Neural networks (NNs) and decision trees (DTs) are both popular models of machine learning, yet coming with mutually exclusive advantages and limitations. To bring the best of the two worlds, a variety of approaches are proposed to integrate NNs and DTs explicitly or implicitly. In this survey, these approaches are organized in a school which we term as neural trees (NTs). This survey aims to present a comprehensive review of NTs and attempts to identify how they enhance the model interpretability. We first propose a thorough taxonomy of NTs that expresses the gradual integration and co-evolution of NNs and DTs. Afterward, we analyze NTs in terms of their interpretability and performance, and suggest possible solutions to the remaining challenges. Finally, this survey concludes with a discussion about other considerations like conditional computation and promising directions towards this field. A list of papers reviewed in this survey, along with their corresponding codes, is available at: https://github.com/zju-vipa/awesome-neural-trees
In this study we worked on the classification of the Chess Endgame problem using different algorithms like logistic regression, decision trees and neural networks. Our experiments indicates that the Neural Networks provides the best accuracy (85%) then the decision trees (79%). We did these experiments using Microsoft Azure Machine Learning as a case-study on using Visual Programming in classification. Our experiments demonstrates that this tool is powerful and save a lot of time, also it could be improved with more features that increase the usability and reduce the learning curve. We also de…
Program translation is an important tool to migrate legacy code in one language into an ecosystem built in a different language. In this work, we are the first to employ deep neural networks toward tackling this problem. We observe that program translation is a modular procedure, in which a sub-tree of the source tree is translated into the corresponding target sub-tree at each step. To capture this intuition, we design a tree-to-tree neural network to translate a source tree into a target one. Meanwhile, we develop an attention mechanism for the tree-to-tree model, so that when the decoder ex…
The paper surveys recent extensions of the Long-Short Term Memory networks to handle tree structures from the perspective of learning non-trivial forms of isomorph structured transductions. It provides a discussion of modern TreeLSTM models, showing the effect of the bias induced by the direction of tree processing. An empirical analysis is performed on real-world benchmarks, highlighting how there is no single model adequate to effectively approach all transduction problems.
We present a self-learning approach that combines deep reinforcement learning and Monte Carlo tree search to solve the traveling salesman problem. The proposed approach has two advantages. First, it adopts deep reinforcement learning to compute the value functions for decision, which removes the need of hand-crafted features and labelled data. Second, it uses Monte Carlo tree search to select the best policy by comparing different value functions, which increases its generalization ability. Experimental results show that the proposed method performs favorably against other methods in small-to-…
High-dimensional policies, such as those represented by neural networks, cannot be reasonably interpreted by humans. This lack of interpretability reduces the trust users have in policy behavior, limiting their use to low-impact tasks such as video games. Unfortunately, many methods rely on neural network representations for effective learning. In this work, we propose a method to build predictable policy trees as surrogates for policies such as neural networks. The policy trees are easily human interpretable and provide quantitative predictions of future behavior. We demonstrate the performan…
In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic graphical models, deserves attention. Its simple structure - a tree - allows simple and efficient inference, while its latent variables capture complex relationships. In the past decade, the latent tree model has been subject to significant theoretical and methodological developments. In this review, we propose a comprehensive study of this model. First we summari…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as is. We believe that this work provides better understanding of neural networks and paves the way to tackle their black-box nature. We share equivalent trees of some neural networks and show that besides providing interpretability, tree representation can also achieve some computational advantages for small networks. The analysis holds both for fully connected…
Turing machine and decision tree have developed independently for a long time. With the recent development of differentiable models, there is an intersection between them. Neural turing machine(NTM) opens door for the memory network. It use differentiable attention mechanism to read/write external memory bank. Differentiable forest brings differentiable properties to classical decision tree. In this short note, we show the deep connection between these two models. That is: differentiable forest is a special case of NTM. Differentiable forest is actually decision tree based neural turing machin…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Texas A & M University（得克萨斯农工大学）；University of Notre Dame（圣母大学）
