Most representative decision tree ensemble methods have been used to examine the variable importance of Treasury term spreads to predict US economic recessions with a balance of generating rules for US economic recession detection. A strategy is proposed for training the classifiers with Treasury term spreads data and the results are compared in order to select the best model for interpretability. We also discuss the use of SHapley Additive exPlanations (SHAP) framework to understand US recession forecasts by analyzing feature importance. Consistently with the existing literature we find the most relevant Treasury term spreads for predicting US economic recession and a methodology for detecting relevant rules for economic recession detection. In this case, the most relevant term spread found is 3 month to 6 month, which is proposed to be monitored by economic authorities. Finally, the methodology detected rules with high lift on predicting economic recession that can be used by these entities for this propose. This latter result stands in contrast to a growing body of literature demonstrating that machine learning methods are useful for interpretation comparing many alternative algorithms and we discuss the interpretation for our result and propose further research lines aligned with this work.
In this paper we propose using the principle of boosting to reduce the bias of a random forest prediction in the regression setting. From the original random forest fit we extract the residuals and then fit another random forest to these residuals. We call the sum of these two random forests a \textit{one-step boosted forest}. We show with simulated and real data that the one-step boosted forest has a reduced bias compared to the original random forest. The paper also provides a variance estimate of the one-step boosted forest by an extension of the infinitesimal Jackknife estimator. Using thi…
University of Liège（列日大学）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Katholieke Universiteit Leuven（鲁汶天主教大学）
Within machine learning, the supervised learning field aims at modeling the input-output relationship of a system, from past observations of its behavior. Decision trees characterize the input-output relationship through a series of nested $if-then-else$ questions, the testing nodes, leading to a set of predictions, the leaf nodes. Several of such trees are often combined together for state-of-the-art performance: random forest ensembles average the predictions of randomized decision trees trained independently in parallel, while tree boosting ensembles train decision trees sequentially to ref…
Erasmus University Rotterdam（鹿特丹伊拉斯姆斯大学）；University of Chicago（芝加哥大学）；Migros T.A.Ş（Migros公司）
We propose two algorithms for interpretation and boosting of tree-based ensemble methods. Both algorithms make use of mathematical programming models that are constructed with a set of rules extracted from an ensemble of decision trees. The objective is to obtain the minimum total impurity with the least number of rules that cover all the samples. The first algorithm uses the collection of decision trees obtained from a trained random forest model. Our numerical results show that the proposed rule covering approach selects only a few rules that could be used for interpreting the random forest …
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。
Travel time is a crucial measure in transportation. Accurate travel time prediction is also fundamental for operation and advanced information systems. A variety of solutions exist for short-term travel time predictions such as solutions that utilize real-time GPS data and optimization methods to track the path of a vehicle. However, reliable long-term predictions remain challenging. We show in this paper the applicability and usefulness of travel time i.e. delivery time prediction for postal services. We investigate several methods such as linear regression models and tree based ensembles suc…
University of Pennsylvania（宾夕法尼亚大学）；Apple Inc.（苹果公司）
There is a large literature explaining why AdaBoost is a successful classifier. The literature on AdaBoost focuses on classifier margins and boosting's interpretation as the optimization of an exponential likelihood function. These existing explanations, however, have been pointed out to be incomplete. A random forest is another popular ensemble method for which there is substantially less explanation in the literature. We introduce a novel perspective on AdaBoost and random forests that proposes that the two algorithms work for similar reasons. While both classifiers achieve similar predictiv…
I develop Macroeconomic Random Forest (MRF), an algorithm adapting the canonical Machine Learning (ML) tool to flexibly model evolving parameters in a linear macro equation. Its main output, Generalized Time-Varying Parameters (GTVPs), is a versatile device nesting many popular nonlinearities (threshold/switching, smooth transition, structural breaks/change) and allowing for sophisticated new ones. The approach delivers clear forecasting gains over numerous alternatives, predicts the 2008 drastic rise in unemployment, and performs well for inflation. Unlike most ML-based methods, MRF is direct…
