The Use of Binary Choice Forests to Model and Estimate Discrete Choices
Rotman School of Management, University of Toronto（多伦多大学罗特曼管理学院）；School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）；Antai College of Economics and Management, Shanghai Jiao Tong University（上海交通大学安泰经济与管理学院）
Problem definition. In retailing, discrete choice models (DCMs) are commonly used to capture the choice behavior of customers when offered an assortment of products. When estimating DCMs using transaction data, flexible models (such as machine learning models or nonparametric models) are typically not interpretable and hard to estimate, while tractable models (such as the multinomial logit model) tend to misspecify the complex behavior represeted in the data. Methodology/results. In this study, we use a forest of binary decision trees to represent DCMs. This approach is based on random forests, a popular machine learning algorithm. The resulting model is interpretable: the decision trees can explain the decision-making process of customers during the purchase. We show that our approach can predict the choice probability of any DCM consistently and thus never suffers from misspecification. Moreover, our algorithm predicts assortments unseen in the training data. The mechanism and errors can be theoretically analyzed. We also prove that the random forest can recover preference rankings of customers thanks to the splitting criterion such as the Gini index and information gain ratio. Managerial implications. The framework has unique practical advantages. It can capture customers' behavioral patterns such as irrationality or sequential searches when purchasing a product. It handles nonstandard formats of training data that result from aggregation. It can measure product importance based on how frequently a random customer would make decisions depending on the presence of the product. It can also incorporate price information and customer features. Our numerical experiments using synthetic and real data show that using random forests to estimate customer choices can outperform existing methods.
We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally extends from single trees to ensembles of trees and applies to methods like random forests. This is useful because while importance values from random forests are used to screen variables, for example they are used to filter high throughput genomic data in Bioinformatics, very little theory exists about their properties.
Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. We propose a novel approach based on a machine learning tool named random forests to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classific…
Binary Classification: Is Boosting stronger than Bagging?
Massachusetts Institute of Technology（麻省理工学院）；Operations Research Center, Massachusetts Institute of Technology（麻省理工学院运筹学中心）；Sloan School of Management, Massachusetts Institute of Technology（麻省理工学院斯隆管理学院）
本文提出 Enhanced Random Forests，通过自适应样本权重与个性化树权重，在 15 个二分类数据集上以默认超参数达到或超过 XGBoost，并利用树重要性恢复部分可解释性。
Renmin University of China（中国人民大学）；University of Stuttgart（斯图加特大学）
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates as each single tree in the forest. In this way, the resulting forest can be more accurate than the original purely random forest. From the theoretical perspective, within the framework of regularized empirical risk minimization penalized on the number of splits, we establish almost optimal convergence rates for the proposed best-scored random trees under cert…
Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies that a higher scale level is used. Versions of ordinal trees are proposed that take the scale level seriously and avoid the assignment of artificial scores. The basic construction principle is based on an investigation of the binary models that are implicitly used in parametric ordinal regression. These building blocks can be fitted by trees and combined in a similar way as in parametric models. The obtained trees use the ordinal scale level only. Since binary trees and ran…
Due to their long-standing reputation as excellent off-the-shelf predictors, random forests continue remain a go-to model of choice for applied statisticians and data scientists. Despite their widespread use, however, until recently, little was known about their inner-workings and about which aspects of the procedure were driving their success. Very recently, two competing hypotheses have emerged -- one based on interpolation and the other based on regularization. This work argues in favor of the latter by utilizing the regularization framework to reexamine the decades-old question of whether …
Comparison of static and dynamic random forests models for EHR data in the presence of competing risks: predicting central line-associated bloodstream infection
KU Leuven（鲁汶大学）；University Hospitals Leuven（鲁汶大学医院）；Maastricht University（马斯特里赫特大学）；Leiden University Medical Center（莱顿大学医学中心）
