Researcher profile

Wouter Verbeke

Wouter Verbeke contributes to research discovery and scholarly infrastructure.

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Published work

12 published item(s)

preprint2026arXiv

Foundation Models for Credit Risk Prediction: A Game Changer?

Predictive models play a pivotal role in credit risk management, guiding critical decisions through accurate estimation of default probabilities and losses. Extensive research has introduced new modeling techniques, complemented by large-scale benchmarking studies consolidating the state-of-the-art. Today, quasi-standards such as gradient-boosting models paired with SHAP explainers have emerged, yet continuous improvement of risk models remains a top priority. Concurrently, rapid advancements in AI, most notably large language models, have disrupted predictive modeling paradigms. Foundation models, pretrained on extensive datasets from diverse domains, have demonstrated remarkable performance by leveraging prior knowledge. While prevalent in natural language processing and computer vision, foundation models for tabular data have only recently emerged. We conjecture that pretraining on out-of-domain data is particularly beneficial in small-data settings, such as SME lending or specialized corporate portfolios, and may help address longstanding challenges including low default portfolios and class imbalance. This paper benchmarks recently proposed tabular foundation models against a broad set of competitors, including established and advanced machine learning techniques, across two core tasks: PD and LGD modeling. Our evaluation encompasses various datasets, performance indicators, and experimental conditions. We find that tabular foundation models generally perform best across datasets and tasks. Moreover, they offer significant improvement in predictive performance as dataset size shrinks. These results are remarkable given that the models are tested out-of-the-box, without hyperparameter tuning, ensuring ease of use and mitigating computational costs.

preprint2022arXiv

A new perspective on classification: optimally allocating limited resources to uncertain tasks

A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a small subset of transactions to their fraud investigations team. Typically, such problems are solved using a classification framework, where the focus is on predicting task outcomes given a set of characteristics. Resources are then allocated to the tasks that are predicted to be the most likely to succeed. However, we argue that using classification to address task uncertainty is inherently suboptimal as it does not take into account the available capacity. Therefore, we first frame the problem as a type of assignment problem. Then, we present a novel solution using learning to rank by directly optimizing the assignment's expected profit given limited, stochastic capacity. This is achieved by optimizing a specific instance of the net discounted cumulative gain, a commonly used class of metrics in learning to rank. Empirically, we demonstrate that our new method achieves higher expected profit and expected precision compared to a classification approach for a wide variety of application areas and data sets. This illustrates the benefit of an integrated approach and of explicitly considering the available resources when learning a predictive model.

preprint2022arXiv

Prescriptive maintenance with causal machine learning

Machine maintenance is a challenging operational problem, where the goal is to plan sufficient preventive maintenance to avoid machine failures and overhauls. Maintenance is often imperfect in reality and does not make the asset as good as new. Although a variety of imperfect maintenance policies have been proposed in the literature, these rely on strong assumptions regarding the effect of maintenance on the machine's condition, assuming the effect is (1) deterministic or governed by a known probability distribution, and (2) machine-independent. This work proposes to relax both assumptions by learning the effect of maintenance conditional on a machine's characteristics from observational data on similar machines using existing methodologies for causal inference. By predicting the maintenance effect, we can estimate the number of overhauls and failures for different levels of maintenance and, consequently, optimize the preventive maintenance frequency to minimize the total estimated cost. We validate our proposed approach using real-life data on more than 4,000 maintenance contracts from an industrial partner. Empirical results show that our novel, causal approach accurately predicts the maintenance effect and results in individualized maintenance schedules that are more accurate and cost-effective than supervised or non-individualized approaches.

