Eibe Frank

Yaqian Zhang, Bernhard Pfahringer, Eibe Frank et al.

Online continual learning (OCL) aims to train neural networks incrementally from a non-stationary data stream with a single pass through data. Rehearsal-based methods attempt to approximate the observed input distributions over time with a small memory and revisit them later to avoid forgetting. Despite its strong empirical performance, rehearsal methods still suffer from a poor approximation of the loss landscape of past data with memory samples. This paper revisits the rehearsal dynamics in online settings. We provide theoretical insights on the inherent memory overfitting risk from the viewpoint of biased and dynamic empirical risk minimization, and examine the merits and limits of repeated rehearsal. Inspired by our analysis, a simple and intuitive baseline, Repeated Augmented Rehearsal (RAR), is designed to address the underfitting-overfitting dilemma of online rehearsal. Surprisingly, across four rather different OCL benchmarks, this simple baseline outperforms vanilla rehearsal by 9%-17% and also significantly improves state-of-the-art rehearsal-based methods MIR, ASER, and SCR. We also demonstrate that RAR successfully achieves an accurate approximation of the loss landscape of past data and high-loss ridge aversion in its learning trajectory. Extensive ablation studies are conducted to study the interplay between repeated and augmented rehearsal and reinforcement learning (RL) is applied to dynamically adjust the hyperparameters of RAR to balance the stability-plasticity trade-off online. Code is available at https://github.com/YaqianZhang/RepeatedAugmentedRehearsal

Xin Xu, Eibe Frank, Geoffrey Holmes

We explore multiple instance verification, a problem setting in which a query instance is verified against a bag of target instances with heterogeneous, unknown relevancy. We show that naive adaptations of attention-based multiple instance learning (MIL) methods and standard verification methods like Siamese neural networks are unsuitable for this setting: directly combining state-of-the-art (SOTA) MIL methods and Siamese networks is shown to be no better, and sometimes significantly worse, than a simple baseline model. Postulating that this may be caused by the failure of the representation of the target bag to incorporate the query instance, we introduce a new pooling approach named "cross-attention pooling" (CAP). Under the CAP framework, we propose two novel attention functions to address the challenge of distinguishing between highly similar instances in a target bag. Through empirical studies on three different verification tasks, we demonstrate that CAP outperforms adaptations of SOTA MIL methods and the baseline by substantial margins, in terms of both classification accuracy and the ability to detect key instances. The superior ability to identify key instances is attributed to the new attention functions by ablation studies. We share our code at https://github.com/xxweka/MIV.

Hongyu Wang, Eibe Frank, Bernhard Pfahringer et al.

Cross-domain few-shot learning (CDFSL) addresses learning problems where knowledge needs to be transferred from one or more source domains into an instance-scarce target domain with an explicitly different distribution. Recently published CDFSL methods generally construct a universal model that combines knowledge of multiple source domains into one feature extractor. This enables efficient inference but necessitates re-computation of the extractor whenever a new source domain is added. Some of these methods are also incompatible with heterogeneous source domain extractor architectures. We propose feature extractor stacking (FES), a new CDFSL method for combining information from a collection of extractors, that can utilise heterogeneous pretrained extractors out of the box and does not maintain a universal model that needs to be re-computed when its extractor collection is updated. We present the basic FES algorithm, which is inspired by the classic stacked generalisation approach, and also introduce two variants: convolutional FES (ConFES) and regularised FES (ReFES). Given a target-domain task, these algorithms fine-tune each extractor independently, use cross-validation to extract training data for stacked generalisation from the support set, and learn a simple linear stacking classifier from this data. We evaluate our FES methods on the well-known Meta-Dataset benchmark, targeting image classification with convolutional neural networks, and show that they can achieve state-of-the-art performance.

Puneet Sharma, Kristian Dalsbø Hindberg, Eibe Frank et al.

Identifying unique polyps in colon capsule endoscopy (CCE) images is a critical yet challenging task for medical personnel due to the large volume of images, the cognitive load it creates for clinicians, and the ambiguity in labeling specific frames. This paper formulates this problem as a multi-instance learning (MIL) task, where a query polyp image is compared with a target bag of images to determine uniqueness. We employ a multi-instance verification (MIV) framework that incorporates attention mechanisms, such as variance-excited multi-head attention (VEMA) and distance-based attention (DBA), to enhance the model's ability to extract meaningful representations. Additionally, we investigate the impact of self-supervised learning using SimCLR to generate robust embeddings. Experimental results on a dataset of 1912 polyps from 754 patients demonstrate that attention mechanisms significantly improve performance, with DBA L1 achieving the highest test accuracy of 86.26\% and a test AUC of 0.928 using a ConvNeXt backbone with SimCLR pretraining. This study underscores the potential of MIL and self-supervised learning in advancing automated analysis of Colon Capsule Endoscopy images, with implications for broader medical imaging applications.