In Random Forests, proximity distances are a metric representation of data into decision space. By observing how changes in input map to the movement of instances in this space we are able to determine the independent contribution of each feature to the decision-making process. For binary feature vectors, this process is fully specified. As these changes in input move particular instances nearer to the in-group or out-group, the independent contribution of each feature can be uncovered. Using this technique, we are able to calculate the contribution of each feature in determining how black-box…
This study investigates the potential effects of different Dynamic Message Signs (DMSs) on driver behavior using a full-scale high-fidelity driving simulator. Different DMSs are categorized by their content, structure, and type of messages. A random forest algorithm is used for three separate behavioral analyses; a route diversion analysis, a route choice analysis and a compliance analysis; to identify the potential and relative influences of different DMSs on these aspects of driver behavior. A total of 390 simulation runs are conducted using a sample of 65 participants from diverse socioecon…
Sloan School of Management and Operations Research Center（斯隆管理学院和运筹学研究中心）；Massachusetts Institute of Technology（麻省理工学院）；Operations Research Center（运筹学研究中心）
Chubu University（中部大学）；NTT Communication Science Laboratories（NTT通信科学实验室）
This paper proposes a novel type of random forests called a denoising random forests that are robust against noises contained in test samples. Such noise-corrupted samples cause serious damage to the estimation performances of random forests, since unexpected child nodes are often selected and the leaf nodes that the input sample reaches are sometimes far from those for a clean sample. Our main idea for tackling this problem originates from a binary indicator vector that encodes a traversal path of a sample in the forest. Our proposed method effectively employs this vector by introducing denoi…
We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification and regression. Individual canonical correlation trees are binary decision trees with hyperplane splits based on local canonical correlation coefficients calculated during training. Unlike axis-aligned alternatives, the decision surfaces of CCFs are not restricted to the coordinate system of the inputs features and therefore more naturally represent data with correlated inputs. CCFs naturally accommodate multiple outputs, provide a similar computational complexity to random forests, and in…
In short, our experiments suggest that yes, on average, rotation forest is better than the most common alternatives when all the attributes are real-valued. Rotation forest is a tree based ensemble that performs transforms on subsets of attributes prior to constructing each tree. We present an empirical comparison of classifiers for problems with only real-valued features. We evaluate classifiers from three families of algorithms: support vector machines; tree-based ensembles; and neural networks tuned with a large grid search. We compare classifiers on unseen data based on the quality of the …
Feature Space Selection and Heterogeneous Effect Estimation for Blood-Brain Barrier Permeability: A Random Forest to the Generalized Random Forest Pipeline
University of Pretoria（比勒陀利亚大学）；Ferdowsi University of Mashhad（马什哈德菲尔多西大学）
Breiman's random forest (RF) can be interpreted as an implicit kernel generator,where the ensuing proximity matrix represents the data-driven RF kernel. Kernel perspective on the RF has been used to develop a principled framework for theoretical investigation of its statistical properties. However, practical utility of the links between kernels and the RF has not been widely explored and systematically evaluated.Focus of our work is investigation of the interplay between kernel methods and the RF. We elucidate the performance and properties of the data driven RF kernels used by regularized lin…
The need to learn from positive and unlabeled data, or PU learning, arises in many applications and has attracted increasing interest. While random forests are known to perform well on many tasks with positive and negative data, recent PU algorithms are generally based on deep neural networks, and the potential of tree-based PU learning is under-explored. In this paper, we propose new random forest algorithms for PU-learning. Key to our approach is a new interpretation of decision tree algorithms for positive and negative data as \emph{recursive greedy risk minimization algorithms}. We extend …
In this paper we analyze, evaluate, and improve the performance of training Random Forest (RF) models on modern CPU architectures. An exact, state-of-the-art binary decision tree building algorithm is used as the basis of this study. Firstly, we investigate the trade-offs between using different tree building algorithms, namely breadth-first-search (BFS) and depth-search-first (DFS). We design a novel, dynamic, hybrid BFS-DFS algorithm and demonstrate that it performs better than both BFS and DFS, and is more robust in the presence of workloads with different characteristics. Secondly, we iden…