This paper presents a novel ensemble learning approach called Residual Likelihood Forests (RLF). Our weak learners produce conditional likelihoods that are sequentially optimized using global loss in the context of previous learners within a boosting-like framework (rather than probability distributions that are measured from observed data) and are combined multiplicatively (rather than additively). This increases the efficiency of our strong classifier, allowing for the design of classifiers which are more compact in terms of model capacity. We apply our method to several machine learning cla…
CoreML Group Apple Inc.（苹果公司CoreML团队）；Department of Mathematics Florida State University（佛罗里达州立大学数学系）；Department of Statistics Florida State University（佛罗里达州立大学统计系）
Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or Random Forest. Previous work showed that boosting algorithms exhibit a cyclic behavior of selecting the same tree again and again due to the way the loss is optimized. At the same time, Random Forest is not based on loss optimization and obtains a more complex and less interpretable model. In this paper we present a novel method for obtaining compact tree e…
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）
McGill University, Department of Mathematics and Statistics（麦吉尔大学数学与统计学系）；Université Marie et Louis Pasteur, CNRS, LmB (UMR 6623)（玛丽·路易斯·帕斯特大学、法国国家科学研究中心、LmB（UMR 6623））
Guided Random Forest and its application to data approximation
Department of Electrical Engineering, Indian Institute of Technology Delhi（印度理工学院德里分校电子工程系）；Center for Computational Biology, Indraprastha Institute of Information Technology（印度信息科技学院计算生物学中心）；Department of Computer Science and Engineering, Indraprastha Institute of Information Technology（印度信息科技学院计算机科学与工程系）；Infosys Center for Artificial Intelligence, Indraprastha Institute of Information Technology（印度信息科技学院人工智能中心）；Institute of Health and Biomedical Innovation, Queensland University of Technology（昆士兰科技大学健康与生物医学创新研究所）；Department of Mathematics, Indian Institute of Technology Delhi（印度理工学院德里分校数学系）
Excellent ranking power along with well calibrated probability estimates are needed in many classification tasks. In this paper, we introduce a technique, Calibrated Boosting-Forest that captures both. This novel technique is an ensemble of gradient boosting machines that can support both continuous and binary labels. While offering superior ranking power over any individual regression or classification model, Calibrated Boosting-Forest is able to preserve well calibrated posterior probabilities. Along with these benefits, we provide an alternative to the tedious step of tuning gradient boosti…
Missing data is an expected issue when large amounts of data is collected, and several imputation techniques have been proposed to tackle this problem. Beneath classical approaches such as MICE, the application of Machine Learning techniques is tempting. Here, the recently proposed missForest imputation method has shown high imputation accuracy under the Missing (Completely) at Random scheme with various missing rates. In its core, it is based on a random forest for classification and regression, respectively. In this paper we study whether this approach can even be enhanced by other methods s…
Columbia University（哥伦比亚大学）；Pontifical Catholic University of Rio de Janeiro (PUC-Rio)（里约热内卢天主教大学）；University of California, Irvine（加州大学尔湾分校）
In this paper, we introduce a new machine learning (ML) model for nonlinear regression called the Boosted Smooth Transition Regression Trees (BooST), which is a combination of boosting algorithms with smooth transition regression trees. The main advantage of the BooST model is the estimation of the derivatives (partial effects) of very general nonlinear models. Therefore, the model can provide more interpretation about the mapping between the covariates and the dependent variable than other tree-based models, such as Random Forests. We present several examples with both simulated and real data…
In recent years, dynamically growing data and incrementally growing number of classes pose new challenges to large-scale data classification research. Most traditional methods struggle to balance the precision and computational burden when data and its number of classes increased. However, some methods are with weak precision, and the others are time-consuming. In this paper, we propose an incremental learning method, namely, heterogeneous incremental Nearest Class Mean Random Forest (hi-RF), to handle this issue. It is a heterogeneous method that either replaces trees or updates trees leaves …
Isomorphic Functionalities between Ant Colony and Ensemble Learning: Part II-On the Strength of Weak Learnability and the Boosting Paradigm
School of Mathematics and Statistics, Rochester Institute of Technology（罗彻斯特理工学院数学与统计学院）；Gosnell School of Life Sciences, Rochester Institute of Technology（罗彻斯特理工学院戈斯内尔生命科学学院）；Center for Imaging Science, Rochester Institute of Technology（罗彻斯特理工学院成像科学中心）
