Boosting is a celebrated machine learning approach which is based on the idea of combining weak and moderately inaccurate hypotheses to a strong and accurate one. We study boosting under the assumption that the weak hypotheses belong to a class of bounded capacity. This assumption is inspired by the common convention that weak hypotheses are "rules-of-thumbs" from an "easy-to-learn class". (Schapire and Freund~'12, Shalev-Shwartz and Ben-David '14.) Formally, we assume the class of weak hypotheses has a bounded VC dimension. We focus on two main questions: (i) Oracle Complexity: How many weak hypotheses are needed to produce an accurate hypothesis? We design a novel boosting algorithm and demonstrate that it circumvents a classical lower bound by Freund and Schapire ('95, '12). Whereas the lower bound shows that $Ω({1}/{γ^2})$ weak hypotheses with $γ$-margin are sometimes necessary, our new method requires only $\tilde{O}({1}/γ)$ weak hypothesis, provided that they belong to a class of bounded VC dimension. Unlike previous boosting algorithms which aggregate the weak hypotheses by majority votes, the new boosting algorithm uses more complex ("deeper") aggregation rules. We complement this result by showing that complex aggregation rules are in fact necessary to circumvent the aforementioned lower bound. (ii) Expressivity: Which tasks can be learned by boosting weak hypotheses from a bounded VC class? Can complex concepts that are "far away" from the class be learned? Towards answering the first question we {introduce combinatorial-geometric parameters which capture expressivity in boosting.} As a corollary we provide an affirmative answer to the second question for well-studied classes, including half-spaces and decision stumps. Along the way, we establish and exploit connections with Discrepancy Theory.
Lucerne University of Applied Sciences and Arts（卢塞恩应用科学与艺术大学）
We introduce a novel boosting algorithm called `KTBoost' which combines kernel boosting and tree boosting. In each boosting iteration, the algorithm adds either a regression tree or reproducing kernel Hilbert space (RKHS) regression function to the ensemble of base learners. Intuitively, the idea is that discontinuous trees and continuous RKHS regression functions complement each other, and that this combination allows for better learning of functions that have parts with varying degrees of regularity such as discontinuities and smooth parts. We empirically show that KTBoost significantly outp…
Developing efficient kernel methods for regression is very popular in the past decade. In this paper, utilizing boosting on kernel-based weaker learners, we propose a novel kernel-based learning algorithm called kernel-based re-scaled boosting with truncation, dubbed as KReBooT. The proposed KReBooT benefits in controlling the structure of estimators and producing sparse estimate, and is near overfitting resistant. We conduct both theoretical analysis and numerical simulations to illustrate the power of KReBooT. Theoretically, we prove that KReBooT can achieve the almost optimal numerical conv…
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…
Stochastic gradient descent (SGD) has been the dominant optimization method for training deep neural networks due to its many desirable properties. One of the more remarkable and least understood quality of SGD is that it generalizes relatively well on unseen data even when the neural network has millions of parameters. We hypothesize that in certain cases it is desirable to relax its intrinsic generalization properties and introduce an extension of SGD called deep gradient boosting (DGB). The key idea of DGB is that back-propagated gradients inferred using the chain rule can be viewed as pseu…
Université de Paris（巴黎大学）；Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）
Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a functional variable. This paper proposes to build upon the proximal point algorithm, when the empirical risk to minimize is not differentiable, in order to introduce a novel boosting approach, called proximal boosting. It comes with a companion algorithm inspired by [1] and called residual proximal boosting, which is aimed at better controlling the approximation er…
Sinovation Ventures AI Institute（创新工场人工智能研究院）；Baiont Technology（百融科技）；Nanjing University（南京大学）
Gradient Boosting Machine has proven to be one successful function approximator and has been widely used in a variety of areas. However, since the training procedure of each base learner has to take the sequential order, it is infeasible to parallelize the training process among base learners for speed-up. In addition, under online or incremental learning settings, GBMs achieved sub-optimal performance due to the fact that the previously trained base learners can not adapt with the environment once trained. In this work, we propose the soft Gradient Boosting Machine (sGBM) by wiring multiple d…
