This paper aims to showcase the measure of structural diversity of an ensemble of 9 classifiers and then map a relationship between this structural diversity and accuracy. The structural diversity was induced by having different architectures or structures of the classifiers The Genetical Algorithms (GA) were used to derive the relationship between diversity and the classification accuracy by evolving the classifiers and then picking 9 classifiers out on an ensemble of 60 classifiers. It was found that as the ensemble became diverse the accuracy improved. However at a certain diversity measure the accuracy began to drop. The Kohavi-Wolpert variance method is used to measure the diversity of the ensemble. A method of voting is used to aggregate the results from each classifier. The lowest error was observed at a diversity measure of 0.16 with a mean square error of 0.274, when taking 0.2024 as maximum diversity measured. The parameters that were varied were: the number of hidden nodes, learning rate and the activation function.
Predicting user positive response (e.g., purchases and clicks) probability is a critical task in Web applications. To identify predictive features from raw data, the state-of-the-art extreme deep factorization machine model (xDeepFM) introduces a new interaction network to leverage feature interactions at the vector-wise level explicitly. However, since each hidden layer in the interaction network is a collection of feature maps, it can be viewed essentially as an ensemble of different feature maps. In this case, only using a single objective to minimize the prediction loss may lead to overfit…
Enhancing Robustness of Asynchronous EEG-Based Movement Prediction using Classifier Ensembles
Robotics Innovation Center（机器人创新中心）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Institute of Medical Technology Systems（医疗技术系统研究所）；University of Duisburg-Essen（杜伊斯堡- Essen大学）
In this paper, we investigate the relationship between diversity metrics, accuracy, and resiliency to natural image corruptions of Deep Learning (DL) image classifier ensembles. We investigate the potential of an attribution-based diversity metric to improve the known accuracy-diversity trade-off of the typical prediction-based diversity. Our motivation is based on analytical studies of design diversity that have shown that a reduction of common failure modes is possible if diversity of design choices is achieved. Using ResNet50 as a comparison baseline, we evaluate the resiliency of multiple …
Ensemble learning is gaining renewed interests in recent years. This paper presents EnsembleBench, a holistic framework for evaluating and recommending high diversity and high accuracy ensembles. The design of EnsembleBench offers three novel features: (1) EnsembleBench introduces a set of quantitative metrics for assessing the quality of ensembles and for comparing alternative ensembles constructed for the same learning tasks. (2) EnsembleBench implements a suite of baseline diversity metrics and optimized diversity metrics for identifying and selecting ensembles with high diversity and high …
Ensemble classifier refers to a group of individual classifiers that are cooperatively trained on data set in a supervised classification problem. In this paper we present a review of commonly used ensemble classifiers in the literature. Some ensemble classifiers are also developed targeting specific applications. We also present some application driven ensemble classifiers in this paper.
Ensemble methods are a cornerstone of modern machine learning. The performance of an ensemble depends crucially upon the level of diversity between its constituent learners. This paper establishes a connection between diversity and degrees of freedom (i.e. the capacity of the model), showing that diversity may be viewed as a form of inverse regularisation. This is achieved by focusing on a previously published algorithm Negative Correlation Learning (NCL), in which model diversity is explicitly encouraged through a diversity penalty term in the loss function. We provide an exact formula for th…
Diversity is an important consideration in the construction of robust neural network ensembles. A collection of well trained models will generalize better if they are diverse in the patterns they respond to and the predictions they make. Diversity is especially important for low-cost ensemble methods because members often share network structure in order to avoid training several independent models from scratch. Diversity is traditionally analyzed by measuring differences between the outputs of models. However, this gives little insight into how knowledge representations differ between ensembl…
In this paper, a novel approach to classifier ensemble creation is presented. While other ensemble creation techniques are based on careful selection of existing classifiers or preprocessing of the data, the presented approach automatically creates an optimal labelling for a number of classifiers, which are then assigned to the original data instances and fed to classifiers. The approach has been evaluated on high-dimensional biomedical datasets. The results show that the approach outperformed individual approaches in all cases.