Technology and collaboration enable dramatic increases in the size of psychological and psychiatric data collections, but finding structure in these large data sets with many collected variables is challenging. Decision tree ensembles like random forests (Strobl, Malley, and Tutz, 2009) are a useful tool for finding structure, but are difficult to interpret with multiple outcome variables which are often of interest in psychology. To find and interpret structure in data sets with multiple outcomes and many predictors (possibly exceeding the sample size), we introduce a multivariate extension t…
Decision forests (Forests), in particular random forests and gradient boosting trees, have demonstrated state-of-the-art accuracy compared to other methods in many supervised learning scenarios. In particular, Forests dominate other methods in tabular data, that is, when the feature space is unstructured, so that the signal is invariant to a permutation of the feature indices. However, in structured data lying on a manifold (such as images, text, and speech) deep networks (Networks), specifically convolutional deep networks (ConvNets), tend to outperform Forests. We conjecture that at least pa…
Fox Chase Cancer Center（福克斯蔡斯癌症中心）；University of Kansas（堪萨斯大学）
Over the past decade, random forest models have become widely used as a robust method for high-dimensional data regression tasks. In part, the popularity of these models arises from the fact that they require little hyperparameter tuning and are not very susceptible to overfitting. Random forest regression models are comprised of an ensemble of decision trees that independently predict the value of a (continuous) dependent variable; predictions from each of the trees are ultimately averaged to yield an overall predicted value from the forest. Using a suite of representative real-world datasets…
This article provides an overview of Supervised Machine Learning (SML) with a focus on applications to banking. The SML techniques covered include Bagging (Random Forest or RF), Boosting (Gradient Boosting Machine or GBM) and Neural Networks (NNs). We begin with an introduction to ML tasks and techniques. This is followed by a description of: i) tree-based ensemble algorithms including Bagging with RF and Boosting with GBMs, ii) Feedforward NNs, iii) a discussion of hyper-parameter optimization techniques, and iv) machine learning interpretability. The paper concludes with a comparison of the …
Vanderbilt University（范德堡大学）；University of Notre Dame（圣母大学）；Department of Psychology and Human Development（心理与人类发展系）；Department of Applied and Computational Mathematics & Statistics（应用与计算数学及统计学系）；Nashville, TN（纳什维尔，田纳西州）；Notre Dame, IN（圣母大学，印第安纳州）
We propose a novel tree-based ensemble method named Selective Cascade of Residual ExtraTrees (SCORE). SCORE draws inspiration from representation learning, incorporates regularized regression with variable selection features, and utilizes boosting to improve prediction and reduce generalization errors. We also develop a variable importance measure to increase the explainability of SCORE. Our computer experiments show that SCORE provides comparable or superior performance in prediction against ExtraTrees, random forest, gradient boosting machine, and neural networks; and the proposed variable i…
University of Amsterdam（阿姆斯特丹大学）；Ahold Delhaize（皇家阿霍德德尔海兹集团）
Understanding how "black-box" models arrive at their predictions has sparked significant interest from both within and outside the AI community. Our work focuses on doing this by generating local explanations about individual predictions for tree-based ensembles, specifically Gradient Boosting Decision Trees (GBDTs). Given a correctly predicted instance in the training set, we wish to generate a counterfactual explanation for this instance, that is, the minimal perturbation of this instance such that the prediction flips to the opposite class. Most existing methods for counterfactual explanati…
University of California, Davis（加州大学戴维斯分校）；Google Research（谷歌研究院）
In this paper, we present a novel massively parallel algorithm for accelerating the decision tree building procedure on GPUs (Graphics Processing Units), which is a crucial step in Gradient Boosted Decision Tree (GBDT) and random forests training. Previous GPU based tree building algorithms are based on parallel multi-scan or radix sort to find the exact tree split, and thus suffer from scalability and performance issues. We show that using a histogram based algorithm to approximately find the best split is more efficient and scalable on GPU. By identifying the difference between classical GPU…
University of Maryland, College Park（马里兰大学帕克分校）；Capital One（第一资本金融公司）
Tabular data underpins numerous high-impact applications of machine learning from fraud detection to genomics and healthcare. Classical approaches to solving tabular problems, such as gradient boosting and random forests, are widely used by practitioners. However, recent deep learning methods have achieved a degree of performance competitive with popular techniques. We devise a hybrid deep learning approach to solving tabular data problems. Our method, SAINT, performs attention over both rows and columns, and it includes an enhanced embedding method. We also study a new contrastive self-superv…