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…
Toyota Technological Institute at Chicago（芝加哥丰田工学院）；University of Waterloo（滑铁卢大学）
We present an oracle-efficient algorithm for boosting the adversarial robustness of barely robust learners. Barely robust learning algorithms learn predictors that are adversarially robust only on a small fraction $β\ll 1$ of the data distribution. Our proposed notion of barely robust learning requires robustness with respect to a "larger" perturbation set; which we show is necessary for strongly robust learning, and that weaker relaxations are not sufficient for strongly robust learning. Our results reveal a qualitative and quantitative equivalence between two seemingly unrelated problems: st…
Institute of Information Science, Academia Sinica（中央研究院信息科学研究所）；Department of Computer Science and Information Engineering, National Taiwan University（台湾大学计算机科学与信息工程学系）
We study the task of online boosting--combining online weak learners into an online strong learner. While batch boosting has a sound theoretical foundation, online boosting deserves more study from the theoretical perspective. In this paper, we carefully compare the differences between online and batch boosting, and propose a novel and reasonable assumption for the online weak learner. Based on the assumption, we design an online boosting algorithm with a strong theoretical guarantee by adapting from the offline SmoothBoost algorithm that matches the assumption closely. We further tackle the t…
University of Michigan（密歇根大学）；Department of Computer Science（计算机科学系）；Department of Statistics（统计系）
We present online boosting algorithms for multiclass classification with bandit feedback, where the learner only receives feedback about the correctness of its prediction. We propose an unbiased estimate of the loss using a randomized prediction, allowing the model to update its weak learners with limited information. Using the unbiased estimate, we extend two full information boosting algorithms (Jung et al., 2017) to the bandit setting. We prove that the asymptotic error bounds of the bandit algorithms exactly match their full information counterparts. The cost of restricted feedback is refl…
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。
Boston University（波士顿大学）；Simon Fraser University（西蒙弗雷泽大学）；University of California, San Diego（加利福尼亚大学圣地亚哥分校）
We introduce a simple framework for designing private boosting algorithms. We give natural conditions under which these algorithms are differentially private, efficient, and noise-tolerant PAC learners. To demonstrate our framework, we use it to construct noise-tolerant and private PAC learners for large-margin halfspaces whose sample complexity does not depend on the dimension. We give two sample complexity bounds for our large-margin halfspace learner. One bound is based only on differential privacy, and uses this guarantee as an asset for ensuring generalization. This first bound illustrate…
Beijing Institute of Technology（北京理工大学）；NICTA（澳大利亚国家信息与通信技术研究院）；Australian National University（澳大利亚国立大学）
In this work, we propose a new optimization framework for multiclass boosting learning. In the literature, AdaBoost.MO and AdaBoost.ECC are the two successful multiclass boosting algorithms, which can use binary weak learners. We explicitly derive these two algorithms' Lagrange dual problems based on their regularized loss functions. We show that the Lagrange dual formulations enable us to design totally-corrective multiclass algorithms by using the primal-dual optimization technique. Experiments on benchmark data sets suggest that our multiclass boosting can achieve a comparable generalizatio…
Boosting is a fundamental approach in machine learning that enjoys both strong theoretical and practical guarantees. At a high-level, boosting algorithms cleverly aggregate weak learners to generate predictions with arbitrarily high accuracy. In this way, boosting algorithms convert weak learners into strong ones. Recently, Brukhim et al. extended boosting to the online agnostic binary classification setting. A key ingredient in their approach is a clean and simple reduction to online convex optimization, one that efficiently converts an arbitrary online convex optimizer to an agnostic online …
Princeton University（普林斯顿大学）；Google AI Princeton（谷歌人工智能普林斯顿（Google AI Princeton））
