How to obtain a model with good interpretability and performance has always been an important research topic. In this paper, we propose rectified decision trees (ReDT), a knowledge distillation based decision trees rectification with high interpretability, small model size, and empirical soundness. Specifically, we extend the impurity calculation and the pure ending condition of the classical decision tree to propose a decision tree extension that allows the use of soft labels generated by a well-trained teacher model in training and prediction process. It is worth noting that for the acquisition of soft labels, we propose a new multiple cross-validation based method to reduce the effects of randomness and overfitting. These approaches ensure that ReDT retains excellent interpretability and even achieves fewer nodes than the decision tree in the aspect of compression while having relatively good performance. Besides, in contrast to traditional knowledge distillation, back propagation of the student model is not necessarily required in ReDT, which is an attempt of a new knowledge distillation approach. Extensive experiments are conducted, which demonstrates the superiority of ReDT in interpretability, compression, and empirical soundness.
The interpretability of complex machine learning models, especially ensemble approaches and deep learning, has been widely concerned. At present, the most widely used machine learning models are mainly forest-based algorithms and DNN, so their interpretability is of great significance. There are a few previous studies on the interpretability of forest-based algorithms. The first work is done by Breiman @cite_15 , who propose to use tree ensemble to generate additional samples for the further construction of a single decision tree. In @cite_29 , Node harvest is proposed to simplify tree ensembles by using the shallow parts of the trees. Considering the simplification of tree ensembles as a model selection problem, and using the Bayesian method for selection is also proposed in @cite_16 . The interpretability research of DNN mainly on three aspects: visualizing the representations in intermediate layers of DNN @cite_31 @cite_6 , representation diagnosis @cite_24 @cite_30 and build explainable DNNs @cite_18 @cite_21 . Recently, a knowledge distillation based method is provided, which uses a trained DNN to create a more explainable model in the form of soft decision trees @cite_11 .
@cite_30 @cite_31 @cite_18 @cite_29 @cite_21 @cite_6 @cite_24 @cite_15 @cite_16 @cite_11
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We study resource-limited online learning, motivated by the problem of conditional-branch outcome prediction in computer architecture. In particular, we consider (parallel) time and space-efficient ensemble learners for online settings, empirically demonstrating benefits similar to those shown previously for offline ensembles. Our learning algorithms are inspired by the previously published “boosting by filtering” framework as well as the offline Arc-x4 boosting-style algorithm. We train ensembles of online decision trees using a novel variant of the ID4 online decision-tree algorithm as the base learner, and show empirical results for both boosting and bagging-style online ensemble methods. Our results evaluate these methods on both our branch prediction domain and online variants of three familiar machine-learning benchmarks. Our data justifies three key claims. First, we show empirically that our extensions to ID4 significantly improve performance for single trees and additionally are critical to achieving performance gains in tree ensembles. Second, our results indicate significant improvements in predictive accuracy with ensemble size for the boosting-style algorithm. The bagging algorithms we tried showed poor performance relative to the boosting-style algorithm (but still improve upon individual base learners). Third, we show that ensembles of small trees are often able to outperform large single trees with the same number of nodes (and similarly outperform smaller ensembles of larger trees that use the same total number of nodes). This makes online boosting particularly useful in domains such as branch prediction with tight space restrictions (i.e., the available real-estate on a microprocessor chip). We present Deep Neural Decision Forests - a novel approach that unifies classification trees with the representation learning functionality known from deep convolutional networks, by training them in an end-to-end manner. To combine these two worlds, we introduce a stochastic and differentiable decision tree model, which steers the representation learning usually conducted in the initial layers of a (deep) convolutional network. Our model differs from conventional deep networks because a decision forest provides the final predictions and it differs from conventional decision forests since we propose a principled, joint and global optimization of split and leaf node parameters. We show experimental results on benchmark machine learning datasets like MNIST and ImageNet and find on-par or superior results when compared to state-of-the-art deep models. Most remarkably, we obtain Top5-Errors of only 7.84 6.38 on ImageNet validation data when integrating our forests in a single-crop, single seven model GoogLeNet architecture, respectively. Thus, even without any form of training data set augmentation we are improving on the 6.67 error obtained by the best GoogLeNet architecture (7 models, 144 crops). Breiman (2001a,b) has recently developed an ensemble classification and regression approach that displayed outstanding performance with regard prediction error on a suite of benchmark datasets. As the base constituents of the ensemble are tree-structured predictors, and since each of these is constructed using an injection of randomness, the method is called ‘random forests’. That the exceptional performance is attained with seemingly only a single tuning parameter, to which sensitivity is minimal, makes the methodology all the more remarkable. The individual trees comprising the forest are all grown to maximal depth. While this helps with regard bias, there is the familiar tradeoff with variance. However, these variability concerns were potentially obscured because of an interesting feature of those benchmarking datasets extracted from the UCI machine learning repository for testing: all these datasets are hard to overfit using tree-structured methods. This raises issues about the scope of the repository. With this as motivation, and coupled with experience from boosting methods, we revisit the formulation of random forests and investigate prediction performance on real-world and simulated datasets for which maximally sized trees do overfit. These explorations reveal that gains can be realized by additional tuning to regulate tree size via limiting the number of splits and or the size of nodes for which splitting is allowed. Nonetheless, even in these settings, good performance for random forests can be attained by using larger (than default) primary tuning parameter values. This paper explores the use of knowledge distillation to improve a Multi-Task Deep Neural Network (MT-DNN) (, 2019) for learning text representations across multiple natural language understanding tasks. Although ensemble learning can improve model performance, serving an ensemble of large DNNs such as MT-DNN can be prohibitively expensive. Here we apply the knowledge distillation method (, 2015) in the multi-task learning setting. For each task, we train an ensemble of different MT-DNNs (teacher) that outperforms any single model, and then train a single MT-DNN (student) via multi-task learning to knowledge from these ensemble teachers. We show that the distilled MT-DNN significantly outperforms the original MT-DNN on 7 out of 9 GLUE tasks, pushing the GLUE benchmark (single model) to 83.7 (1.5 absolute improvement Based on the GLUE leaderboard at this https URL as of April 1, 2019. ). The code and pre-trained models will be made publicly available at this https URL.