Labs（8080实验室）；Department of Statistics, TU Dortmund University（多特蒙德工业大学统计系）
The induction of additional randomness in parallel and sequential ensemble methods has proven to be worthwhile in many aspects. In this manuscript, we propose and examine a novel random tree depth injection approach suitable for sequential and parallel tree-based approaches including Boosting and Random Forests. The resulting methods are called \emph{Random Boost} and \emph{Random$^2$ Forest}. Both approaches serve as valuable extensions to the existing literature on the gradient boosting framework and random forests. A Monte Carlo simulation, in which tree-shaped data sets with different numb…
National Research University Higher School of Economics（国立研究型大学高等经济学院）
In machine learning ensemble methods have demonstrated high accuracy for the variety of problems in different areas. Two notable ensemble methods widely used in practice are gradient boosting and random forests. In this paper we present InfiniteBoost - a novel algorithm, which combines important properties of these two approaches. The algorithm constructs the ensemble of trees for which two properties hold: trees of the ensemble incorporate the mistakes done by others; at the same time the ensemble could contain the infinite number of trees without the over-fitting effect. The proposed algorit…
We consider the problem of learning a forest of nonlinear decision rules with general loss functions. The standard methods employ boosted decision trees such as Adaboost for exponential loss and Friedman's gradient boosting for general loss. In contrast to these traditional boosting algorithms that treat a tree learner as a black box, the method we propose directly learns decision forests via fully-corrective regularized greedy search using the underlying forest structure. Our method achieves higher accuracy and smaller models than gradient boosting (and Adaboost with exponential loss) on many…
Huazhong University of Science and Technology（华中科技大学）；Shenzhen Huazhong University of Science and Technology Research Institute（深圳华中科技大学研究院）；Autonomous Intelligence Unmanned Systems Engineering Research Center of Ministry of Education of China（教育部自主智能无人系统工程研究中心）；State Key Lab of Digital Manufacturing Equipment and Technology（数字制造装备与技术国家重点实验室）
Bootstrap aggregating (Bagging) and boosting are two popular ensemble learning approaches, which combine multiple base learners to generate a composite model for more accurate and more reliable performance. They have been widely used in biology, engineering, healthcare, etc. This paper proposes BoostForest, which is an ensemble learning approach using BoostTree as base learners and can be used for both classification and regression. BoostTree constructs a tree model by gradient boosting. It increases the randomness (diversity) by drawing the cut-points randomly at node splitting. BoostForest f…
State Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；University of Cambridge（剑桥大学）
The random subspace method, known as the pillar of random forests, is good at making precise and robust predictions. However, there is not a straightforward way yet to combine it with deep learning. In this paper, we therefore propose Neural Random Subspace (NRS), a novel deep learning based random subspace method. In contrast to previous forest methods, NRS enjoys the benefits of end-to-end, data-driven representation learning, as well as pervasive support from deep learning software and hardware platforms, hence achieving faster inference speed and higher accuracy. Furthermore, as a non-line…
This research focuses on predicting the demand for air taxi urban air mobility (UAM) services during different times of the day in various geographic regions of New York City using machine learning algorithms (MLAs). Several ride-related factors (such as month of the year, day of the week and time of the day) and weather-related variables (such as temperature, weather conditions and visibility) are used as predictors for four popular MLAs, namely, logistic regression, artificial neural networks, random forests, and gradient boosting. Experimental results suggest gradient boosting to consistent…
Due to their accuracies, methods based on ensembles of regression trees are a popular approach for making predictions. Some common examples include Bayesian additive regression trees, boosting and random forests. This paper focuses on honest random forests, which add honesty to the original form of random forests and are proved to have better statistical properties. The main contribution is a new method that quantifies the uncertainties of the estimates and predictions produced by honest random forests. The proposed method is based on the generalized fiducial methodology, and provides a fiduci…
