Gradient tree boosting is a prediction algorithm that sequentially produces a model in the form of linear combinations of decision trees, by solving an infinite-dimensional optimization problem. We combine gradient boosting and Nesterov's accelerated descent to design a new algorithm, which we call AGB (for Accelerated Gradient Boosting). Substantial numerical evidence is provided on both synthetic and real-life data sets to assess the excellent performance of the method in a large variety of prediction problems. It is empirically shown that AGB is much less sensitive to the shrinkage parameter and outputs predictors that are considerably more sparse in the number of trees, while retaining the exceptional performance of gradient boosting.
As an adaptive, interpretable, robust, and accurate meta-algorithm for arbitrary differentiable loss functions, gradient tree boosting is one of the most popular machine learning techniques, though the computational expensiveness severely limits its usage. Stochastic gradient boosting could be adopted to accelerates gradient boosting by uniformly sampling training instances, but its estimator could introduce a high variance. This situation arises motivation for us to optimize gradient tree boosting. We combine gradient tree boosting with importance sampling, which achieves better performance b…
Point Zero One Technology（Point Zero One科技公司）；Fordham University（福特汉姆大学）；Imperial College London（帝国理工学院）；Massachusetts Institute of Technology（麻省理工学院）
In this survey, we discuss several different types of gradient boosting algorithms and illustrate their mathematical frameworks in detail: 1. introduction of gradient boosting leads to 2. objective function optimization, 3. loss function estimations, and 4. model constructions. 5. application of boosting in ranking.
Yandex；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；HSE University（俄罗斯国立高等经济学院）
This paper introduces Stochastic Gradient Langevin Boosting (SGLB) - a powerful and efficient machine learning framework that may deal with a wide range of loss functions and has provable generalization guarantees. The method is based on a special form of the Langevin diffusion equation specifically designed for gradient boosting. This allows us to theoretically guarantee the global convergence even for multimodal loss functions, while standard gradient boosting algorithms can guarantee only local optimum. We also empirically show that SGLB outperforms classic gradient boosting when applied to…
Lucerne University of Applied Sciences and Arts（卢塞恩应用科学与艺术大学）
Boosting algorithms are frequently used in applied data science and in research. To date, the distinction between boosting with either gradient descent or second-order Newton updates is often not made in both applied and methodological research, and it is thus implicitly assumed that the difference is irrelevant. The goal of this article is to clarify this situation. In particular, we present gradient and Newton boosting, as well as a hybrid variant of the two, in a unified framework. We compare these boosting algorithms with trees as base learners using various datasets and loss functions. Ou…
Yandex；HSE University（高等经济大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
For many practical, high-risk applications, it is essential to quantify uncertainty in a model's predictions to avoid costly mistakes. While predictive uncertainty is widely studied for neural networks, the topic seems to be under-explored for models based on gradient boosting. However, gradient boosting often achieves state-of-the-art results on tabular data. This work examines a probabilistic ensemble-based framework for deriving uncertainty estimates in the predictions of gradient boosting classification and regression models. We conducted experiments on a range of synthetic and real datase…
Peter the Great St.Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
The gradient boosting machine is a powerful ensemble-based machine learning method for solving regression problems. However, one of the difficulties of its using is a possible discontinuity of the regression function, which arises when regions of training data are not densely covered by training points. In order to overcome this difficulty and to reduce the computational complexity of the gradient boosting machine, we propose to apply the partially randomized trees which can be regarded as a special case of the extremely randomized trees applied to the gradient boosting. The gradient boosting …
Peter the Great St.Petersburg Polytechnic University（圣彼得堡彼得大帝理工大学）
The gradient boosting machine is one of the powerful tools for solving regression problems. In order to cope with its shortcomings, an approach for constructing ensembles of gradient boosting models is proposed. The main idea behind the approach is to use the stacking algorithm in order to learn a second-level meta-model which can be regarded as a model for implementing various ensembles of gradient boosting models. First, the linear regression of the gradient boosting models is considered as a simplest realization of the meta-model under condition that the linear model is differentiable with …
Stanford University（斯坦福大学）；Harvard Medical School（哈佛医学院）
We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparame…