Boosting is a widely used machine learning approach based on the idea of aggregating weak learning rules. While in statistical learning numerous boosting methods exist both in the realizable and agnostic settings, in online learning they exist only in the realizable case. In this work we provide the first agnostic online boosting algorithm; that is, given a weak learner with only marginally-better-than-trivial regret guarantees, our algorithm boosts it to a strong learner with sublinear regret. Our algorithm is based on an abstract (and simple) reduction to online convex optimization, which ef…
University of Michigan（密歇根大学）；Department of Statistics（统计系）
We consider the multi-label ranking approach to multi-label learning. Boosting is a natural method for multi-label ranking as it aggregates weak predictions through majority votes, which can be directly used as scores to produce a ranking of the labels. We design online boosting algorithms with provable loss bounds for multi-label ranking. We show that our first algorithm is optimal in terms of the number of learners required to attain a desired accuracy, but it requires knowledge of the edge of the weak learners. We also design an adaptive algorithm that does not require this knowledge and is…
We study online boosting, the task of converting any weak online learner into a strong online learner. Based on a novel and natural definition of weak online learnability, we develop two online boosting algorithms. The first algorithm is an online version of boost-by-majority. By proving a matching lower bound, we show that this algorithm is essentially optimal in terms of the number of weak learners and the sample complexity needed to achieve a specified accuracy. This optimal algorithm is not adaptive however. Using tools from online loss minimization, we derive an adaptive online boosting a…
Gradient Boosting Machines (GBM) are among the go-to algorithms on tabular data, which produce state of the art results in many prediction tasks. Despite its popularity, the GBM framework suffers from a fundamental flaw in its base learners. Specifically, most implementations utilize decision trees that are typically biased towards categorical variables with large cardinalities. The effect of this bias was extensively studied over the years, mostly in terms of predictive performance. In this work, we extend the scope and study the effect of biased base learners on GBM feature importance (FI) m…
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting with respect to any convex objective and introduce a new measure of weak learner performance into this setting which generalizes existing work. We present the weak to strong learning guarantees for the existing gradient boosting work for strongly-smooth, strongly-convex objectives under this new measure of performance, and also demonstrate that this work fails…
University of Amsterdam（阿姆斯特丹大学）；QuSoft（QuSoft 量子软件研究中心）；CWI（荷兰国家数学与计算机科学研究中心）
Boosting is a general method to convert a weak learner (which generates hypotheses that are just slightly better than random) into a strong learner (which generates hypotheses that are much better than random). Recently, Arunachalam and Maity gave the first quantum improvement for boosting, by combining Freund and Schapire's AdaBoost algorithm with a quantum algorithm for approximate counting. Their booster is faster than classical boosting as a function of the VC-dimension of the weak learner's hypothesis class, but worse as a function of the quality of the weak learner. In this paper we give…
Object recognition in images involves identifying objects with partial occlusions, viewpoint changes, varying illumination, cluttered backgrounds. Recent work in object recognition uses machine learning techniques SVM-KNN, Local Ensemble Kernel Learning, Multiple Kernel Learning. In this paper, we want to utilize SVM as week learners in AdaBoost. Experiments are done with classifiers like near- est neighbor, k-nearest neighbor, Support vector machines, Local learning(SVM- KNN) and AdaBoost. Models use Scale-Invariant descriptors and Pyramid his- togram of gradient descriptors. AdaBoost is trai…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of California-San Diego（加州大学圣地亚哥分校）
We study the problem of boosting the accuracy of a weak learner in the (distribution-independent) PAC model with Massart noise. In the Massart noise model, the label of each example $x$ is independently misclassified with probability $η(x) \leq η$, where $η<1/2$. The Massart model lies between the random classification noise model and the agnostic model. Our main positive result is the first computationally efficient boosting algorithm in the presence of Massart noise that achieves misclassification error arbitrarily close to $η$. Prior to our work, no non-trivial booster was known in this set…
Projected Boosting with Fairness Constraints: Quantifying the Cost of Fair Training Distributions