Ensemble learning is a process by which multiple base learners are strategically generated and combined into one composite learner. There are two features that are essential to an ensemble's performance, the individual accuracies of the component learners and the overall diversity in the ensemble. The right balance of learner accuracy and ensemble diversity can improve the performance of machine learning tasks on benchmark and real-world data sets, and recent theoretical and practical work has demonstrated the subtle trade-off between accuracy and diversity in an ensemble. In this paper, we ex…
Prince of Songkla University（宋卡王子大学）；Khon Kaen University（孔敬大学）
In this paper ensemble learning based feature selection and classifier ensemble model is proposed to improve classification accuracy. The hypothesis is that good feature sets contain features that are highly correlated with the class from ensemble feature selection to SVM ensembles which can be achieved on the performance of classification accuracy. The proposed approach consists of two phases: (i) to select feature sets that are likely to be the support vectors by applying ensemble based feature selection methods; and (ii) to construct an SVM ensemble using the selected features. The proposed…
Deep ensembles excel in large-scale image classification tasks both in terms of prediction accuracy and calibration. Despite being simple to train, the computation and memory cost of deep ensembles limits their practicability. While some recent works propose to distill an ensemble model into a single model to reduce such costs, there is still a performance gap between the ensemble and distilled models. We propose a simple approach for reducing this gap, i.e., making the distilled performance close to the full ensemble. Our key assumption is that a distilled model should absorb as much function…
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）
Many dynamic ensemble selection (DES) methods are known in the literature. A previously-developed by the authors, method consists in building a randomized classifier which is treated as a model of the base classifier. The model is equivalent to the base classifier in a certain probabilistic sense. Next, the probability of correct classification of randomized classifier is taken as the competence of the evaluated classifier. In this paper, a novel randomized model of base classifier is developed. In the proposed method, the random operation of the model results from a random selection of the le…
Ensemble classification is an emerging approach to land cover mapping whereby the final classification output is a result of a consensus of classifiers. Intuitively, an ensemble system should consist of base classifiers which are diverse i.e. classifiers whose decision boundaries err differently. In this paper ensemble feature selection is used to impose diversity in ensembles. The features of the constituent base classifiers for each ensemble were created through an exhaustive search algorithm using different separability indices. For each ensemble, the classification accuracy was derived as …
Designing adaptive classifiers for an evolving data stream is a challenging task due to the data size and its dynamically changing nature. Combining individual classifiers in an online setting, the ensemble approach, is a well-known solution. It is possible that a subset of classifiers in the ensemble outperforms others in a time-varying fashion. However, optimum weight assignment for component classifiers is a problem which is not yet fully addressed in online evolving environments. We propose a novel data stream ensemble classifier, called Geometrically Optimum and Online-Weighted Ensemble (…
Center for Data Science, Peking University（北京大学数据科学中心）；National Engineering Laboratory for Big Data Analysis and Applications（大数据分析与应用技术国家工程实验室）；Key Laboratory of High Confidence Software Technologies (MOE), Peking University（北京大学高可信软件技术教育部重点实验室）；ETH Zurich（苏黎世联邦理工学院）；School of Computer Science, Beijing University of Posts and Telecommunications（北京邮电大学计算机学院）
The ensemble of deep neural networks has been shown, both theoretically and empirically, to improve generalization accuracy on the unseen test set. However, the high training cost hinders its efficiency since we need a sufficient number of base models and each one in the ensemble has to be separately trained. Lots of methods are proposed to tackle this problem, and most of them are based on the feature that a pre-trained network can transfer its knowledge to the next base model and then accelerate the training process. However, these methods suffer a severe problem that all of them transfer kn…
Peking University（北京大学）；Tencent Inc.（腾讯公司）；ZTE Corporation（中兴通讯股份有限公司）；Mila - Québec AI Institute（米拉-魁北克人工智能研究所）；Institute of Computational Social Science, Peking University (Qingdao)（北京大学（青岛）计算社会科学研究院）
The Combined Algorithm Selection and Hyperparameters optimization (CASH) problem is one of the fundamental problems in Automated Machine Learning (AutoML). Motivated by the success of ensemble learning, recent AutoML systems build post-hoc ensembles to output the final predictions instead of using the best single learner. However, while most CASH methods focus on searching for a single learner with the best performance, they neglect the diversity among base learners (i.e., they may suggest similar configurations to previously evaluated ones), which is also a crucial consideration when building…