This paper shows that gradient boosting based on symmetric decision trees can be equivalently reformulated as a kernel method that converges to the solution of a certain Kernel Ridge Regression problem. Thus, we obtain the convergence to a Gaussian Process' posterior mean, which, in turn, allows us to easily transform gradient boosting into a sampler from the posterior to provide better knowledge uncertainty estimates through Monte-Carlo estimation of the posterior variance. We show that the proposed sampler allows for better knowledge uncertainty estimates leading to improved out-of-domain de…
A novel gradient boosting framework is proposed where shallow neural networks are employed as ``weak learners''. General loss functions are considered under this unified framework with specific examples presented for classification, regression, and learning to rank. A fully corrective step is incorporated to remedy the pitfall of greedy function approximation of classic gradient boosting decision tree. The proposed model rendered outperforming results against state-of-the-art boosting methods in all three tasks on multiple datasets. An ablation study is performed to shed light on the effect of…
In this paper, we propose a gradient boosting algorithm called \textit{adaptive boosting histogram transform} (\textit{ABHT}) for regression to illustrate the local adaptivity of gradient boosting algorithms in histogram transform ensemble learning. From the theoretical perspective, when the target function lies in a locally Hölder continuous space, we show that our ABHT can filter out the regions with different orders of smoothness. Consequently, we are able to prove that the upper bound of the convergence rates of ABHT is strictly smaller than the lower bound of \textit{parallel ensemble his…
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…
We present a unified probabilistic gradient boosting framework for regression tasks that models and predicts the entire conditional distribution of a univariate response variable as a function of covariates. Our likelihood-based approach allows us to either model all conditional moments of a parametric distribution, or to approximate the conditional cumulative distribution function via Normalizing Flows. As underlying computational backbones, our framework is based on XGBoost and LightGBM. Modelling and predicting the entire conditional distribution greatly enhances existing tree-based gradien…
University of Michigan（密歇根大学）；ShanghaiTech University（上海科技大学）；IBM Research（IBM研究院）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）
We consider the task of enforcing individual fairness in gradient boosting. Gradient boosting is a popular method for machine learning from tabular data, which arise often in applications where algorithmic fairness is a concern. At a high level, our approach is a functional gradient descent on a (distributionally) robust loss function that encodes our intuition of algorithmic fairness for the ML task at hand. Unlike prior approaches to individual fairness that only work with smooth ML models, our approach also works with non-smooth models such as decision trees. We show that our algorithm conv…
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…
Google（谷歌）；University of Chicago（芝加哥大学）；EPFL（洛桑联邦理工学院）
Gradient Boosting Machine (GBM) is an extremely powerful supervised learning algorithm that is widely used in practice. GBM routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In this work, we propose Accelerated Gradient Boosting Machine (AGBM) by incorporating Nesterov's acceleration techniques into the design of GBM. The difficulty in accelerating GBM lies in the fact that weak (inexact) learners are commonly used, and therefore the errors can accumulate in the momentum term. To overcome it, we design a "corrected pseudo residual" and fi…
In this paper we present CatBoost, a new open-sourced gradient boosting library that successfully handles categorical features and outperforms existing publicly available implementations of gradient boosting in terms of quality on a set of popular publicly available datasets. The library has a GPU implementation of learning algorithm and a CPU implementation of scoring algorithm, which are significantly faster than other gradient boosting libraries on ensembles of similar sizes.
The University of California, San Diego（加州大学圣地亚哥分校）
Natural gradient has been recently introduced to the field of boosting to enable the generic probabilistic predication capability. Natural gradient boosting shows promising performance improvements on small datasets due to better training dynamics, but it suffers from slow training speed overhead especially for large datasets. We present a replication study of NGBoost(Duan et al., 2019) training that carefully examines the impacts of key hyper-parameters under the circumstance of best-first decision tree learning. We find that with the regularization of leaf number clipping, the performance of…
TF Boosted Trees (TFBT) is a new open-sourced frame-work for the distributed training of gradient boosted trees. It is based on TensorFlow, and its distinguishing features include a novel architecture, automatic loss differentiation, layer-by-layer boosting that results in smaller ensembles and faster prediction, principled multi-class handling, and a number of regularization techniques to prevent overfitting.