Department of Biostatistics, Vanderbilt University Medical Center, Nashville, TN 37232, USA（生物统计学系，范德比尔特大学医学中心）；Department of Informatics, King's College London, WC2R 2LS London, UK（信息学系，伦敦国王学院）
Recent work has extended the theoretical analysis of boosting algorithms to multiclass problems and to online settings. However, the multiclass extension is in the batch setting and the online extensions only consider binary classification. We fill this gap in the literature by defining, and justifying, a weak learning condition for online multiclass boosting. This condition leads to an optimal boosting algorithm that requires the minimal number of weak learners to achieve a certain accuracy. Additionally, we propose an adaptive algorithm which is near optimal and enjoys an excellent performan…
Reducing Learner Redundancy in Boosting via Residual Orthogonalization
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；College of Information Science and Technology, Beijing University of Chemical Technology（北京化工大学信息科学与技术学院）；Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）；School of Computer Science, Central China Normal University（华中师范大学计算机学院）；the School of Computing, Engineering and Mathematical Sciences, La Trobe University（拉筹伯大学计算、工程与数学科学学院）
Wepresentanovelcolumngenerationbasedboostingmethod for multi-class classification. Our multi-class boosting is formulated in a single optimization problem as in Shen and Hao (2011). Different from most existing multi-class boosting methods, which use the same set of weak learners for all the classes, we train class specified weak learners (i.e., each class has a different set of weak learners). We show that using separate weak learner sets for each class leads to fast convergence, without introducing additional computational overhead in the training procedure. To further make the training more…
We present a simple unified framework for multi-class cost-sensitive boosting. The minimum-risk class is estimated directly, rather than via an approximation of the posterior distribution. Our method jointly optimizes binary weak learners and their corresponding output vectors, requiring classes to share features at each iteration. By training in a cost-sensitive manner, weak learners are invested in separating classes whose discrimination is important, at the expense of less relevant classification boundaries. Additional contributions are a family of loss functions along with proof that our a…
Machine learning based computational intelligence methods are widely used to analyze large scale data sets in this age of big data. Extracting useful predictive modeling from these types of data sets is a challenging problem due to their high complexity. Analyzing large amount of streaming data that can be leveraged to derive business value is another complex problem to solve. With high levels of data availability (\textit{i.e. Big Data}) automatic classification of them has become an important and complex task. Hence, we explore the power of applying MapReduce based Distributed AdaBoosting of…
We consider the problem of boosting the accuracy of weak learning algorithms in the agnostic learning framework of Haussler (1992) and Kearns et al. (1992). Known algorithms for this problem (Ben-David et al., 2001; Gavinsky, 2002; Kalai et al., 2008) follow the same strategy as boosting algorithms in the PAC model: the weak learner is executed on the same target function but over different distributions on the domain. We demonstrate boosting algorithms for the agnostic learning framework that only modify the distribution on the labels of the points (or, equivalently, modify the target functio…
Boosting is a popular ensemble algorithm that generates more powerful learners by linearly combining base models from a simpler hypothesis class. In this work, we investigate the problem of adapting batch gradient boosting for minimizing convex loss functions to online setting where the loss at each iteration is i.i.d sampled from an unknown distribution. To generalize from batch to online, we first introduce the definition of online weak learning edge with which for strongly convex and smooth loss functions, we present an algorithm, Streaming Gradient Boosting (SGB) with exponential shrinkage…
For various optimization methods, gradient descent-based algorithms can achieve outstanding performance and have been widely used in various tasks. Among those commonly used algorithms, ADAM owns many advantages such as fast convergence with both the momentum term and the adaptive learning rate. However, since the loss functions of most deep neural networks are non-convex, ADAM also shares the drawback of getting stuck in local optima easily. To resolve such a problem, the idea of combining genetic algorithm with base learners is introduced to rediscover the best solutions. Nonetheless, from o…