In this work a novel, automated process for constructing and initializing deep feed-forward neural networks based on decision trees is presented. The proposed algorithm maps a collection of decision trees trained on the data into a collection of initialized neural networks, with the structures of the networks determined by the structures of the trees. The tree-informed initialization acts as a warm-start to the neural network training process, resulting in efficiently trained, accurate networks. These models, referred to as "deep jointly-informed neural networks" (DJINN), demonstrate high pred…
University of Bologna（博洛尼亚大学）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
We propose a novel architecture for Graph Neural Networks that is inspired by the idea behind Tree Kernels of measuring similarity between trees by taking into account their common substructures, named fragments. By imposing a series of regularization constraints to the learning problem, we exploit a pooling mechanism that incorporates such notion of fragments within the node soft assignment function that produces the embeddings. We present an extensive experimental evaluation on a collection of sentence classification tasks conducted on several argument mining corpora, showing that the propos…
Data mining information about people is becoming increasingly important in the data-driven society of the 21st century. Unfortunately, sometimes there are real-world considerations that conflict with the goals of data mining; sometimes the privacy of the people being data mined needs to be considered. This necessitates that the output of data mining algorithms be modified to preserve privacy while simultaneously not ruining the predictive power of the outputted model. Differential privacy is a strong, enforceable definition of privacy that can be used in data mining algorithms, guaranteeing th…
Retrosynthesis is a technique to plan the chemical synthesis of organic molecules, for example drugs, agro- and fine chemicals. In retrosynthesis, a search tree is built by analysing molecules recursively and dissecting them into simpler molecular building blocks until one obtains a set of known building blocks. The search space is intractably large, and it is difficult to determine the value of retrosynthetic positions. Here, we propose to model retrosynthesis as a Markov Decision Process. In combination with a Deep Neural Network policy learned from essentially the complete published knowled…
Deep neural networks have been proven powerful at processing perceptual data, such as images and audio. However for tabular data, tree-based models are more popular. A nice property of tree-based models is their natural interpretability. In this work, we present Deep Neural Decision Trees (DNDT) -- tree models realised by neural networks. A DNDT is intrinsically interpretable, as it is a tree. Yet as it is also a neural network (NN), it can be easily implemented in NN toolkits, and trained with gradient descent rather than greedy splitting. We evaluate DNDT on several tabular datasets, verify …
Dipartimento di Informatica - Università di Pisa（比萨大学信息学系）
The paper introduces two new aggregation functions to encode structural knowledge from tree-structured data. They leverage the Canonical and Tensor-Train decompositions to yield expressive context aggregation while limiting the number of model parameters. Finally, we define two novel neural recursive models for trees leveraging such aggregation functions, and we test them on two tree classification tasks, showing the advantage of proposed models when tree outdegree increases.
In this paper we propose a method to build a neural network that is similar to an ensemble of decision trees. We first illustrate how to convert a learned ensemble of decision trees to a single neural network with one hidden layer and an input transformation. We then relax some properties of this network such as thresholds and activation functions to train an approximately equivalent decision tree ensemble. The final model, Hammock, is surprisingly simple: a fully connected two layers neural network where the input is quantized and one-hot encoded. Experiments on large and small datasets show …
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models like LSTMs are in fact able to discover and implicitly use recursive compositional structure, at least for tasks with clear cues to that structure in the data. We demonstrate this possibility using an artificial data task for which recursive compositional structure is crucial, and find an LSTM-based sequence model can indeed learn to exploit the underlying t…