Booz Allen Hamilton, Strategic Innovation Group（博思艾伦咨询公司战略创新集团）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
The potential lack of fairness in the outputs of machine learning algorithms has recently gained attention both within the research community as well as in society more broadly. Surprisingly, there is no prior work developing tree-induction algorithms for building fair decision trees or fair random forests. These methods have widespread popularity as they are one of the few to be simultaneously interpretable, non-linear, and easy-to-use. In this paper we develop, to our knowledge, the first technique for the induction of fair decision trees. We show that our "Fair Forest" retains the benefits …
School of Management（管理学院）；University of Science and Technology of China（中国科学技术大学）；School of Mathematics and Statistics（数学与统计学院）；Academy of Mathematics and Systems Science（数学与系统科学研究院）；Chinese Academy of Sciences（中国科学院）
Despite the latest prevailing success of deep neural networks (DNNs), several concerns have been raised against their usage, including the lack of intepretability the gap between DNNs and other well-established machine learning models, and the growingly expensive computational costs. A number of recent works [1], [2], [3] explored the alternative to sequentially stacking decision tree/random forest building blocks in a purely feed-forward way, with no need of back propagation. Since decision trees enjoy inherent reasoning transparency, such deep forest models can also facilitate the understand…
In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine learning as a coding and dimensionality reduction problem, and further proposed a simple unsupervised dimensionality reduction method, entitled deep distributed random samplings (DDRS). In this paper, we further extend it to supervised learning incrementally. The key idea here is to incorporate label information into the coding process by reformulating that each center in DDRS has multiple output units indicating which class the center belongs to. The supervised learning method seems somewhat similar with random forests…
École Polytechnique（巴黎综合理工学院）；CNRS（法国国家科学研究中心）；Université de Paris（巴黎大学）；Ecole normale supérieure（巴黎高等师范学院）
Random Forests (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree-ensemble methods comes from a combination of several characteristics: a remarkable accuracy in a variety of tasks, a small number of parameters to tune, robustness with respect to features scaling, a reasonable computational cost for training and prediction, and their suitability in high-dimensional settings. The most commonly used RF variants however are "offline" algorithms, which require the availability of the whole dataset at once. In…
This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review emphasizes mostly the solution proposed by Pudlo et al. (2016) on the use of random forests for aggregating summary statistics and and for estimating the posterior probability of the most likely model via a secondary random fores.
Multi forests: Variable importance for multi-class outcomes
Institute for Medical Information Processing, Biometry and Epidemiology, LMU Munich（慕尼黑大学医学信息处理、生物统计学与流行病学研究所）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Institute of AI and Informatics in Medicine, TUM School of Medicine and Health, Technical University of Munich（慕尼黑工业大学医学与健康学院医学人工智能与信息学研究所）
As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the underlying mechanisms has led to some important recent theoretical results on the consistency of the random forests algorithm and its variants. However, to our knowledge, almost all existing works concerning random forests consistency in high dimensional setting were established for various modified random forests models where the splitting rules are independent of…
University of Malaya（马来亚大学）；Imperial College London（帝国理工学院）；Peking University（北京大学）
Image understanding is an important research domain in the computer vision due to its wide real-world applications. For an image understanding framework that uses the Bag-of-Words model representation, the visual codebook is an essential part. Random forest (RF) as a tree-structure discriminative codebook has been a popular choice. However, the performance of the RF can be degraded if the local patch labels are poorly assigned. In this paper, we tackle this problem by a novel way to update the RF codebook learning for a more discriminative codebook with the introduction of the soft class label…
Isolation forest or "iForest" is an intuitive and widely used algorithm for anomaly detection that follows a simple yet effective idea: in a given data distribution, if a threshold (split point) is selected uniformly at random within the range of some variable and data points are divided according to whether they are greater or smaller than this threshold, outlier points are more likely to end up alone or in the smaller partition. The original procedure suggested the choice of variable to split and split point within a variable to be done uniformly at random at each step, but this paper shows …
University of New South Wales（新南威尔士大学）；Fudan University（复旦大学）