National University of Singapore（新加坡国立大学）；Tsinghua University（清华大学）；Renmin University of China（中国人民大学）；University of Science and Technology of China（中国科学技术大学）；Hefei Comprehensive National Science Center（合肥综合性国家科学中心）
Under stringent model type and variable distribution assumptions, differentiable score-based causal discovery methods learn a directed acyclic graph (DAG) from observational data by evaluating candidate graphs over an average score function. Despite great success in low-dimensional linear systems, it has been observed that these approaches overly exploit easier-to-fit samples, thus inevitably learning spurious edges. Worse still, inherent mostly in these methods the common homogeneity assumption can be easily violated, due to the widespread existence of heterogeneous data in the real world, re…
National Technical University of Athens（雅典国家技术大学）；Hellenic Air Force（希腊空军）
Machine learning algorithms have been extensively exploited in energy research, due to their flexibility, automation and ability to handle big data. Among the most prominent machine learning algorithms are the boosting ones, which are known to be "garnering wisdom from a council of fools", thereby transforming weak learners to strong learners. Boosting algorithms are characterized by both high flexibility and high interpretability. The latter property is the result of recent developments by the statistical community. In this work, we provide understanding on the properties of boosting algorith…
Yale University（耶鲁大学）；Renmin University of China（中国人民大学）；JD Technology Group（京东科技集团）
Federated learning, conducive to solving data privacy and security problems, has attracted increasing attention recently. However, the existing federated boosting model sequentially builds a decision tree model with the weak base learner, resulting in redundant boosting steps and high interactive communication costs. In contrast, the federated bagging model saves time by building multi-decision trees in parallel, but it suffers from performance loss. With the aim of obtaining an outstanding performance with less time cost, we propose a novel model in a vertically federated setting termed as Fe…
Universidad Autónoma de Madrid（马德里自治大学）；Escuela Politécnica Superior（高等理工学院）
Vote-boosting is a sequential ensemble learning method in which the individual classifiers are built on different weighted versions of the training data. To build a new classifier, the weight of each training instance is determined in terms of the degree of disagreement among the current ensemble predictions for that instance. For low class-label noise levels, especially when simple base learners are used, emphasis should be made on instances for which the disagreement rate is high. When more flexible classifiers are used and as the noise level increases, the emphasis on these uncertain instan…
Boosting is a method for learning a single accurate predictor by linearly combining a set of less accurate weak learners. Recently, structured learning has found many applications in computer vision. Inspired by structured support vector machines (SSVM), here we propose a new boosting algorithm for structured output prediction, which we refer to as StructBoost. StructBoost supports nonlinear structured learning by combining a set of weak structured learners. As SSVM generalizes SVM, our StructBoost generalizes standard boosting approaches such as AdaBoost, or LPBoost to structured learning. Th…
We present a theory of boosting probabilistic classifiers. We place ourselves in the situation of a user who only provides a stopping parameter and a probabilistic weak learner/classifier and compare three types of boosting algorithms: probabilistic Adaboost, decision tree, and tree of trees of ... of trees, which we call matryoshka. "Nested tree," "embedded tree" and "recursive tree" are also appropriate names for this algorithm, which is one of our contributions. Our other contribution is the theoretical analysis of the algorithms, in which we give training error bounds. This analysis sugges…
Combining the merits of both denoising diffusion probabilistic models and gradient boosting, the diffusion boosting paradigm is introduced for tackling supervised learning problems. We develop Diffusion Boosted Trees (DBT), which can be viewed as both a new denoising diffusion generative model parameterized by decision trees (one single tree for each diffusion timestep), and a new boosting algorithm that combines the weak learners into a strong learner of conditional distributions without making explicit parametric assumptions on their density forms. We demonstrate through experiments the adva…