Deep neural networks have proved to be a very effective way to perform classification tasks. They excel when the input data is high dimensional, the relationship between the input and the output is complicated, and the number of labeled training examples is large. But it is hard to explain why a learned network makes a particular classification decision on a particular test case. This is due to their reliance on distributed hierarchical representations. If we could take the knowledge acquired by the neural net and express the same knowledge in a model that relies on hierarchical decisions inst…
Faculty of Engineering and Information Technology, University of Technology Sydney（悉尼科技大学工程与信息技术学院）
Gradient Boosting Decision Tree (GBDT) are popular machine learning algorithms with implementations such as LightGBM and in popular machine learning toolkits like Scikit-Learn. Many implementations can only produce trees in an offline manner and in a greedy manner. We explore ways to convert existing GBDT implementations to known neural network architectures with minimal performance loss in order to allow decision splits to be updated in an online manner and provide extensions to allow splits points to be altered as a neural architecture search problem. We provide learning bounds for our neura…
The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学）；National Institute of Informatics（国立信息学研究所）
In practical situations, the tree ensemble is one of the most popular models along with neural networks. A soft tree is a variant of a decision tree. Instead of using a greedy method for searching splitting rules, the soft tree is trained using a gradient method in which the entire splitting operation is formulated in a differentiable form. Although ensembles of such soft trees have been used increasingly in recent years, little theoretical work has been done to understand their behavior. By considering an ensemble of infinite soft trees, this paper introduces and studies the Tree Neural Tange…
Our project probes the relationship between temperatures and the blossom date of cherry trees. Through modeling, future flowering will become predictive, helping the public plan travels and avoid pollen season. To predict the date when the cherry trees will blossom exactly could be viewed as a multiclass classification problem, so we applied the multi-class Support Vector Classifier (SVC) and Recurrent Neural Network (RNN), particularly Long Short-term Memory (LSTM), to formulate the problem. In the end, we evaluate and compare the performance of these approaches to find out which one might be…
University of Chinese Academy of Sciences（中国科学院大学）；Department of Computer Science, University of California Santa Barbara（加州大学圣塔芭芭拉分校计算机科学系）；WeChat Search Application Department, Tencent（腾讯微信搜索应用部）
Different from other sequential data, sentences in natural language are structured by linguistic grammars. Previous generative conversational models with chain-structured decoder ignore this structure in human language and might generate plausible responses with less satisfactory relevance and fluency. In this study, we aim to incorporate the results from linguistic analysis into the process of sentence generation for high-quality conversation generation. Specifically, we use a dependency parser to transform each response sentence into a dependency tree and construct a training corpus of sente…
Friedrich-Schiller-University Jena（耶拿弗里德里希·席勒大学）；Ernst Abbe University of Applied Sciences Jena（恩斯特·阿贝耶拿应用科学大学）；Technical University Kaiserslautern（凯泽斯劳滕工业大学）；Data Assessment Solutions GmbH（数据评估解决方案有限公司）
Capsule neural networks replace simple, scalar-valued neurons with vector-valued capsules. They are motivated by the pattern recognition system in the human brain, where complex objects are decomposed into a hierarchy of simpler object parts. Such a hierarchy is referred to as a parse-tree. Conceptually, capsule neural networks have been defined to realize such parse-trees. The capsule neural network (CapsNet), by Sabour, Frosst, and Hinton, is the first actual implementation of the conceptual idea of capsule neural networks. CapsNets achieved state-of-the-art performance on simple image recog…
Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their expressive power. In this work, we propose a new GNN architecture -- the Neural Tree. The neural tree architecture does not perform message passing on the input graph, but on a tree-structured graph, called the H-tree, that is constructed from the input graph. Nodes in the H-tree correspond to subgraphs in the input graph, and they are reorganized in a hierarchica…
This paper proposes a tree-based convolutional neural network (TBCNN) for discriminative sentence modeling. Our models leverage either constituency trees or dependency trees of sentences. The tree-based convolution process extracts sentences' structural features, and these features are aggregated by max pooling. Such architecture allows short propagation paths between the output layer and underlying feature detectors, which enables effective structural feature learning and extraction. We evaluate our models on two tasks: sentiment analysis and question classification. In both experiments, TBCN…