Faculty of Economics and Business, KU Leuven（比利时鲁汶大学经济与管理学院）；LRisk, Leuven Research Center on Insurance and Financial Risk Analysis, KU Leuven（比利时鲁汶大学保险与金融风险分析研究中心（LRisk））；École d’actuariat, Université Laval（加拿大拉瓦尔大学精算学院）；Faculty of Economics and Business, University of Amsterdam（荷兰阿姆斯特丹大学经济与管理学院）；Faculty of Economics and Business, KU Leuven, Belgium（比利时鲁汶大学经济与管理学院）；LRisk, Leuven Research Center on Insurance and Financial Risk Analysis, KU Leuven, Belgium（比利时鲁汶大学保险与金融风险分析研究中心（LRisk））
Pricing actuaries typically operate within the framework of generalized linear models (GLMs). With the upswing of data analytics, our study puts focus on machine learning methods to develop full tariff plans built from both the frequency and severity of claims. We adapt the loss functions used in the algorithms such that the specific characteristics of insurance data are carefully incorporated: highly unbalanced count data with excess zeros and varying exposure on the frequency side combined with scarce, but potentially long-tailed data on the severity side. A key requirement is the need for t…
The Ohio State University（俄亥俄州立大学）；Columbia University（哥伦比亚大学）；Cold Spring Harbor Laboratory（冷泉港实验室）
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performance is consistently robust even when the data contain large amounts of label noise. Very little theory is available to explain these observations. The vast majority of theoretical analyses of generaliza…
Bayesian Optimization is a popular tool for tuning algorithms in automatic machine learning (AutoML) systems. Current state-of-the-art methods leverage Random Forests or Gaussian processes to build a surrogate model that predicts algorithm performance given a certain set of hyperparameter settings. In this paper, we propose a new surrogate model based on gradient boosting, where we use quantile regression to provide optimistic estimates of the performance of an unobserved hyperparameter setting, and combine this with a distance metric between unobserved and observed hyperparameter settings to …
Multi-layered representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are the dominant methods for modeling discrete or tabular data, they are hard to incorporate with such representation learning ability. In this work, we propose the multi-layered GBDT forest (mGBDTs), with an explicit emphasis on exploring the ability to learn hierarchical representations by stacking several layers of regression GBDTs as its building block. The model can be …
We propose a new method for supervised learning. The hubNet procedure fits a hub-based graphical model to the predictors, to estimate the amount of "connection" that each predictor has with other predictors. This yields a set of predictor weights that are then used in a regularized regression such as the lasso or elastic net. The resulting procedure is easy to implement, can sometimes yields higher prediction accuracy that the lasso, and can give insights into the underlying structure of the predictors. HubNet can also be generalized seamlessly to other supervised problems such as regularized …
Statistical Inference for Gradient Boosting Regression
School of Economics, Fudan University（复旦大学经济学院）；Department of Statistics and Data Science, The Wharton School, University of Pennsylvania（宾夕法尼亚大学沃顿商学院统计与数据科学系）
This paper extends recent work on boosting random forests to model non-Gaussian responses. Given an exponential family $\mathbb{E}[Y|X] = g^{-1}(f(X))$ our goal is to obtain an estimate for $f$. We start with an MLE-type estimate in the link space and then define generalised residuals from it. We use these residuals and some corresponding weights to fit a base random forest and then repeat the same to obtain a boost random forest. We call the sum of these three estimators a \textit{generalised boosted forest}. We show with simulated and real data that both the random forest steps reduces test-…
Aix-Marseille University（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）；EHESS（社会科学高等学院）；Aix-Marseille Graduate School of Management – IAE（艾克斯-马赛管理学院-IAE）
Despite their high predictive performance, random forest and gradient boosting are often considered as black boxes or uninterpretable models which has raised concerns from practitioners and regulators. As an alternative, we propose in this paper to use partial linear models that are inherently interpretable. Specifically, this article introduces GAM-lasso (GAMLA) and GAM-autometrics (GAMA), denoted as GAM(L)A in short. GAM(L)A combines parametric and non-parametric functions to accurately capture linearities and non-linearities prevailing between dependent and explanatory variables, and a vari…
University of Twente（特文特大学）；Renmin University of China（中国人民大学）；Peking University（北京大学）
In this paper, we propose a gradient boosting algorithm for large-scale regression problems called \textit{Gradient Boosted Binary Histogram Ensemble} (GBBHE) based on binary histogram partition and ensemble learning. From the theoretical perspective, by assuming the Hölder continuity of the target function, we establish the statistical convergence rate of GBBHE in the space $C^{0,α}$ and $C^{1,0}$, where a lower bound of the convergence rate for the base learner demonstrates the advantage of boosting. Moreover, in the space $C^{1,0}$, we prove that the number of iterations to achieve the fast…