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and flexible than conventional axis-aligned cutting strategies. However, due to its batch learning setting, it is not well suited to large-scale classification and regression problems. In this paper, we develop an online BSP-Forest framework to address this limitation. With the arrival of new data, the resulting online algorithm can simultaneously expand the space…
UCLA Anderson School of Management, University of California, Los Angeles（加州大学洛杉矶分校安德森管理学院）
Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision…
University of New South Wales（新南威尔士大学）；Fudan University（复旦大学）
The Binary Space Partitioning~(BSP)-Tree process is proposed to produce flexible 2-D partition structures which are originally used as a Bayesian nonparametric prior for relational modelling. It can hardly be applied to other learning tasks such as regression trees because extending the BSP-Tree process to a higher dimensional space is nontrivial. This paper is the first attempt to extend the BSP-Tree process to a d-dimensional (d>2) space. We propose to generate a cutting hyperplane, which is assumed to be parallel to d-2 dimensions, to cut each node in the d-dimensional BSP-tree. By designin…
Federal University of São Carlos（圣卡洛斯联邦大学）；University of Western São Paulo（西圣保罗大学）；São Paulo State University（圣保罗州立大学）
Probabilistic-driven classification techniques extend the role of traditional approaches that output labels (usually integer numbers) only. Such techniques are more fruitful when dealing with problems where one is not interested in recognition/identification only, but also into monitoring the behavior of consumers and/or machines, for instance. Therefore, by means of probability estimates, one can take decisions to work better in a number of scenarios. In this paper, we propose a probabilistic-based Optimum Path Forest (OPF) classifier to handle with binary classification problems, and we show…
An increasingly common methodological issue in the field of social science is high-dimensional and highly correlated datasets that are unamenable to the traditional deductive framework of study. Analysis of candidate choice in the 2020 Presidential Election is one area in which this issue presents itself: in order to test the many theories explaining the outcome of the election, it is necessary to use data such as the 2020 Cooperative Election Study Common Content, with hundreds of highly correlated features. We present the Fuzzy Forests algorithm, a variant of the popular Random Forests ensem…
Simon Fraser University（西蒙弗雷泽大学）；Nankai University（南开大学）；University of Oxford（牛津大学）
Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is often limited by the requirement that the cuts be axis aligned. The Ostomachion process and the self-consistent binary space partitioning-tree process were recently introduced as generalizations of the Mondrian process for space partitioning with non-axis aligned cuts in the two dimensional plane. Motivated by the need for a multi-dimensional partitioning tre…
Institut Pasteur（巴斯德研究所）；Université Paris Cité（巴黎城市大学）；Inserm（法国国家健康与医学研究院）；Institut de l’Audition（听觉研究所）；IHU reConnect（reConnect 医院研究所）；INRIA（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）；Univ. Paris-Saclay（巴黎-萨克雷大学）；University of California Santa Barbara（加州大学圣巴巴拉分校）；Institute of Statistical Mathematics（统计数学研究所）
Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local linear regression adjustment to better capture smoothness. The resulting procedure, local linear forests, enables us to improve on asymptotic rates of convergence for random forests with smooth signals, and provides substantial gains in accuracy on both real and simulated data. We …
Virginia Tech（弗吉尼亚理工大学）；US Army Research Laboratory（美国陆军研究实验室）
In this paper, we examine the use of a deep multi-layer perceptron architecture to classify received signals as one of seven common waveforms, single carrier (SC), single-carrier frequency division multiple access (SC-FDMA), orthogonal frequency division multiplexing (OFDM), linear frequency modulation (LFM), amplitude modulation (AM), frequency modulation (FM), and phase-coded pulse modulation used in communication and radar networks. Synchronization of the signals is not needed as we assume there is an unknown and uncompensated time and frequency offset. The classifier is open-set meaning it…
Thakur Institute Of Management Studies, Career Development & Research（塔库尔管理研究、职业发展与研究学院）；University of Mumbai（孟买大学）
High dimensional data for classification does create many difficulties for machine learning algorithms. The generalization can be done using ensemble learning methods such as bagging based supervised non-parametric random forest algorithm. In this paper we solve the problem of binary classification for high dimensional data using random forest for polycystic ovary syndrome dataset. We have performed the implementation and provided a detailed visualization of the data for general inference. The training accuracy that we have achieved is 95.6% and validation accuracy over 91.74% respectively.