Xin Xu, Eibe Frank, Geoffrey Holmes

We investigate cross-domain few-shot learning under the constraint that fine-tuning of backbones (i.e., feature extractors) is impossible or infeasible -- a scenario that is increasingly common in practical use cases. Handling the low-quality and static embeddings produced by frozen, "black-box" backbones leads to a problem representation of few-shot classification as a series of multiple instance verification (MIV) tasks. Inspired by this representation, we introduce a novel approach to few-shot domain adaptation, named the "MIV-head", akin to a classification head that is agnostic to any pretrained backbone and computationally efficient. The core components designed for the MIV-head, when trained on few-shot data from a target domain, collectively yield strong performance on test data from that domain. Importantly, it does so without fine-tuning the backbone, and within the "meta-testing" phase. Experimenting under various settings and on an extension of the Meta-dataset benchmark for cross-domain few-shot image classification, using representative off-the-shelf convolutional neural network and vision transformer backbones pretrained on ImageNet1K, we show that the MIV-head achieves highly competitive accuracy when compared to state-of-the-art "adapter" (or partially fine-tuning) methods applied to the same backbones, while incurring substantially lower adaptation cost. We also find well-known "classification head" approaches lag far behind in terms of accuracy. Ablation study empirically justifies the core components of our approach. We share our code at https://github.com/xxweka/MIV-head.

Zac Pullar-Strecker, Katharina Dost, Eibe Frank et al.

Active learning allows machine learning models to be trained using fewer labels while retaining similar performance to traditional supervised learning. An active learner selects the most informative data points, requests their labels, and retrains itself. While this approach is promising, it raises the question of how to determine when the model is `good enough' without the additional labels required for traditional evaluation. Previously, different stopping criteria have been proposed aiming to identify the optimal stopping point. Yet, optimality can only be expressed as a domain-dependent trade-off between accuracy and the number of labels, and no criterion is superior in all applications. As a further complication, a comparison of criteria for a particular real-world application would require practitioners to collect additional labelled data they are aiming to avoid by using active learning in the first place. This work enables practitioners to employ active learning by providing actionable recommendations for which stopping criteria are best for a given real-world scenario. We contribute the first large-scale comparison of stopping criteria for pool-based active learning, using a cost measure to quantify the accuracy/label trade-off, public implementations of all stopping criteria we evaluate, and an open-source framework for evaluating stopping criteria. Our research enables practitioners to substantially reduce labelling costs by utilizing the stopping criterion which best suits their domain.

Rory Mitchell, Andrey Adinets, Thejaswi Rao et al.

We describe the multi-GPU gradient boosting algorithm implemented in the XGBoost library (https://github.com/dmlc/xgboost). Our algorithm allows fast, scalable training on multi-GPU systems with all of the features of the XGBoost library. We employ data compression techniques to minimise the usage of scarce GPU memory while still allowing highly efficient implementation. Using our algorithm we show that it is possible to process 115 million training instances in under three minutes on a publicly available cloud computing instance. The algorithm is implemented using end-to-end GPU parallelism, with prediction, gradient calculation, feature quantisation, decision tree construction and evaluation phases all computed on device.

Sabino Francesco Roselli, Eibe Frank

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear combinations of predictor variables in their leaf nodes to form predictions, which can help achieve higher accuracy and smaller trees. Typical algorithms for learning model trees from training data work in a greedy fashion, growing the tree in a top-down manner by recursively splitting the data into smaller and smaller subsets. Crucially, the selected splits are only locally optimal, potentially rendering the tree overly complex and less accurate than a tree whose structure is globally optimal for the training data. In this paper, we empirically investigate the effect of constructing globally optimal model trees for classification and regression with linear support vector machines at the leaf nodes. To this end, we present mixed-integer linear programming formulations to learn optimal trees, compute such trees for a large collection of benchmark data sets, and compare their performance against greedily grown model trees in terms of interpretability and accuracy. We also compare to classic optimal and greedily grown decision trees, random forests, and support vector machines. Our results show that optimal model trees can achieve competitive accuracy with very small trees. We also investigate the effect on the accuracy of replacing axis-parallel splits with multivariate ones, foregoing interpretability while potentially obtaining greater accuracy.