Yandex（Yandex（俄罗斯搜索引擎公司，可译为扬德克斯））；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Sberbank（俄罗斯联邦储蓄银行）
Stochastic Gradient Boosting (SGB) is a widely used approach to regularization of boosting models based on decision trees. It was shown that, in many cases, random sampling at each iteration can lead to better generalization performance of the model and can also decrease the learning time. Different sampling approaches were proposed, where probabilities are not uniform, and it is not currently clear which approach is the most effective. In this paper, we formulate the problem of randomization in SGB in terms of optimization of sampling probabilities to maximize the estimation accuracy of split…
University of Pennsylvania（宾夕法尼亚大学）；University of California, San Francisco（加利福尼亚大学旧金山分校）；University of Maryland Medical Center（马里兰大学医学中心）
Additive models, such as produced by gradient boosting, and full interaction models, such as classification and regression trees (CART), are widely used algorithms that have been investigated largely in isolation. We show that these models exist along a spectrum, revealing never-before-known connections between these two approaches. This paper introduces a novel technique called tree-structured boosting for creating a single decision tree, and shows that this method can produce models equivalent to CART or gradient boosted stumps at the extremes by varying a single parameter. Although tree-str…
Residual Networks (ResNets) have become state-of-the-art models in deep learning and several theoretical studies have been devoted to understanding why ResNet works so well. One attractive viewpoint on ResNet is that it is optimizing the risk in a functional space by combining an ensemble of effective features. In this paper, we adopt this viewpoint to construct a new gradient boosting method, which is known to be very powerful in data analysis. To do so, we formalize the gradient boosting perspective of ResNet mathematically using the notion of functional gradients and propose a new method ca…
Ricoh Institute of Information and Communication Technology（理光信息与通信技术研究所）；Ricoh Company（理光公司）
This study proposes a logic architecture for the high-speed and power efficiently training of a gradient boosting decision tree model of binary classification. We implemented the proposed logic architecture on an FPGA and compared training time and power efficiency with three general GBDT software libraries using CPU and GPU. The training speed of the logic architecture on the FPGA was 26-259 times faster than the software libraries. The power efficiency of the logic architecture was 90-1,104 times higher than the software libraries. The results show that the logic architecture suits for high-…
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…
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…
In this paper we introduce a significant improvement to the popular tree-based Stochastic Gradient Boosting algorithm using a wavelet decomposition of the trees. This approach is based on harmonic analysis and approximation theoretical elements, and as we show through extensive experimentation, our wavelet based method generally outperforms existing methods, particularly in difficult scenarios of class unbalance and mislabeling in the training data.