Department of Electronic Science, Xiamen University（厦门大学电子科学系）
We present a general architecture of deep differentiable forest and its sparse attention mechanism. The differentiable forest has the advantages of both trees and neural networks. Its structure is a simple binary tree, easy to use and understand. It has full differentiability and all variables are learnable parameters. We would train it by the gradient-based optimization method, which shows great power in the training of deep CNN. We find and analyze the attention mechanism in the differentiable forest. That is, each decision depends on only a few important features, and others are irrelevant.…
Georgia Institute of Technology（佐治亚理工学院）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）
Rapid and accurate detection of community outbreaks is critical to address the threat of resurgent waves of COVID-19. A practical challenge in outbreak detection is balancing accuracy vs. speed. In particular, while estimation accuracy improves with longer fitting windows, speed degrades. This paper presents a machine learning framework to balance this tradeoff using generalized random forests (GRF), and applies it to detect county level COVID-19 outbreaks. This algorithm chooses an adaptive fitting window size for each county based on relevant features affecting the disease spread, such as ch…
The challenge in engaging malware activities involves the correct identification and classification of different malware variants. Various malwares incorporate code obfuscation methods that alters their code signatures effectively countering antimalware detection techniques utilizing static methods and signature database. In this study, we utilized an approach of converting a malware binary into an image and use Random Forest to classify various malware families. The resulting accuracy of 0.9562 exhibits the effectivess of the method in detecting malware
Decision forest algorithms typically model data by learning a binary tree structure recursively where every node splits the feature space into two sub-regions, sending examples into the left or right branch as a result. In axis-aligned decision forests, the "decision" to route an input example is the result of the evaluation of a condition on a single dimension in the feature space. Such conditions are learned using efficient, often greedy algorithms that optimize a local loss function. For example, a node's condition may be a threshold function applied to a numerical feature, and its paramete…
On the Trade-off between the Number of Nodes and the Number of Trees in a Random Forest
Bioinformatics Center, Institute for Chemical Research, Kyoto University（京都大学生物信息学中心，化学研究所）；Department of Computer Science, Ben-Gurion University of the Negev（巴伊兰大学内盖夫分校计算机科学系）；National Institute of Informatics, Chiyoda-ku, Tokyo, Japan（日本东京千代田区国立信息研究所）
College of Computer Science（计算机学院）；Chongqing University（重庆大学）
Ensemble learning methods whose base classifier is a decision tree usually belong to the bagging or boosting. However, no previous work has ever built the ensemble classifier by maximizing long-term returns to the best of our knowledge. This paper proposes a decision forest building method called MA-H-SAC-DF for binary classification via deep reinforcement learning. First, the building process is modeled as a decentralized partial observable Markov decision process, and a set of cooperative agents jointly constructs all base classifiers. Second, the global state and local observations are defi…
Computing Institute（计算研究所）；University of Campinas（坎皮纳斯大学）
We tested 14 very different classification algorithms (random forest, gradient boosting machines, SVM - linear, polynomial, and RBF - 1-hidden-layer neural nets, extreme learning machines, k-nearest neighbors and a bagging of knn, naive Bayes, learning vector quantization, elastic net logistic regression, sparse linear discriminant analysis, and a boosting of linear classifiers) on 115 real life binary datasets. We followed the Demsar analysis and found that the three best classifiers (random forest, gbm and RBF SVM) are not significantly different from each other. We also discuss that a chang…
University of New South Wales（新南威尔士大学）；School of Computer Science and Engineering, University of New South Wales（新南威尔士大学计算机科学与工程学院）
Online reviews play an important role in influencing buyers' daily purchase decisions. However, fake and meaningless reviews, which cannot reflect users' genuine purchase experience and opinions, widely exist on the Web and pose great challenges for users to make right choices. Therefore,it is desirable to build a fair model that evaluates the quality of products by distinguishing spamming reviews. We present an end-to-end trainable unified model to leverage the appealing properties from Autoencoder and random forest. A stochastic decision tree model is implemented to guide the global paramete…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present an extension to the model-free anomaly detection algorithm, Isolation Forest. This extension, named Extended Isolation Forest (EIF), resolves issues with assignment of anomaly score to given data points. We motivate the problem using heat maps for anomaly scores. These maps suffer from artifacts generated by the criteria for branching operation of the binary tree. We explain this problem in detail and demonstrate the mechanism by which it occurs visually. We then propose two different approaches for improving the situation. First we propose transforming the data randomly before crea…
Innovative Oncology Business Solutions（创新肿瘤商业解决方案公司）
We have applied a little-known data transformation to subsets of the Surveillance, Epidemiology, and End Results (SEER) publically available data of the National Cancer Institute (NCI) to make it suitable input to standard machine learning classifiers. This transformation properly treats the right-censored data in the SEER data and the resulting Random Forest and Multi-Layer Perceptron models predict full survival curves. Treating the 6, 12, and 60 months points of the resulting survival curves as 3 binary classifiers, the 18 resulting classifiers have AUC values ranging from .765 to .885. Fur…
In critical situations involving discrimination, gender inequality, economic damage, and even the possibility of casualties, machine learning models must be able to provide clear interpretations for their decisions. Otherwise, their obscure decision-making processes can lead to socioethical issues as they interfere with people's lives. In the aforementioned sectors, random forest algorithms strive, thus their ability to explain themselves is an obvious requirement. In this paper, we present LionForests, which relies on a preliminary work of ours. LionForests is a random forest-specific interpr…