Heterogeneous ensembles that can aggregate an unrestricted number and variety of base predictors can effectively address challenging prediction problems. In particular, accurate ensembles that are also parsimonious, i.e., consist of as few base predictors as possible, can help reveal potentially useful knowledge about the target problem domain. Although ensemble selection offers a potential approach to achieving these goals, the currently available algorithms are limited in their abilities. In this paper, we present several algorithms that incorporate ensemble diversity into a reinforcement le…
Wrocław University of Science and Technology（弗罗茨瓦夫理工大学）
The ensemble methods are meta-algorithms that combine several base machine learning techniques to increase the effectiveness of the classification. Many existing committees of classifiers use the classifier selection process to determine the optimal set of base classifiers. In this article, we propose the classifiers selection framework with relearning base classifiers. Additionally, we use in the proposed framework the new generated feature, which can be obtained after the relearning process. The proposed technique was compared with state-of-the-art ensemble methods using three benchmark data…
Pohang University of Science and Technology (POSTECH)（浦项科技大学）；Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）
There is a growing need for empirical benchmarks that support researchers and practitioners in selecting the best machine learning technique for given prediction tasks. In this paper, we consider the next event prediction task in business process predictive monitoring and we extend our previously published benchmark by studying the impact on the performance of different encoding windows and of using ensemble schemes. The choice of whether to use ensembles and which scheme to use often depends on the type of data and classification task. While there is a general understanding that ensembles per…
Computer Vision and Systems Laboratory / REPARTI and Big Data Research Centre（计算机视觉与系统实验室/REPARTI与大数据研究中心）；Université Laval（拉瓦尔大学）
Calibrating the confidence of supervised learning models is important for a variety of contexts where the certainty over predictions should be reliable. However, it has been reported that deep neural network models are often too poorly calibrated for achieving complex tasks requiring reliable uncertainty estimates in their prediction. In this work, we are proposing a strategy for training deep ensembles with a diversity function regularization, which improves the calibration property while maintaining a similar prediction accuracy.
In this paper, we propose a diversity-aware ensemble learning based algorithm, referred to as DAMVI, to deal with imbalanced binary classification tasks. Specifically, after learning base classifiers, the algorithm i) increases the weights of positive examples (minority class) which are "hard" to classify with uniformly weighted base classifiers; and ii) then learns weights over base classifiers by optimizing the PAC-Bayesian C-Bound that takes into account the accuracy and diversity between the classifiers. We show efficiency of the proposed approach with respect to state-of-art models on pre…
Ensemble learning is a methodology that integrates multiple DNN learners for improving prediction performance of individual learners. Diversity is greater when the errors of the ensemble prediction is more uniformly distributed. Greater diversity is highly correlated with the increase in ensemble accuracy. Another attractive property of diversity optimized ensemble learning is its robustness against deception: an adversarial perturbation attack can mislead one DNN model to misclassify but may not fool other ensemble DNN members consistently. In this paper we first give an overview of the conce…
National Kapodistrian Univ. of Athens (NKUA/UoA)（雅典国立卡波季斯特里安大学）；University of Houston (UH)（休斯顿大学）
In this paper, a novel approach for the optimal combination of binary classifiers is proposed. The classifier combination problem is approached from a Game Theory perspective. The proposed framework of adapted weighted majority rules (WMR) is tested against common rank-based, Bayesian and simple majority models, as well as two soft-output averaging rules. Experiments with ensembles of Support Vector Machines (SVM), Ordinary Binary Tree Classifiers (OBTC) and weighted k-nearest-neighbor (w/k-NN) models on benchmark datasets indicate that this new adaptive WMR model, employing local accuracy est…
Recently ensemble selection for consensus clustering has emerged as a research problem in Machine Intelligence. Normally consensus clustering algorithms take into account the entire ensemble of clustering, where there is a tendency of generating a very large size ensemble before computing its consensus. One can avoid considering the entire ensemble and can judiciously select few partitions in the ensemble without compromising on the quality of the consensus. This may result in an efficient consensus computation technique and may save unnecessary computational overheads. The ensemble selection …
Al-Hussein Bin Talal University（阿尔侯赛因·本·塔拉勒大学）；Mu'tah University（穆塔大学）
This paper presents a new solution for choosing the K parameter in the k-nearest neighbor (KNN) algorithm, the solution depending on the idea of ensemble learning, in which a weak KNN classifier is used each time with a different K, starting from one to the square root of the size of the training set. The results of the weak classifiers are combined using the weighted sum rule. The proposed solution was tested and compared to other solutions using a group of experiments in real life problems. The experimental results show that the proposed classifier outperforms the traditional KNN classifier …