Yaqian Zhang, Bernhard Pfahringer, Eibe Frank et al.

Despite their success, large pretrained vision models remain vulnerable to catastrophic forgetting when adapted to new tasks in class-incremental settings. Parameter-efficient fine-tuning (PEFT) alleviates this by restricting trainable parameters, yet most approaches still rely on cross-entropy (CE) loss, a surrogate for the 0-1 loss, to learn from new data. We revisit this choice and revive the true objective (0-1 loss) through a reinforcement learning perspective. By formulating classification as a one-step Markov Decision Process, we derive an Expected Policy Gradient (EPG) method that directly minimizes misclassification error with a low-variance gradient estimation. Our analysis shows that CE can be interpreted as EPG with an additional sample-weighting mechanism: CE encourages exploration by emphasizing low-confidence samples, while EPG prioritizes high-confidence ones. Building on this insight, we propose adaptive entropy annealing (aEPG), a training strategy that transitions from exploratory (CE-like) to exploitative (EPG-like) learning. aEPG-based methods outperform CE-based methods across diverse benchmarks and with various PEFT modules. More broadly, we evaluate various entropy regularization methods and demonstrate that lower entropy of the output prediction distribution enhances adaptation in pretrained vision models.

Julia R. Falconer, Eibe Frank, Devon L. L. Polaschek et al.

Recent work [ 14 ] has introduced a method for prior elicitation that utilizes records of expert decisions to infer a prior distribution. While this method provides a promising approach to eliciting expert uncertainty, it has only been demonstrated using tabular data, which may not entirely represent the information used by experts to make decisions. In this paper, we demonstrate how analysts can adopt a deep learning approach to utilize the method proposed in [14 ] with the actual information experts use. We provide an overview of deep learning models that can effectively model expert decision-making to elicit distributions that capture expert uncertainty and present an example examining the risk of colon cancer to show in detail how these models can be used.

Attaullah Sahito, Eibe Frank, Bernhard Pfahringer

Neural networks have been successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are more difficult to train successfully for semi-supervised problems where small amounts of labeled instances are available along with a large number of unlabeled instances. This work explores a new training method for semi-supervised learning that is based on similarity function learning using a Siamese network to obtain a suitable embedding. The learned representations are discriminative in Euclidean space, and hence can be used for labeling unlabeled instances using a nearest-neighbor classifier. Confident predictions of unlabeled instances are used as true labels for retraining the Siamese network on the expanded training set. This process is applied iteratively. We perform an empirical study of this iterative self-training algorithm. For improving unlabeled predictions, local learning with global consistency [22] is also evaluated.

Attaullah Sahito, Eibe Frank, Bernhard Pfahringer

Deep neural networks produce state-of-the-art results when trained on a large number of labeled examples but tend to overfit when small amounts of labeled examples are used for training. Creating a large number of labeled examples requires considerable resources, time, and effort. If labeling new data is not feasible, so-called semi-supervised learning can achieve better generalisation than purely supervised learning by employing unlabeled instances as well as labeled ones. The work presented in this paper is motivated by the observation that transfer learning provides the opportunity to potentially further improve performance by exploiting models pretrained on a similar domain. More specifically, we explore the use of transfer learning when performing semi-supervised learning using self-learning. The main contribution is an empirical evaluation of transfer learning using different combinations of similarity metric learning methods and label propagation algorithms in semi-supervised learning. We find that transfer learning always substantially improves the model's accuracy when few labeled examples are available, regardless of the type of loss used for training the neural network. This finding is obtained by performing extensive experiments on the SVHN, CIFAR10, and Plant Village image classification datasets and applying pretrained weights from Imagenet for transfer learning.

Attaullah Sahito, Eibe Frank, Bernhard Pfahringer

Self-training is a simple semi-supervised learning approach: Unlabelled examples that attract high-confidence predictions are labelled with their predictions and added to the training set, with this process being repeated multiple times. Recently, self-supervision -- learning without manual supervision by solving an automatically-generated pretext task -- has gained prominence in deep learning. This paper investigates three different ways of incorporating self-supervision into self-training to improve accuracy in image classification: self-supervision as pretraining only, self-supervision performed exclusively in the first iteration of self-training, and self-supervision added to every iteration of self-training. Empirical results on the SVHN, CIFAR-10, and PlantVillage datasets, using both training from scratch, and Imagenet-pretrained weights, show that applying self-supervision only in the first iteration of self-training can greatly improve accuracy, for a modest increase in computation time.