preprint2021arXiv

To do or not to do: cost-sensitive causal decision-making

Causal classification models are adopted across a variety of operational business processes to predict the effect of a treatment on a categorical business outcome of interest depending on the process instance characteristics. This allows optimizing operational decision-making and selecting the optimal treatment to apply in each specific instance, with the aim of maximizing the positive outcome rate. While various powerful approaches have been presented in the literature for learning causal classification models, no formal framework has been elaborated for optimal decision-making based on the estimated individual treatment effects, given the cost of the various treatments and the benefit of the potential outcomes. In this article, we therefore extend upon the expected value framework and formally introduce a cost-sensitive decision boundary for double binary causal classification, which is a linear function of the estimated individual treatment effect, the positive outcome probability and the cost and benefit parameters of the problem setting. The boundary allows causally classifying instances in the positive and negative treatment class to maximize the expected causal profit, which is introduced as the objective at hand in cost-sensitive causal classification. We introduce the expected causal profit ranker which ranks instances for maximizing the expected causal profit at each possible threshold for causally classifying instances and differs from the conventional ranking approach based on the individual treatment effect. The proposed ranking approach is experimentally evaluated on synthetic and marketing campaign data sets. The results indicate that the presented ranking method effectively outperforms the cost-insensitive ranking approach and allows boosting profitability.

preprint2020arXiv

A Comparative Study of Social Network Classifiers for Predicting Churn in the Telecommunication Industry

Relational learning in networked data has been shown to be effective in a number of studies. Relational learners, composed of relational classifiers and collective inference methods, enable the inference of nodes in a network given the existence and strength of links to other nodes. These methods have been adapted to predict customer churn in telecommunication companies showing that incorporating them may give more accurate predictions. In this research, the performance of a variety of relational learners is compared by applying them to a number of CDR datasets originating from the telecommunication industry, with the goal to rank them as a whole and investigate the effects of relational classifiers and collective inference methods separately. Our results show that collective inference methods do not improve the performance of relational classifiers and the best performing relational classifier is the network-only link-based classifier, which builds a logistic model using link-based measures for the nodes in the network.

preprint2020arXiv

A study of the U.S. domestic air transportation network: Temporal evolution of network topology and robustness from 2001 to 2016

The U.S. air transportation network (ATN) is critical to the mobility and the functioning of the United States. It is thus necessary to ensure that it is well-connected, efficient, and robust. Despite extensive research on its topology, the temporal evolution of the network's robustness and tolerance remains largely unexplored. In the present paper, a temporal study of the domestic U.S. ATN was performed based on annual flight data from 1996 to 2016 and network analytics were used to examine the effects of restructuring that followed the 9/11 events along with the current state of the system. Centrality measures were computed to assess the system's topology and its global robustness. A node deletion method was applied to assess the network's tolerance by simulating a targeted attack scenario. The study showed that the 9/11 terrorist attacks triggered vast restructuring of the network, in terms of efficiency and security. Air traffic expanded, as new airports and air routes were introduced. Airlines reconsidered their strategy and optimized their operations, thus allowing the network to recover rapidly and become even more efficient. Security concerns resulted in significant improvement of the network's robustness. Since 2001, the global traffic and topological properties of the U.S. ATN have displayed continuous growth, due to the network's expansion. On the other hand, the robustness of the system has not shown an improving tendency. Findings suggest that although the system's ability to sustain its operational level under extreme circumstances has lately improved, its tolerance to targeted attacks has deteriorated. The presented methodology may be applied on different network levels or different transportation networks, to provide a general perspective of the system's vulnerabilities.

preprint2020arXiv

Autoencoders for strategic decision support

In the majority of executive domains, a notion of normality is involved in most strategic decisions. However, few data-driven tools that support strategic decision-making are available. We introduce and extend the use of autoencoders to provide strategically relevant granular feedback. A first experiment indicates that experts are inconsistent in their decision making, highlighting the need for strategic decision support. Furthermore, using two large industry-provided human resources datasets, the proposed solution is evaluated in terms of ranking accuracy, synergy with human experts, and dimension-level feedback. This three-point scheme is validated using (a) synthetic data, (b) the perspective of data quality, (c) blind expert validation, and (d) transparent expert evaluation. Our study confirms several principal weaknesses of human decision-making and stresses the importance of synergy between a model and humans. Moreover, unsupervised learning and in particular the autoencoder are shown to be valuable tools for strategic decision-making.

preprint2020arXiv

HydaLearn: Highly Dynamic Task Weighting for Multi-task Learning with Auxiliary Tasks