We propose the fully explainable Decision Tree Graph Neural Network (DT+GNN) architecture. In contrast to existing black-box GNNs and post-hoc explanation methods, the reasoning of DT+GNN can be inspected at every step. To achieve this, we first construct a differentiable GNN layer, which uses a categorical state space for nodes and messages. This allows us to convert the trained MLPs in the GNN into decision trees. These trees are pruned using our newly proposed method to ensure they are small and easy to interpret. We can also use the decision trees to compute traditional explanations. We de…
University of Twente（特文特大学）；University of Duisburg-Essen（杜伊斯堡-埃森大学）
Prototype-based methods use interpretable representations to address the black-box nature of deep learning models, in contrast to post-hoc explanation methods that only approximate such models. We propose the Neural Prototype Tree (ProtoTree), an intrinsically interpretable deep learning method for fine-grained image recognition. ProtoTree combines prototype learning with decision trees, and thus results in a globally interpretable model by design. Additionally, ProtoTree can locally explain a single prediction by outlining a decision path through the tree. Each node in our binary tree contain…
Graph neural networks have been successful in many learning problems and real-world applications. A recent line of research explores the power of graph neural networks to solve combinatorial and graph algorithmic problems such as subgraph isomorphism, detecting cliques, and the traveling salesman problem. However, many NP-complete problems are as of yet unexplored using this method. In this paper, we tackle the Steiner Tree Problem. We employ four learning frameworks to compute low cost Steiner trees: feed-forward neural networks, graph neural networks, graph convolutional networks, and a grap…
The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学（SOKENDAI））；National Institute of Informatics（国立信息学研究所）
A soft tree is an actively studied variant of a decision tree that updates splitting rules using the gradient method. Although soft trees can take various architectures, their impact is not theoretically well known. In this paper, we formulate and analyze the Neural Tangent Kernel (NTK) induced by soft tree ensembles for arbitrary tree architectures. This kernel leads to the remarkable finding that only the number of leaves at each depth is relevant for the tree architecture in ensemble learning with an infinite number of trees. In other words, if the number of leaves at each depth is fixed, t…
NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Safran Electronics & Defense（赛峰电子与防务公司）；LAMSADE, Paris-Dauphine（巴黎第九大学LAMSADE实验室）；Universities Space Research Association（大学空间研究协会）；CREC Saint-Cyr Coetquidan（圣西尔-科埃基当军事院校研究中心）
Scheduling in the presence of uncertainty is an area of interest in artificial intelligence due to the large number of applications. We study the problem of dynamic controllability (DC) of disjunctive temporal networks with uncertainty (DTNU), which seeks a strategy to satisfy all constraints in response to uncontrollable action durations. We introduce a more restricted, stronger form of controllability than DC for DTNUs, time-based dynamic controllability (TDC), and present a tree search approach to determine whether or not a DTNU is TDC. Moreover, we leverage the learning capability of a mes…
Faculty of Engineering and Information Technology（工程与信息技术学院）；University of Technology Sydney（悉尼科技大学）
This work presents an approach to automatically induction for non-greedy decision trees constructed from neural network architecture. This construction can be used to transfer weights when growing or pruning a decision tree, allowing non-greedy decision tree algorithms to automatically learn and adapt to the ideal architecture. In this work, we examine the underpinning ideas within ensemble modelling and Bayesian model averaging which allow our neural network to asymptotically approach the ideal architecture through weights transfer. Experimental results demonstrate that this approach improves…
Recurrent neural networks (RNNs) process input text sequentially and model the conditional transition between word tokens. In contrast, the advantages of recursive networks include that they explicitly model the compositionality and the recursive structure of natural language. However, the current recursive architecture is limited by its dependence on syntactic tree. In this paper, we introduce a robust syntactic parsing-independent tree structured model, Neural Tree Indexers (NTI) that provides a middle ground between the sequential RNNs and the syntactic treebased recursive models. NTI const…
Regression-via-Classification (RvC) is the process of converting a regression problem to a classification one. Current approaches for RvC use ad-hoc discretization strategies and are suboptimal. We propose a neural regression tree model for RvC. In this model, we employ a joint optimization framework where we learn optimal discretization thresholds while simultaneously optimizing the features for each node in the tree. We empirically show the validity of our model by testing it on two challenging regression tasks where we establish the state of the art.
