以樹為基礎的方法之精神在於學習規則，有很多的機器學習演算法皆以樹為 基礎，一些較複雜的樹學習器可能提供更高準確的預測模型，卻也犧牲了模型的解 釋性。表徵學習的精神在於從表面的資料中萃取抽象的概念，深度神經網路是最熱 門的表徵學習方法，然而，不可究責的表徵學習特性一直以來是深度神經網路的缺 點。在本篇論文中，我們提出了一種方法名為深度規則森林，能夠在層疊結構中藉 由隨機森林學習區域的表徵，學習到的區域表徵能夠搭配其他機器學習演算法，我 們以深度規則森林習得的區域表徵來訓練 CART 決策樹，並發現預測率有時甚至 會高於整體學習的方法。

The spirit of tree-based methods is to learn rules. A large number of machine learning techniques are tree-based. More complicated tree learners may result in higher predictive models, but may sacrifice for model interpretability. On the other hand, the spirit of representation learning is to extract abstractive concepts from manifestations of the data.
For instance, Deep Neural networks (DNNs) is the most popular method in representation learning. However, unaccountable feature representation is the shortcoming of DNNs. In this paper, we proposed an approach, Deep Rule Forest (DRF), to learn region representations based on random forest in the deep layer-wise structures. The learned interpretable rules region representations combine other machine learning algorithms. We trained CART which learned from DRF region representations, and found that the prediction accuracies sometime are better than ensemble learning methods.

[論文審定書+i]
[中文摘要+ii]
[Abstract+iii]
[Table of content+iv]
[1. Introduction+1]
[2. Background Review+3]
[2.1. Tree-based methods+3]
[2.2. Representation learning+9]
[2.3. Forward thinking+11]
[2.4. Explainable A+14]
[2.5. Information processing+15]
[3. Building Deep Rule Forest+19]
[3.1. Forward forest structur+19]
[3.2. Growing stage and pruning stage+22]
[3.3. Interpretabilit+24]
[3.4. Hyper-parameters+26]
[4.Experiment+28]
[4.1. Prediction accuracy+30]
[4.2. Information bottleneck principle+31]
[4.3. Influence of hyper-parameters+34]
[4.4. Backtracking rules+38]
[5. Conclusion+43]
[6. Reference+45]
[7. Appendix A+48]