Rory Mitchell, Joshua Cooper, Eibe Frank et al.

Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the computation of Shapley values can be expressed as a summation over a set of permutations, a common approach is to sample a subset of these permutations for approximation. Unfortunately, standard Monte Carlo sampling methods can exhibit slow convergence, and more sophisticated quasi-Monte Carlo methods have not yet been applied to the space of permutations. To address this, we investigate new approaches based on two classes of approximation methods and compare them empirically. First, we demonstrate quadrature techniques in a RKHS containing functions of permutations, using the Mallows kernel in combination with kernel herding and sequential Bayesian quadrature. The RKHS perspective also leads to quasi-Monte Carlo type error bounds, with a tractable discrepancy measure defined on permutations. Second, we exploit connections between the hypersphere $\mathbb{S}^{d-2}$ and permutations to create practical algorithms for generating permutation samples with good properties. Experiments show the above techniques provide significant improvements for Shapley value estimates over existing methods, converging to a smaller RMSE in the same number of model evaluations.

Rory Mitchell, Eibe Frank, Geoffrey Holmes

SHAP (SHapley Additive exPlanation) values provide a game theoretic interpretation of the predictions of machine learning models based on Shapley values. While exact calculation of SHAP values is computationally intractable in general, a recursive polynomial-time algorithm called TreeShap is available for decision tree models. However, despite its polynomial time complexity, TreeShap can become a significant bottleneck in practical machine learning pipelines when applied to large decision tree ensembles. Unfortunately, the complicated TreeShap algorithm is difficult to map to hardware accelerators such as GPUs. In this work, we present GPUTreeShap, a reformulated TreeShap algorithm suitable for massively parallel computation on graphics processing units. Our approach first preprocesses each decision tree to isolate variable sized sub-problems from the original recursive algorithm, then solves a bin packing problem, and finally maps sub-problems to single-instruction, multiple-thread (SIMT) tasks for parallel execution with specialised hardware instructions. With a single NVIDIA Tesla V100-32 GPU, we achieve speedups of up to 19x for SHAP values, and speedups of up to 340x for SHAP interaction values, over a state-of-the-art multi-core CPU implementation executed on two 20-core Xeon E5-2698 v4 2.2 GHz CPUs. We also experiment with multi-GPU computing using eight V100 GPUs, demonstrating throughput of 1.2M rows per second -- equivalent CPU-based performance is estimated to require 6850 CPU cores.

Moi Hoon Yap, Ryo Hachiuma, Azadeh Alavi et al.

There has been a substantial amount of research involving computer methods and technology for the detection and recognition of diabetic foot ulcers (DFUs), but there is a lack of systematic comparisons of state-of-the-art deep learning object detection frameworks applied to this problem. DFUC2020 provided participants with a comprehensive dataset consisting of 2,000 images for training and 2,000 images for testing. This paper summarises the results of DFUC2020 by comparing the deep learning-based algorithms proposed by the winning teams: Faster R-CNN, three variants of Faster R-CNN and an ensemble method; YOLOv3; YOLOv5; EfficientDet; and a new Cascade Attention Network. For each deep learning method, we provide a detailed description of model architecture, parameter settings for training and additional stages including pre-processing, data augmentation and post-processing. We provide a comprehensive evaluation for each method. All the methods required a data augmentation stage to increase the number of images available for training and a post-processing stage to remove false positives. The best performance was obtained from Deformable Convolution, a variant of Faster R-CNN, with a mean average precision (mAP) of 0.6940 and an F1-Score of 0.7434. Finally, we demonstrate that the ensemble method based on different deep learning methods can enhanced the F1-Score but not the mAP.

Jacob Montiel, Rory Mitchell, Eibe Frank et al.

Boosting is an ensemble method that combines base models in a sequential manner to achieve high predictive accuracy. A popular learning algorithm based on this ensemble method is eXtreme Gradient Boosting (XGB). We present an adaptation of XGB for classification of evolving data streams. In this setting, new data arrives over time and the relationship between the class and the features may change in the process, thus exhibiting concept drift. The proposed method creates new members of the ensemble from mini-batches of data as new data becomes available. The maximum ensemble size is fixed, but learning does not stop when this size is reached because the ensemble is updated on new data to ensure consistency with the current concept. We also explore the use of concept drift detection to trigger a mechanism to update the ensemble. We test our method on real and synthetic data with concept drift and compare it against batch-incremental and instance-incremental classification methods for data streams.