International Institute of Information Technology（国际信息技术学院）
A contextual care protocol is used by a medical practitioner for patient healthcare, given the context or situation that the specified patient is in. This paper proposes a method to build an automated self-adapting protocol which can help make relevant, early decisions for effective healthcare delivery. The hybrid model leverages neural networks and decision trees. The neural network estimates the chances of each disease and each tree in the decision trees represents care protocol for a disease. These trees are subject to change in case of aberrations found by the diagnosticians. These correct…
University of Maryland（马里兰大学）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Johns Hopkins University（约翰斯·霍普金斯大学）
Boosting is a method for finding a highly accurate hypothesis by linearly combining many ``weak" hypotheses, each of which may be only moderately accurate. Thus, boosting is a method for learning an ensemble of classifiers. While boosting has been shown to be very effective for decision trees, its impact on neural networks has not been extensively studied. We prove one important difference between sums of decision trees compared to sums of convolutional neural networks (CNNs) which is that a sum of decision trees cannot be represented by a single decision tree with the same number of parameter…
Georgia Institute of Technology（佐治亚理工学院）；UMI2958 GT-CNRS（佐治亚理工学院-法国国家科学研究中心 UMI2958 国际联合实验室）
The analysis of the internal structure of trees is highly important for both forest experts, biological scientists, and the wood industry. Traditionally, CT-scanners are considered as the most efficient way to get an accurate inner representation of the tree. However, this method requires an important investment and reduces the cost-effectiveness of this operation. Our goal is to design neural-network-based methods to predict the internal density of the tree from its external bark shape. This paper compares different image-to-image(2D), volume-to-volume(3D) and Convolutional Long Short Term Me…
In this work, the TREPAN algorithm is enhanced and extended for extracting decision trees from neural networks. We empirically evaluated the performance of the algorithm on a set of databases from real world events. This benchmark enhancement was achieved by adapting Single-test TREPAN and C4.5 decision tree induction algorithms to analyze the datasets. The models are then compared with X-TREPAN for comprehensibility and classification accuracy. Furthermore, we validate the experimentations by applying statistical methods. Finally, the modified algorithm is extended to work with multi-class re…
Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one route (root-to-leaf) that is dependent on the input data. In this paper, we present DecisioNet (DN), a binary-tree structured neural network. We propose a systematic way to convert an existing DNN into a DN to create a lightweight version of the original model. DecisioNet takes the best of both worlds - it uses neural modules to perform representational learn…
Though traditional algorithms could be embedded into neural architectures with the proposed principle of \cite{xiao2017hungarian}, the variables that only occur in the condition of branch could not be updated as a special case. To tackle this issue, we multiply the conditioned branches with Dirac symbol (i.e. $\mathbf{1}_{x>0}$), then approximate Dirac symbol with the continuous functions (e.g. $1 - e^{-α|x|}$). In this way, the gradients of condition-specific variables could be worked out in the back-propagation process, approximately, making a fully functioned neural graph. Within our novel …
How resources are deployed to secure critical targets in networks can be modelled by Network Security Games (NSGs). While recent advances in deep learning (DL) provide a powerful approach to dealing with large-scale NSGs, DL methods such as NSG-NFSP suffer from the problem of data inefficiency. Furthermore, due to centralized control, they cannot scale to scenarios with a large number of resources. In this paper, we propose a novel DL-based method, NSGZero, to learn a non-exploitable policy in NSGs. NSGZero improves data efficiency by performing planning with neural Monte Carlo Tree Search (MC…
Efficiently Transforming Neural Networks into Decision Trees: A Path to Ground Truth Explanations with RENTT
Fraunhofer Institute for Manufacturing Engineering and Automation IPA（弗劳恩霍夫制造工程与自动化研究所）；Institute of Industrial Manufacturing and Management IFF, University of Stuttgart（工业制造与管理研究所，斯图加特大学）；Technical University Munich（慕尼黑技术大学）
Singapore Management University（新加坡管理大学）；The Open University, UK（英国开放大学）