Transferring a deep neural network trained on one problem to another requires only a small amount of data and little additional computation time. The same behaviour holds for ensembles of deep learning models typically superior to a single model. However, a transfer of deep neural networks ensemble demands relatively high computational expenses. The probability of overfitting also increases. Our approach for the transfer learning of ensembles consists of two steps: (a) shifting weights of encoders of all models in the ensemble by a single shift vector and (b) doing a tiny fine-tuning for each …
Academic College of Tel Aviv-Yaffo（特拉维夫-雅法学院）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Interdisciplinary Center (IDC) Herzliya（赫兹利亚跨学科中心）
We present a novel approach for the construction of ensemble classifiers based on dimensionality reduction. Dimensionality reduction methods represent datasets using a small number of attributes while preserving the information conveyed by the original dataset. The ensemble members are trained based on dimension-reduced versions of the training set. These versions are obtained by applying dimensionality reduction to the original training set using different values of the input parameters. This construction meets both the diversity and accuracy criteria which are required to construct an ensemb…
University of Science and Technology of China (USTC)（中国科学技术大学）
Ensembles, as a widely used and effective technique in the machine learning community, succeed within a key element -- "diversity." The relationship between diversity and generalization, unfortunately, is not entirely understood and remains an open research issue. To reveal the effect of diversity on the generalization of classification ensembles, we investigate three issues on diversity, i.e., the measurement of diversity, the relationship between the proposed diversity and the generalization error, and the utilization of this relationship for ensemble pruning. In the diversity measurement, w…
Exploring label correlations using decision templates for ensemble of classifier chains
Victor F. Rocha Department of Computer Science, Federal University of Esp\' rito Santo, Vit\' o ria, Esp\' rito Santo, 29075-910, Brazil Alexandre L. Rodrigues Department of Statistics, Federal University of Esp\' rito Santo, Vit\' o ria, Esp\' rito Santo, 29075-910, Brazil Thiago Oliveira-Santos Department of Computer Science, Federal University of Esp\' rito Santo, Vit\' o ria, Esp\' rito Santo, 29075-910, Brazil Fl\' a vio M. Varej\ a o Department of Computer Science, Federal University of Esp\' rito Santo, Vit\' o ria, Esp\' rito Santo, 29075-910, Brazil Corresponding author: Victor F. Rocha
Using bag of words representations of time series is a popular approach to time series classification. These algorithms involve approximating and discretising windows over a series to form words, then forming a count of words over a given dictionary. Classifiers are constructed on the resulting histograms of word counts. A 2017 evaluation of a range of time series classifiers found the bag of symbolic-fourier approximation symbols (BOSS) ensemble the best of the dictionary based classifiers. It forms one of the components of hierarchical vote collective of transformation-based ensembles (HIVE-…
An ensemble method should cleverly combine a group of base classifiers to yield an improved classifier. The majority vote is an example of a methodology used to combine classifiers in an ensemble method. In this paper, we propose to combine classifiers using an associative memory model. Precisely, we introduce ensemble methods based on recurrent correlation associative memories (RCAMs) for binary classification problems. We show that an RCAM-based ensemble classifier can be viewed as a majority vote classifier whose weights depend on the similarity between the base classifiers and the resultin…
Deutsche Telekom Laboratories（德国电信实验室）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）
Selecting the best classifier among the available ones is a difficult task, especially when only instances of one class exist. In this work we examine the notion of combining one-class classifiers as an alternative for selecting the best classifier. In particular, we propose two new one-class classification performance measures to weigh classifiers and show that a simple ensemble that implements these measures can outperform the most popular one-class ensembles. Furthermore, we propose a new one-class ensemble scheme, TUPSO, which uses meta-learning to combine one-class classifiers. Our experi…
A Kernel Fisher Discriminant Analysis-Based Tree Ensemble Classifier: KFDA Forest
School of Industrial Management Engineering, Korea University（韩国大学工业管理工程学院）；School of Mechanical Engineering, Chungnam National University（Chungnam国立大学机械工程学院）
We present and empirically evaluate an efficient algorithm that learns to aggregate the predictions of an ensemble of binary classifiers. The algorithm uses the structure of the ensemble predictions on unlabeled data to yield significant performance improvements. It does this without making assumptions on the structure or origin of the ensemble, without parameters, and as scalably as linear learning. We empirically demonstrate these performance gains with random forests.