Bengio, Y. (2009). Learning deep architectures for AI. Foundations and Trends® in Machine Learning, 2(1), 1–127.
Bengio, Y., Courville, A., & Vincent, P. (2012). Representation Learning: A Review and New Perspectives. ArXiv:1206.5538 [Cs]. Retrieved from http://arxiv.org/abs/1206.5538
Bolton, A., Huang, A., Guez, A., Silver, D., Hassabis, D., Hui, F., … Chen, Y. (2017). Mastering the game of Go without human knowledge. Nature, 550(7676), 354. https://doi.org/10.1038/nature24270
Breiman, L. (1996). Bagging predictors. Machine Learning, 24(2), 123–140. https://doi.org/10.1007/BF00058655
Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
Breiman, L., Friedman, J., Stone, C. J., & Olshen, R. A. (1984). Classification and Regression Trees. Taylor & Francis.
Chen, T., & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. In Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 785–794). New York, NY, USA: ACM. https://doi.org/10.1145/2939672.2939785
Chen, T., He, T., & Benesty, M. (2015). Xgboost: extreme gradient boosting. R Package Version 0.4-2, 1–4.
Cover, T. M., & Thomas, J. A. (2012). Elements of information theory. John Wiley & Sons.
Dietterich, T. G. (2002). Ensemble learning. The Handbook of Brain Theory and Neural Networks, 2, 110–125.
Freund, Y., Schapire, R., & Abe, N. (1999). A short introduction to boosting. Journal-Japanese Society For Artificial Intelligence, 14(771–780), 1612.
Fürnkranz, J., Gamberger, D., & Lavrač, N. (2012). Foundations of rule learning. Springer Science & Business Media.
Goodman, B., & Flaxman, S. (2016). European Union regulations on algorithmic decision-making and a" right to explanation". ArXiv Preprint ArXiv:1606.08813.
Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006). A fast learning algorithm for deep belief nets. Neural Computation, 18(7), 1527–1554.
Hyvärinen, A., Karhunen, J., & Oja, E. (2004). Independent component analysis (Vol. 46). John Wiley & Sons.
Kohavi, R., John, G., Long, R., Manley, D., & Pfleger, K. (1994). MLC++: A machine learning library in C++. In Proceedings Sixth International Conference on Tools with Artificial Intelligence. TAI 94 (pp. 740–743). IEEE.
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2012). ImageNet Classification with Deep Convolutional Neural Networks. In F. Pereira, C. J. C. Burges, L. Bottou, & K. Q. Weinberger (Eds.), Advances in Neural Information Processing Systems 25 (pp. 1097–1105). Curran Associates, Inc. Retrieved from http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf
Kuhn, M., Weston, S., Coulter, N., & Quinlan, R. (2014). C50: C5. 0 decision trees and rule-based models. R Package Version 0.1. 0-21, URL Http://CRAN. R-Project. Org/Package C, 50.
LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436.
Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755), 788.
Lending Club Statistics | LendingClub. (n.d.). Retrieved July 17, 2018, from https://www.lendingclub.com/info/download-data.action
Liaw, A., & Wiener, M. (2002). Classification and regression by randomForest. R News, 2(3), 18–22.
Lichman, M. (2013). UCI Machine Learning Repository. Retrieved November 22, 2017, from https://archive.ics.uci.edu/ml/index.php
Lipton, Z. C. (2016). The mythos of model interpretability. ArXiv Preprint ArXiv:1606.03490.
Miller, K., Hettinger, C., Humpherys, J., Jarvis, T., & Kartchner, D. (2017). Forward Thinking: Building Deep Random Forests. ArXiv:1705.07366 [Cs, Stat]. Retrieved from http://arxiv.org/abs/1705.07366
Quinlan, J. R. (1986). Induction of decision trees. Machine Learning, 1(1), 81–106. https://doi.org/10.1007/BF00116251
Quinlan, J. Ross. (2014). C4. 5: programs for machine learning. Elsevier.
Ribeiro, M. T., Singh, S., & Guestrin, C. (2016). “Why Should I Trust You?”: Explaining the Predictions of Any Classifier. ArXiv:1602.04938 [Cs, Stat]. Retrieved from http://arxiv.org/abs/1602.04938
Samek, W., Wiegand, T., & Müller, K.-R. (2017). Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models. ArXiv:1708.08296 [Cs, Stat]. Retrieved from http://arxiv.org/abs/1708.08296
Schapire, R. E. (2013). Explaining AdaBoost. In Empirical Inference (pp. 37–52). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41136-6_5
Su, G., Wei, D., Varshney, K. R., & Malioutov, D. M. (2016). Interpretable Two-level Boolean Rule Learning for Classification. ArXiv:1606.05798 [Cs, Stat]. Retrieved from http://arxiv.org/abs/1606.05798
Therneau, T., Atkinson, B., & Ripley, B. (2015). rpart: Recursive Partitioning and Regression Trees. R package version 4.1–10.
Tishby, N., & Zaslavsky, N. (2015). Deep learning and the information bottleneck principle. In Information Theory Workshop (ITW), 2015 IEEE (pp. 1–5). IEEE.
Wold, S., Esbensen, K., & Geladi, P. (1987). Principal component analysis. Chemometrics and Intelligent Laboratory Systems, 2(1–3), 37–52.
Wright, M. N., & Ziegler, A. (2015). Ranger: a fast implementation of random forests for high dimensional data in C++ and R. ArXiv Preprint ArXiv:1508.04409.
Zhou, Z.-H., & Feng, J. (2017). Deep Forest: Towards An Alternative to Deep Neural Networks. ArXiv:1702.08835 [Cs, Stat]. Retrieved from http://arxiv.org/abs/1702.08835