Towards the vision of translating code that implements an algorithm from one programming language into another, this paper proposes an approach for automated program classification using bilateral tree-based convolutional neural networks (BiTBCNNs). It is layered on top of two tree-based convolutional neural networks (TBCNNs), each of which recognizes the algorithm of code written in an individual programming language. The combination layer of the networks recognizes the similarities and differences among code in different programming languages. The BiTBCNNs are trained using the source code i…
Fraunhofer Institute for Manufacturing Engineering and Automation IPA（弗劳恩霍夫制造工程与自动化研究所IPA）；University of Stuttgart（斯图加特大学）；Stuttgart Media University（斯图加特媒体大学）
One obstacle that so far prevents the introduction of machine learning models primarily in critical areas is the lack of explainability. In this work, a practicable approach of gaining explainability of deep artificial neural networks (NN) using an interpretable surrogate model based on decision trees is presented. Simply fitting a decision tree to a trained NN usually leads to unsatisfactory results in terms of accuracy and fidelity. Using L1-orthogonal regularization during training, however, preserves the accuracy of the NN, while it can be closely approximated by small decision trees. Test…
As neural networks have become more powerful, there has been a rising desire to deploy them in the real world; however, the power and accuracy of neural networks is largely due to their depth and complexity, making them difficult to deploy, especially in resource-constrained devices. Neural network quantization has recently arisen to meet this demand of reducing the size and complexity of neural networks by reducing the precision of a network. With smaller and simpler networks, it becomes possible to run neural networks within the constraints of their target hardware. This paper surveys the ma…
In this paper we propose a synergistic melting of neural networks and decision trees (DT) we call neural decision trees (NDT). NDT is an architecture a la decision tree where each splitting node is an independent multilayer perceptron allowing oblique decision functions or arbritrary nonlinear decision function if more than one layer is used. This way, each MLP can be seen as a node of the tree. We then show that with the weight sharing asumption among those units, we end up with a Hashing Neural Network (HNN) which is a multilayer perceptron with sigmoid activation function for the last layer…
Machine learning applications such as finance and medicine demand accurate and justifiable predictions, barring most deep learning methods from use. In response, previous work combines decision trees with deep learning, yielding models that (1) sacrifice interpretability for accuracy or (2) sacrifice accuracy for interpretability. We forgo this dilemma by jointly improving accuracy and interpretability using Neural-Backed Decision Trees (NBDTs). NBDTs replace a neural network's final linear layer with a differentiable sequence of decisions and a surrogate loss. This forces the model to learn h…
Understanding generalization and robustness of machine learning models fundamentally relies on assuming an appropriate metric on the data space. Identifying such a metric is particularly challenging for non-Euclidean data such as graphs. Here, we propose a pseudometric for attributed graphs, the Tree Mover's Distance (TMD), and study its relation to generalization. Via a hierarchical optimal transport problem, TMD reflects the local distribution of node attributes as well as the distribution of local computation trees, which are known to be decisive for the learning behavior of graph neural ne…
Nanjing University（南京大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Squirrel AI Learning（松鼠AI智适应教育）
The celebrated Seq2Seq technique and its numerous variants achieve excellent performance on many tasks such as neural machine translation, semantic parsing, and math word problem solving. However, these models either only consider input objects as sequences while ignoring the important structural information for encoding, or they simply treat output objects as sequence outputs instead of structural objects for decoding. In this paper, we present a novel Graph-to-Tree Neural Networks, namely Graph2Tree consisting of a graph encoder and a hierarchical tree decoder, that encodes an augmented grap…
Machine learning-based applications are increasingly prevalent in IoT devices. The power and storage constraints of these devices make it particularly challenging to run modern neural networks, limiting the number of new applications that can be deployed on an IoT system. A number of compression techniques have been proposed, each with its own trade-offs. We propose a hybrid network which combines the strengths of current neural- and tree-based learning techniques in conjunction with ternary quantization, and show a detailed analysis of the associated model design space. Using this hybrid mode…