École de technologie supérieure (ÉTS), Université du Québec（魁北克大学高等技术学院）；Pontifícia Universidade Católica do Paraná (PUCPR)（巴拉那天主教大学）；Universidade Federal do Paraná (UFPR)（巴拉那联邦大学）
The Ensemble of Classifiers (EoC) has been shown to be effective in improving the performance of single classifiers by combining their outputs, and one of the most important properties involved in the selection of the best EoC from a pool of classifiers is considered to be classifier diversity. In general, classifier diversity does not occur randomly, but is generated systematically by various ensemble creation methods. By using diverse data subsets to train classifiers, these methods can create diverse classifiers for the EoC. In this work, we propose a scheme to measure data diversity direct…
Promoting Ensemble Diversity with Interactive Bayesian Distributional Robustness for Fine-tuning Foundation Models
Qualcomm AI Research, Qualcomm Vietnam Company Limited（高通人工智能研究, 高通越南公司）；National University of Singapore, Singapore（新加坡国立大学）；Monash University, Australia（墨尔本大学）
Guardian of the Ensembles: Introducing Pairwise Adversarially Robust Loss for Resisting Adversarial Attacks in DNN Ensembles
Centre for Computational and Data Sciences, IIT Kharagpur（印度理工学院克勒格布尔分校计算与数据科学中心）；Computer Science and Engineering Department, IIT Kharagpur（印度理工学院克勒格布尔分校计算机科学与工程系）；Center for Cyber Security, New York University Abu Dhabi（纽约大学阿布扎比分校网络安全中心）；Department of Artificial Intelligence, IIT Kharagpur（印度理工学院克勒格布尔分校人工智能系）；Computer Science and Engineering Department, IIT Patna（印度理工学院巴特那分校计算机科学与工程系）
Boston University（波士顿大学）；University of Michigan（密歇根大学）
We propose a Bayesian approach for recursively estimating the classifier weights in online learning of a classifier ensemble. In contrast with past methods, such as stochastic gradient descent or online boosting, our approach estimates the weights by recursively updating its posterior distribution. For a specified class of loss functions, we show that it is possible to formulate a suitably defined likelihood function and hence use the posterior distribution as an approximation to the global empirical loss minimizer. If the stream of training data is sampled from a stationary process, we can al…
University of Science and Technology Beijing（北京科技大学）；Chinese Academy of Sciences（中国科学院）
Classifier ensemble generally should combine diverse component classifiers. However, it is difficult to give a definitive connection between diversity measure and ensemble accuracy. Given a list of available component classifiers, how to adaptively and diversely ensemble classifiers becomes a big challenge in the literature. In this paper, we argue that diversity, not direct diversity on samples but adaptive diversity with data, is highly correlated to ensemble accuracy, and we propose a novel technology for classifier ensemble, learning to diversify, which learns to adaptively combine classif…
When constructing a classifier ensemble, diversity among the base classifiers is one of the important characteristics. Several studies have been made in the context of standard static data, in particular, when analyzing the relationship between a high ensemble predictive performance and the diversity of its components. Besides, ensembles of learning machines have been performed to learn in the presence of concept drift and adapt to it. However, diversity measures have not received much research interest in evolving data streams. Only a few researchers directly consider promoting diversity whil…
Université Laval（拉瓦尔大学）；Element AI, a ServiceNow company（ServiceNow旗下Element AI公司）
Background: Understanding the relationship between the Omics and the phenotype is a central problem in precision medicine. The high dimensionality of metabolomics data challenges learning algorithms in terms of scalability and generalization. Most learning algorithms do not produce interpretable models -- Method: We propose an ensemble learning algorithm based on conjunctions or disjunctions of decision rules. -- Results : Applications on metabolomics data shows that it produces models that achieves high predictive performances. The interpretability of the models makes them useful for biomarke…
ISCAS（中国科学院软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）；École normale supérieure de Rennes（雷恩高等师范学校）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；IRISA（法国信息与随机系统研究所）；East China Normal University（华东师范大学）；Nanjing Institute of Software Technology, ISCAS（中国科学院软件研究所南京软件技术研究院）；Guangdong Artificial Intelligence and Digital Economy Laboratory（广东人工智能与数字经济实验室）