Multi-task learning (MTL) can improve performance on a task by sharing representations with one or more related auxiliary-tasks. Usually, MTL-networks are trained on a composite loss function formed by a constant weighted combination of the separate task losses. In practice, constant loss weights lead to poor results for two reasons: (i) the relevance of the auxiliary tasks can gradually drift throughout the learning process; (ii) for mini-batch based optimisation, the optimal task weights vary significantly from one update to the next depending on mini-batch sample composition. We introduce HydaLearn, an intelligent weighting algorithm that connects main-task gain to the individual task gradients, in order to inform dynamic loss weighting at the mini-batch level, addressing i and ii. Using HydaLearn, we report performance increases on synthetic data, as well as on two supervised learning domains.

preprint2020arXiv

Instance-Dependent Cost-Sensitive Learning for Detecting Transfer Fraud

Card transaction fraud is a growing problem affecting card holders worldwide. Financial institutions increasingly rely upon data-driven methods for developing fraud detection systems, which are able to automatically detect and block fraudulent transactions. From a machine learning perspective, the task of detecting fraudulent transactions is a binary classification problem. Classification models are commonly trained and evaluated in terms of statistical performance measures, such as likelihood and AUC, respectively. These measures, however, do not take into account the actual business objective, which is to minimize the financial losses due to fraud. Fraud detection is to be acknowledged as an instance-dependent cost-sensitive classification problem, where the costs due to misclassification vary between instances, and requiring adapted approaches for learning a classification model. In this article, an instance-dependent threshold is derived, based on the instance-dependent cost matrix for transfer fraud detection, that allows for making the optimal cost-based decision for each transaction. Two novel classifiers are presented, based on lasso-regularized logistic regression and gradient tree boosting, which directly minimize the proposed instance-dependent cost measure when learning a classification model. The proposed methods are implemented in the R packages cslogit and csboost, and compared against state-of-the-art methods on a publicly available data set from the machine learning competition website Kaggle and a proprietary card transaction data set. The results of the experiments highlight the potential of reducing fraud losses by adopting the proposed methods.

preprint2020arXiv

Learning to rank for uplift modeling

Uplift modeling has effectively been used in fields such as marketing and customer retention, to target those customers that are most likely to respond due to the campaign or treatment. Uplift models produce uplift scores which are then used to essentially create a ranking. We instead investigate to learn to rank directly by looking into the potential of learning-to-rank techniques in the context of uplift modeling. We propose a unified formalisation of different global uplift modeling measures in use today and explore how these can be integrated into the learning-to-rank framework. Additionally, we introduce a new metric for learning-to-rank that focusses on optimizing the area under the uplift curve called the promoted cumulative gain (PCG). We employ the learning-to-rank technique LambdaMART to optimize the ranking according to PCG and show improved results over standard learning-to-rank metrics and equal to improved results when compared with state-of-the-art uplift modeling. Finally, we show how learning-to-rank models can learn to optimize a certain targeting depth, however, these results do not generalize on the test set.

preprint2020arXiv

Misclassification cost-sensitive ensemble learning: A unifying framework

Over the years, a plethora of cost-sensitive methods have been proposed for learning on data when different types of misclassification errors incur different costs. Our contribution is a unifying framework that provides a comprehensive and insightful overview on cost-sensitive ensemble methods, pinpointing their differences and similarities via a fine-grained categorization. Our framework contains natural extensions and generalisations of ideas across methods, be it AdaBoost, Bagging or Random Forest, and as a result not only yields all methods known to date but also some not previously considered.

preprint2020arXiv

Social Network Analytics for Churn Prediction in Telco: Model Building, Evaluation and Network Architecture

Social network analytics methods are being used in the telecommunication industry to predict customer churn with great success. In particular it has been shown that relational learners adapted to this specific problem enhance the performance of predictive models. In the current study we benchmark different strategies for constructing a relational learner by applying them to a total of eight distinct call-detail record datasets, originating from telecommunication organizations across the world. We statistically evaluate the effect of relational classifiers and collective inference methods on the predictive power of relational learners, as well as the performance of models where relational learners are combined with traditional methods of predicting customer churn in the telecommunication industry. Finally we investigate the effect of network construction on model performance; our findings imply that the definition of edges and weights in the network does have an impact on the results of the predictive models. As a result of the study, the best configuration is a non-relational learner enriched with network variables, without collective inference, using binary weights and undirected networks. In addition, we provide guidelines on how to apply social networks analytics for churn prediction in the telecommunication industry in an optimal way, ranging from network architecture to model building and evaluation.