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.

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.

We explore multiple-instance verification, a problem setting where 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 quality of the explanations provided for the classifications. Ablation studies confirm the superior ability of the new attention functions to identify key instances.

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.

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 their strong empirical performance, rehearsal methods still suffer from a poor approximation of past data's loss landscape 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 the 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.

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.

Game-theoretic attribution techniques based on Shapley values are used extensively 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 are not well defined on 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 to obtain explicit convergence rates of $O(1/n)$, improving on $O(1/\sqrt{n})$ for plain Monte Carlo. 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.

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.

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.

We present an online algorithm that induces decision trees using gradient information as the source of supervision. In contrast to previous approaches to gradient-based tree learning, we do not require soft splits or construction of a new tree for every update. In experiments, our method performs comparably to standard incremental classification trees and outperforms state of the art incremental regression trees. We also show how the method can be used to construct a novel type of neural network layer suited to learning representations from tabular data and find that it increases accuracy of multiclass and multi-label classification.