Low-order functional ANOVA (fANOVA) models have been rediscovered in the machine learning (ML) community under the guise of inherently interpretable machine learning. Explainable Boosting Machines or EBM (Lou et al. 2013) and GAMI-Net (Yang et al. 2021) are two recently proposed ML algorithms for fitting functional main effects and second-order interactions. We propose a new algorithm, called GAMI-Tree, that is similar to EBM, but has a number of features that lead to better performance. It uses model-based trees as base learners and incorporates a new interaction filtering method that is better at capturing the underlying interactions. In addition, our iterative training method converges to a model with better predictive performance, and the embedded purification ensures that interactions are hierarchically orthogonal to main effects. The algorithm does not need extensive tuning, and our implementation is fast and efficient. We use simulated and real datasets to compare the performance and interpretability of GAMI-Tree with EBM and GAMI-Net.
Statistical Inference for Explainable Boosting Machines
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）
University of Electronic Science and Technology of China（电子科技大学）
Due to the gap between a substitute model and a victim model, the gradient-based noise generated from a substitute model may have low transferability for a victim model since their gradients are different. Inspired by the fact that the decision boundaries of different models do not differ much, we conduct experiments and discover that the gradients of different models are more similar on the decision boundary than in the original position. Moreover, since the decision boundary in the vicinity of an input image is flat along most directions, we conjecture that the boundary gradients can help fi…
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…
In this paper, we introduce and evaluate a data-driven staged mixture modeling technique for building density, regression, and classification models. Our basic approach is to sequentially add components to a finite mixture model using the structural expectation maximization (SEM) algorithm. We show that our technique is qualitatively similar to boosting. This correspondence is a natural byproduct of the fact that we use the SEM algorithm to sequentially fit the mixture model. Finally, in our experimental evaluation, we demonstrate the effectiveness of our approach on a variety of prediction an…
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…
We present a new variable selection method based on model-based gradient boosting and randomly permuted variables. Model-based boosting is a tool to fit a statistical model while performing variable selection at the same time. A drawback of the fitting lies in the need of multiple model fits on slightly altered data (e.g. cross-validation or bootstrap) to find the optimal number of boosting iterations and prevent overfitting. In our proposed approach, we augment the data set with randomly permuted versions of the true variables, so called shadow variables, and stop the step-wise fitting as soo…
IBM Research – Zürich（IBM苏黎世研究部）；ETH Zürich（苏黎世联邦理工学院）
Modern gradient boosting software frameworks, such as XGBoost and LightGBM, implement Newton descent in a functional space. At each boosting iteration, their goal is to find the base hypothesis, selected from some base hypothesis class, that is closest to the Newton descent direction in a Euclidean sense. Typically, the base hypothesis class is fixed to be all binary decision trees up to a given depth. In this work, we study a Heterogeneous Newton Boosting Machine (HNBM) in which the base hypothesis class may vary across boosting iterations. Specifically, at each boosting iteration, the base h…
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…
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…
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…
TensorCell；University of Warsaw（华沙大学）；Jagiellonian University（雅盖隆大学）
We analyze the accuracy of traffic simulations metamodels based on neural networks and gradient boosting models (LightGBM), applied to traffic optimization as fitness functions of genetic algorithms. Our metamodels approximate outcomes of traffic simulations (the total time of waiting on a red signal) taking as an input different traffic signal settings, in order to efficiently find (sub)optimal settings. Their accuracy was proven to be very good on randomly selected test sets, but it turned out that the accuracy may drop in case of settings expected (according to genetic algorithms) to be clo…
We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the per-family error rate (PFER). The model is fitted repeatedly to subsampled data and variables with high selection frequencies are extracted. To apply stability selection to boosted GAMLSS, we develop a new "noncyclical" fitting algorithm that incorporates an additional selection step of the best-fitting distribution parameter in each iteration. This new alg…
Shanghai Jiao Tong University（上海交通大学）；Sun Yat-sen University（中山大学）；Huazhong University of Science and Technology（华中科技大学）
This paper aims to understand and improve the utility of the dropout operation from the perspective of game-theoretic interactions. We prove that dropout can suppress the strength of interactions between input variables of deep neural networks (DNNs). The theoretic proof is also verified by various experiments. Furthermore, we find that such interactions were strongly related to the over-fitting problem in deep learning. Thus, the utility of dropout can be regarded as decreasing interactions to alleviate the significance of over-fitting. Based on this understanding, we propose an interaction l…
Diffusion-weighted magnetic resonance imaging (DWI) and fiber tractography are the only methods to measure the structure of the white matter in the living human brain. The diffusion signal has been modelled as the combined contribution from many individual fascicles of nerve fibers passing through each location in the white matter. Typically, this is done via basis pursuit, but estimation of the exact directions is limited due to discretization. The difficulties inherent in modeling DWI data are shared by many other problems involving fitting non-parametric mixture models. Ekanadaham et al. pr…
Gradient boosted decision trees are a popular machine learning technique, in part because of their ability to give good accuracy with small models. We describe two extensions to the standard tree boosting algorithm designed to increase this advantage. The first improvement extends the boosting formalism from scalar-valued trees to vector-valued trees. This allows individual trees to be used as multiclass classifiers, rather than requiring one tree per class, and drastically reduces the model size required for multiclass problems. We also show that some other popular vector-valued gradient boos…
Supervised Machine Learning (SML) algorithms, such as Gradient Boosting, Random Forest, and Neural Networks, have become popular in recent years due to their superior predictive performance over traditional statistical methods. However, their complexity makes the results hard to interpret without additional tools. There has been a lot of recent work in developing global and local diagnostics for interpreting SML models. In this paper, we propose a locally-interpretable model that takes the fitted ML response surface, partitions the predictor space using model-based regression trees, and fits i…
This paper compares the performances of three supervised machine learning algorithms in terms of predictive ability and model interpretation on structured or tabular data. The algorithms considered were scikit-learn implementations of extreme gradient boosting machines (XGB) and random forests (RFs), and feedforward neural networks (FFNNs) from TensorFlow. The paper is organized in a findings-based manner, with each section providing general conclusions supported by empirical results from simulation studies that cover a wide range of model complexity and correlation structures among predictors…
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…
Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well understood. The most cited prior works have focused on deriving pointwise consistency guarantees for CART in a classical nonparametric regression setting. We take a different approach, and advocate studying the generalization performance of decision trees with respect to different generative regression models. This allows us to elicit their inductive bias, t…