Bill Cassidy, Neil D. Reeves, Pappachan Joseph et al.

Every 20 seconds, a limb is amputated somewhere in the world due to diabetes. This is a global health problem that requires a global solution. The MICCAI challenge discussed in this paper, which concerns the automated detection of diabetic foot ulcers using machine learning techniques, will accelerate the development of innovative healthcare technology to address this unmet medical need. In an effort to improve patient care and reduce the strain on healthcare systems, recent research has focused on the creation of cloud-based detection algorithms. These can be consumed as a service by a mobile app that patients (or a carer, partner or family member) could use themselves at home to monitor their condition and to detect the appearance of a diabetic foot ulcer (DFU). Collaborative work between Manchester Metropolitan University, Lancashire Teaching Hospital and the Manchester University NHS Foundation Trust has created a repository of 4,000 DFU images for the purpose of supporting research toward more advanced methods of DFU detection. Based on a joint effort involving the lead scientists of the UK, US, India and New Zealand, this challenge will solicit original work, and promote interactions between researchers and interdisciplinary collaborations. This paper presents a dataset description and analysis, assessment methods, benchmark algorithms and initial evaluation results. It facilitates the challenge by providing useful insights into state-of-the-art and ongoing research. This grand challenge takes on even greater urgency in a peri and post-pandemic period, where stresses on resource utilization will increase the need for technology that allows people to remain active, healthy and intact in their home.

Rhys Compton, Eibe Frank, Panos Patros et al.

Automatic source code analysis in key areas of software engineering, such as code security, can benefit from Machine Learning (ML). However, many standard ML approaches require a numeric representation of data and cannot be applied directly to source code. Thus, to enable ML, we need to embed source code into numeric feature vectors while maintaining the semantics of the code as much as possible. code2vec is a recently released embedding approach that uses the proxy task of method name prediction to map Java methods to feature vectors. However, experimentation with code2vec shows that it learns to rely on variable names for prediction, causing it to be easily fooled by typos or adversarial attacks. Moreover, it is only able to embed individual Java methods and cannot embed an entire collection of methods such as those present in a typical Java class, making it difficult to perform predictions at the class level (e.g., for the identification of malicious Java classes). Both shortcomings are addressed in the research presented in this paper. We investigate the effect of obfuscating variable names during the training of a code2vec model to force it to rely on the structure of the code rather than specific names and consider a simple approach to creating class-level embeddings by aggregating sets of method embeddings. Our results, obtained on a challenging new collection of source-code classification problems, indicate that obfuscating variable names produces an embedding model that is both impervious to variable naming and more accurately reflects code semantics. The datasets, models, and code are shared for further ML research on source code.

Jesse Read, Bernhard Pfahringer, Geoff Holmes et al.

The family of methods collectively known as classifier chains has become a popular approach to multi-label learning problems. This approach involves linking together off-the-shelf binary classifiers in a chain structure, such that class label predictions become features for other classifiers. Such methods have proved flexible and effective and have obtained state-of-the-art empirical performance across many datasets and multi-label evaluation metrics. This performance led to further studies of how exactly it works, and how it could be improved, and in the recent decade numerous studies have explored classifier chains mechanisms on a theoretical level, and many improvements have been made to the training and inference procedures, such that this method remains among the state-of-the-art options for multi-label learning. Given this past and ongoing interest, which covers a broad range of applications and research themes, the goal of this work is to provide a review of classifier chains, a survey of the techniques and extensions provided in the literature, as well as perspectives for this approach in the domain of multi-label classification in the future. We conclude positively, with a number of recommendations for researchers and practitioners, as well as outlining a number of areas for future research.

Henry Gouk, Bernhard Pfahringer, Eibe Frank

We present an algorithm for learning decision trees using stochastic gradient information as the source of supervision. In contrast to previous approaches to gradient-based tree learning, our method operates in the incremental learning setting rather than the batch learning setting, and does not make use of soft splits or require the construction of a new tree for every update. We demonstrate how one can apply these decision trees to different problems by changing only the loss function, using classification, regression, and multi-instance learning as example applications. In the experimental evaluation, our method performs similarly to standard incremental classification trees, outperforms state of the art incremental regression trees, and achieves comparable performance with batch multi-instance learning methods.

Tim Leathart, Eibe Frank, Bernhard Pfahringer et al.