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 …
GPU-based algorithms have greatly accelerated many machine learning methods; however, GPU memory is typically smaller than main memory, limiting the size of training data. In this paper, we describe an out-of-core GPU gradient boosting algorithm implemented in the XGBoost library. We show that much larger datasets can fit on a given GPU, without degrading model accuracy or training time. To the best of our knowledge, this is the first out-of-core GPU implementation of gradient boosting. Similar approaches can be applied to other machine learning algorithms
Gradient boosting of regression trees is a competitive procedure for learning predictive models of continuous data that fits the data with an additive non-parametric model. The classic version of gradient boosting assumes that the data is independent and identically distributed. However, relational data with interdependent, linked instances is now common and the dependencies in such data can be exploited to improve predictive performance. Collective inference is one approach to exploit relational correlation patterns and significantly reduce classification error. However, much of the work on c…
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 …
Credit scoring plays a vital role in the field of consumer finance. Survival analysis provides an advanced solution to the credit-scoring problem by quantifying the probability of survival time. In order to deal with highly heterogeneous industrial data collected in Chinese market of consumer finance, we propose a nonparametric ensemble tree model called gradient boosting survival tree (GBST) that extends the survival tree models with a gradient boosting algorithm. The survival tree ensemble is learned by minimizing the negative log-likelihood in an additive manner. The proposed model optimize…
Peking University（北京大学）；University of Twente（特文特大学）；Pazhou Lab（琶洲实验室）
In this paper, we propose a density estimation algorithm called \textit{Gradient Boosting Histogram Transform} (GBHT), where we adopt the \textit{Negative Log Likelihood} as the loss function to make the boosting procedure available for the unsupervised tasks. From a learning theory viewpoint, we first prove fast convergence rates for GBHT with the smoothness assumption that the underlying density function lies in the space $C^{0,α}$. Then when the target density function lies in spaces $C^{1,α}$, we present an upper bound for GBHT which is smaller than the lower bound of its corresponding bas…
Peter the Great St.Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
A new attention-based model for the gradient boosting machine (GBM) called AGBoost (the attention-based gradient boosting) is proposed for solving regression problems. The main idea behind the proposed AGBoost model is to assign attention weights with trainable parameters to iterations of GBM under condition that decision trees are base learners in GBM. Attention weights are determined by applying properties of decision trees and by using the Huber's contamination model which provides an interesting linear dependence between trainable parameters of the attention and the attention weights. This…
CNRS（法国国家科学研究中心）；Inria Lille - Nord Europe（法国里尔-北欧数字科学研究所）
We propose a Gradient Boosting algorithm for learning an ensemble of kernel functions adapted to the task at hand. Unlike state-of-the-art Multiple Kernel Learning techniques that make use of a pre-computed dictionary of kernel functions to select from, at each iteration we fit a kernel by approximating it as a weighted sum of Random Fourier Features (RFF) and by optimizing their barycenter. This allows us to obtain a more versatile method, easier to setup and likely to have better performance. Our study builds on a recent result showing one can learn a kernel from RFF by computing the minimum…
Boosting is one of the most successful ideas in machine learning, achieving great practical performance with little fine-tuning. The success of boosted classifiers is most often attributed to improvements in margins. The focus on margin explanations was pioneered in the seminal work by Schapire et al. (1998) and has culminated in the $k$'th margin generalization bound by Gao and Zhou (2013), which was recently proved to be near-tight for some data distributions (Gronlund et al. 2019). In this work, we first demonstrate that the $k$'th margin bound is inadequate in explaining the performance of…
In many applications of supervised learning, multiple classification or regression outputs have to be predicted jointly. We consider several extensions of gradient boosting to address such problems. We first propose a straightforward adaptation of gradient boosting exploiting multiple output regression trees as base learners. We then argue that this method is only expected to be optimal when the outputs are fully correlated, as it forces the partitioning induced by the tree base learners to be shared by all outputs. We then propose a novel extension of gradient tree boosting to specifically ad…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
In this paper, we present a data-driven model for forecasting the production increase after hydraulic fracturing (HF). We use data from fracturing jobs performed at one of the Siberian oilfields. The data includes features, characterizing the jobs, and geological information. To predict an oil rate after the fracturing machine learning (ML) technique was applied. We compared the ML-based prediction to a prediction based on the experience of reservoir and production engineers responsible for the HF-job planning. We discuss the potential for further development of ML techniques for predicting ch…
