being
proposed in literature. We show that Confusion Entropy, a recently introduced
classifier performance measure for multi-class problems, has a strong
(monotone) relation with the multi-class generalization of a classical metric,
the Matthews Correlation Coefficient. Computational evidence in support of the
claim is provided, together with an outline of the theoretical explanation.

本文研究了一种针对多类问题的分类器性能度量 Confusion Entropy 与传统度量 Matthews Correlation Coefficient 的多分类推广之间的关系，并通过理论和计算证据支持了这一结果。