Nested dichotomies are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification model learns to discriminate between the two subsets of classes at each node. In this paper, we demonstrate that these nested dichotomies typically exhibit poor probability calibration, even when the base binary models are well calibrated. We also show that this problem is exacerbated when the binary models are poorly calibrated. We discuss the effectiveness of different calibration strategies and show that accuracy and log-loss can be significantly improved by calibrating both the internal base models and the full nested dichotomy structure, especially when the number of classes is high.

Tim Leathart, Eibe Frank, Bernhard Pfahringer et al.

A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary classifier for each split. Many methods have been proposed to perform this split, each with various advantages and disadvantages. In this paper, we present a simple, general method for improving the predictive performance of nested dichotomies produced by any subset selection techniques that employ randomness to construct the subsets. We provide a theoretical expectation for performance improvements, as well as empirical results showing that our method improves the root mean squared error of nested dichotomies, regardless of whether they are employed as an individual model or in an ensemble setting.

Tim Leathart, Eibe Frank, Geoffrey Holmes et al.

Obtaining accurate and well calibrated probability estimates from classifiers is useful in many applications, for example, when minimising the expected cost of classifications. Existing methods of calibrating probability estimates are applied globally, ignoring the potential for improvements by applying a more fine-grained model. We propose probability calibration trees, a modification of logistic model trees that identifies regions of the input space in which different probability calibration models are learned to improve performance. We compare probability calibration trees to two widely used calibration methods---isotonic regression and Platt scaling---and show that our method results in lower root mean squared error on average than both methods, for estimates produced by a variety of base learners.

Henry Gouk, Bernhard Pfahringer, Eibe Frank et al.

Effective regularisation of neural networks is essential to combat overfitting due to the large number of parameters involved. We present an empirical analogue to the Lipschitz constant of a feed-forward neural network, which we refer to as the maximum gain. We hypothesise that constraining the gain of a network will have a regularising effect, similar to how constraining the Lipschitz constant of a network has been shown to improve generalisation. A simple algorithm is provided that involves rescaling the weight matrix of each layer after each parameter update. We conduct a series of studies on common benchmark datasets, and also a novel dataset that we introduce to enable easier significance testing for experiments using convolutional networks. Performance on these datasets compares favourably with other common regularisation techniques.

Henry Gouk, Eibe Frank, Bernhard Pfahringer et al.

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple $p$-norms---of a feed forward neural network composed of commonly used layer types. Our technique is then used to formulate training a neural network with a bounded Lipschitz constant as a constrained optimisation problem that can be solved using projected stochastic gradient methods. Our evaluation study shows that the performance of the resulting models exceeds that of models trained with other common regularisers. We also provide evidence that the hyperparameters are intuitive to tune, demonstrate how the choice of norm for computing the Lipschitz constant impacts the resulting model, and show that the performance gains provided by our method are particularly noticeable when only a small amount of training data is available.

Michael Mayo, Eibe Frank

Can we evolve better training data for machine learning algorithms? To investigate this question we use population-based optimisation algorithms to generate artificial surrogate training data for naive Bayes for regression. We demonstrate that the generalisation performance of naive Bayes for regression models is enhanced by training them on the artificial data as opposed to the real data. These results are important for two reasons. Firstly, naive Bayes models are simple and interpretable but frequently underperform compared to more complex "black box" models, and therefore new methods of enhancing accuracy are called for. Secondly, the idea of using the real training data indirectly in the construction of the artificial training data, as opposed to directly for model training, is a novel twist on the usual machine learning paradigm.

Tim Leathart, Bernhard Pfahringer, Eibe Frank

A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish between each subset. Even though ensembles of nested dichotomies with random structure have been shown to perform well in practice, using a more sophisticated class subset selection method can be used to improve classification accuracy. We investigate an approach to this problem called random-pair selection, and evaluate its effectiveness compared to other published methods of subset selection. We show that our method outperforms other methods in many cases when forming ensembles of nested dichotomies, and is at least on par in all other cases.

Eibe Frank, Mark Hall, Bernhard Pfahringer

Despite its simplicity, the naive Bayes classifier has surprised machine learning researchers by exhibiting good performance on a variety of learning problems. Encouraged by these results, researchers have looked to overcome naive Bayes primary weakness - attribute independence - and improve the performance of the algorithm. This paper presents a locally weighted version of naive Bayes that relaxes the independence assumption by learning local models at prediction time. Experimental results show that locally weighted naive Bayes rarely degrades accuracy compared to standard naive Bayes and, in many cases, improves accuracy dramatically. The main advantage of this method compared to other techniques for enhancing naive Bayes is its conceptual and computational simplicity.