Automatic machine learning performs predictive modeling with high performing machine learning tools without human interference. This is achieved by making machine learning applications parameter-free, i.e. only a dataset is provided while the complete model selection and model building process is handled internally through (often meta) optimization. Projects like Auto-WEKA and auto-sklearn aim to solve the Combined Algorithm Selection and Hyperparameter optimization (CASH) problem resulting in huge configuration spaces. However, for most real-world applications, the optimization over only a fe…
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…
Gradient Boosting Machines (GBM) are hugely popular for solving tabular data problems. However, practitioners are not only interested in point predictions, but also in probabilistic predictions in order to quantify the uncertainty of the predictions. Creating such probabilistic predictions is difficult with existing GBM-based solutions: they either require training multiple models or they become too computationally expensive to be useful for large-scale settings. We propose Probabilistic Gradient Boosting Machines (PGBM), a method to create probabilistic predictions with a single ensemble of d…
Gradient Regularized Newton Boosting Trees with Global Convergence
Department of Mathematics, Imperial College London, UK（帝国理工学院伦敦数学系）；School of Computer Science, University of St. Gallen, Switzerland（圣加尔登大学计算机科学学院）；Department of Mathematics, Stockholm University, Sweden（斯德哥尔摩大学数学系）
Washington University in St. Louis（圣路易斯华盛顿大学）；Microsoft Research（微软研究院）
As machine learning transitions increasingly towards real world applications controlling the test-time cost of algorithms becomes more and more crucial. Recent work, such as the Greedy Miser and Speedboost, incorporate test-time budget constraints into the training procedure and learn classifiers that provably stay within budget (in expectation). However, so far, these algorithms are limited to the supervised learning scenario where sufficient amounts of labeled data are available. In this paper we investigate the common scenario where labeled data is scarce but unlabeled data is available in …
Peter the Great St.Petersburg Polytechnic University（圣彼得堡彼得大帝理工大学）
A method for the local and global interpretation of a black-box model on the basis of the well-known generalized additive models is proposed. It can be viewed as an extension or a modification of the algorithm using the neural additive model. The method is based on using an ensemble of gradient boosting machines (GBMs) such that each GBM is learned on a single feature and produces a shape function of the feature. The ensemble is composed as a weighted sum of separate GBMs resulting a weighted sum of shape functions which form the generalized additive model. GBMs are built in parallel using ran…
Parallel gradient boosting for flexible estimation of conditional distributions
Université Paris-Saclay（巴黎萨克雷大学）；UVSQ（凡尔赛圣康丁伊夫林大学）；Inserm（法国国家健康与医学研究院）；CESP（健康与医学研究中心）；Université Paris Cité（巴黎西岱大学）；ENS Paris-Saclay（巴黎萨克雷高等师范学院）；CNRS（法国国家科学研究中心）；SSA（法国军队卫生服务局）；Centre Borelli（博雷利中心）；École du Val-de-Grâce（瓦尔-德-格拉斯学校）；Service de Santé des Armées（法国军队卫生服务局）
The geographically weighted regression (GWR) is an essential tool for estimating the spatial variation of relationships between dependent and independent variables in geographical contexts. However, GWR suffers from the problem that classical linear regressions, which compose the GWR model, are more prone to be underfitting, especially for significant volume and complex nonlinear data, causing inferior comparative performance. Nevertheless, some advanced models, such as the decision tree and the support vector machine, can learn features from complex data more effectively while they cannot pro…
It is already reported in the literature that the performance of a machine learning algorithm is greatly impacted by performing proper Hyper-Parameter optimization. One of the ways to perform Hyper-Parameter optimization is by manual search but that is time consuming. Some of the common approaches for performing Hyper-Parameter optimization are Grid search Random search and Bayesian optimization using Hyperopt. In this paper, we propose a brand new approach for hyperparameter improvement i.e. Randomized-Hyperopt and then tune the hyperparameters of the XGBoost i.e. the Extreme Gradient Boostin…
Fair classification has become an important topic in machine learning research. While most bias mitigation strategies focus on neural networks, we noticed a lack of work on fair classifiers based on decision trees even though they have proven very efficient. In an up-to-date comparison of state-of-the-art classification algorithms in tabular data, tree boosting outperforms deep learning. For this reason, we have developed a novel approach of adversarial gradient tree boosting. The objective of the algorithm is to predict the output $Y$ with gradient tree boosting while minimizing the ability o…
Accurately predicting customer churn using large scale time-series data is a common problem facing many business domains. The creation of model features across various time windows for training and testing can be particularly challenging due to temporal issues common to time-series data. In this paper, we will explore the application of extreme gradient boosting (XGBoost) on a customer dataset with a wide-variety of temporal features in order to create a highly-accurate customer churn model. In particular, we describe an effective method for handling temporally sensitive feature engineering. T…