In this paper, we propose a framework of filter-based ensemble of deep neuralnetworks (DNNs) to defend against adversarial attacks. The framework builds an ensemble of sub-models -- DNNs with differentiated preprocessing filters. From the theoretical perspective of DNN robustness, we argue that under the assumption of high quality of the filters, the weaker the correlations of the sensitivity of the filters are, the more robust the ensemble model tends to be, and this is corroborated by the experiments of transfer-based attacks. Correspondingly, we propose a principle that chooses the specific…
Calibration and uncertainty estimation are crucial topics in high-risk environments. We introduce a new diversity regularizer for classification tasks that uses out-of-distribution samples and increases the overall accuracy, calibration and out-of-distribution detection capabilities of ensembles. Following the recent interest in the diversity of ensembles, we systematically evaluate the viability of explicitly regularizing ensemble diversity to improve calibration on in-distribution data as well as under dataset shift. We demonstrate that diversity regularization is highly beneficial in archit…
The main principle of stacked generalization (or Stacking) is using a second-level generalizer to combine the outputs of base classifiers in an ensemble. In this paper, we investigate different combination types under the stacking framework; namely weighted sum (WS), class-dependent weighted sum (CWS) and linear stacked generalization (LSG). For learning the weights, we propose using regularized empirical risk minimization with the hinge loss. In addition, we propose using group sparsity for regularization to facilitate classifier selection. We performed experiments using two different ensembl…
Pontifícia Universidade Católica do Paraná (PUCPR)（天主教大学联邦大学（PUCPR））；State University of Ponta Grossa (UEPG)（蓬塔格罗萨州立大学（UEPG））；Federal University of Paraná (UFPR)（联邦大学（UFPR））；École de Technologie Supérieure (ÉTS), Université du Québec（魁北克大学高等技术学院（ÉTS））；Université du Québec（魁北克大学（Université du Québec））；PPGIa（PPGIa（需保留原文））
This paper describes a classifier pool generation method guided by the diversity estimated on the data complexity and classifier decisions. First, the behavior of complexity measures is assessed by considering several subsamples of the dataset. The complexity measures with high variability across the subsamples are selected for posterior pool adaptation, where an evolutionary algorithm optimizes diversity in both complexity and decision spaces. A robust experimental protocol with 28 datasets and 20 replications is used to evaluate the proposed method. Results show significant accuracy improvem…
Both the median-based classifier and the quantile-based classifier are useful for discriminating high-dimensional data with heavy-tailed or skewed inputs. But these methods are restricted as they assign equal weight to each variable in an unregularized way. The ensemble quantile classifier is a more flexible regularized classifier that provides better performance with high-dimensional data, asymmetric data or when there are many irrelevant extraneous inputs. The improved performance is demonstrated by a simulation study as well as an application to text categorization. It is proven that the es…
In machine learning area, as the number of labeled input samples becomes very large, it is very difficult to build a classification model because of input data set is not fit in a memory in training phase of the algorithm, therefore, it is necessary to utilize data partitioning to handle overall data set. Bagging and boosting based data partitioning methods have been broadly used in data mining and pattern recognition area. Both of these methods have shown a great possibility for improving classification model performance. This study is concerned with the analysis of data set partitioning with…
Suppose some classifiers are selected from a set of hypothesis classifiers to form an equally-weighted ensemble that selects a member classifier at random for each input example. Then the ensemble has an error bound consisting of the average error bound for the member classifiers, a term for selectivity that varies from zero (if all hypothesis classifiers are selected) to a standard uniform error bound (if only a single classifier is selected), and small constants. There is no penalty for using a richer hypothesis set if the same fraction of the hypothesis classifiers are selected for the ense…
