arXiv subjects

Tim Verdonck

Publications and source records attributed to Tim Verdonck.

At least 37 records · Page 2Linked to original sources

arXiv2023

Fast Linear Model Trees by PILOT

Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard for standard decision trees. But most existing methods for fitting linear model trees are time consuming and therefore not scalable to large data sets. In addition, they are more prone to overfitting and extrapolation issues than standard regression trees. In this paper we introduce PILOT, a new algorithm for linear model trees that is fast, regularized, stable and interpretable. PILOT trains in a greedy fashion like classic regression trees, but incorporates an $L^2$ boosting approach and a model selection rule for fitting linear models in the nodes. The abbreviation PILOT stands for $PI$ecewise $L$inear $O$rganic $T$ree, where `organic' refers to the fact that no pruning is carried out. PILOT has the same low time and space complexity as CART without its pruning. An empirical study indicates that PILOT tends to outperform standard decision trees and other linear model trees on a variety of data sets. Moreover, we prove its consistency in an additive model setting under weak assumptions. When the data is generated by a linear model, the convergence rate is polynomial.

stat.ML↗

arXiv2023

On the causality-preservation capabilities of generative modelling

Modeling lies at the core of both the financial and the insurance industry for a wide variety of tasks. The rise and development of machine learning and deep learning models have created many opportunities to improve our modeling toolbox. Breakthroughs in these fields often come with the requirement of large amounts of data. Such large datasets are often not publicly available in finance and insurance, mainly due to privacy and ethics concerns. This lack of data is currently one of the main hurdles in developing better models. One possible option to alleviating this issue is generative modeling. Generative models are capable of simulating fake but realistic-looking data, also referred to as synthetic data, that can be shared more freely. Generative Adversarial Networks (GANs) is such a model that increases our capacity to fit very high-dimensional distributions of data. While research on GANs is an active topic in fields like computer vision, they have found limited adoption within the human sciences, like economics and insurance. Reason for this is that in these fields, most questions are inherently about identification of causal effects, while to this day neural networks, which are at the center of the GAN framework, focus mostly on high-dimensional correlations. In this paper we study the causal preservation capabilities of GANs and whether the produced synthetic data can reliably be used to answer causal questions. This is done by performing causal analyses on the synthetic data, produced by a GAN, with increasingly more lenient assumptions. We consider the cross-sectional case, the time series case and the case with a complete structural model. It is shown that in the simple cross-sectional scenario where correlation equals causation the GAN preserves causality, but that challenges arise for more advanced analyses.

cs.LG↗

arXiv2022

Fraud Analytics: A Decade of Research -- Organizing Challenges and Solutions in the Field

The literature on fraud analytics and fraud detection has seen a substantial increase in output in the past decade. This has led to a wide range of research topics and overall little organization of the many aspects of fraud analytical research. The focus of academics ranges from identifying fraudulent credit card payments to spotting illegitimate insurance claims. In addition, there is a wide range of methods and research objectives. This paper aims to provide an overview of fraud analytics in research and aims to more narrowly organize the discipline and its many subfields. We analyze a sample of almost 300 records on fraud analytics published between 2011 and 2020. In a systematic way, we identify the most prominent domains of application, challenges faced, performance metrics, and methods used. In addition, we build a framework for fraud analytical methods and propose a keywording strategy for future research. One of the key challenges in fraud analytics is access to public datasets. To further aid the community, we provide eight requirements for suitable data sets in research motivated by our research. We structure our sample of the literature in an online database. The database is available online for fellow researchers to investigate and potentially build upon.

cs.CR↗

arXiv2022

mCube: Multinomial Micro-level reserving Model

This paper presents a multinomial multi-state micro-level reserving model, denoted mCube. We propose a unified framework for modelling the time and the payment process for IBNR and RBNS claims and for modeling IBNR claim counts. We use multinomial distributions for the time process and spliced mixture models for the payment process. We illustrate the excellent performance of the proposed model on a real data set of a major insurance company consisting of bodily injury claims. It is shown that the proposed model produces a best estimate distribution that is centered around the true reserve.

stat.AP↗

arXiv2022

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.

econ.GN↗

arXiv2022

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.

cs.LG↗

arXiv2021

Weight-of-evidence 2.0 with shrinkage and spline-binning

In many practical applications, such as fraud detection, credit risk modeling or medical decision making, classification models for assigning instances to a predefined set of classes are required to be both precise as well as interpretable. Linear modeling methods such as logistic regression are often adopted, since they offer an acceptable balance between precision and interpretability. Linear methods, however, are not well equipped to handle categorical predictors with high-cardinality or to exploit non-linear relations in the data. As a solution, data preprocessing methods such as weight-of-evidence are typically used for transforming the predictors. The binning procedure that underlies the weight-of-evidence approach, however, has been little researched and typically relies on ad-hoc or expert driven procedures. The objective in this paper, therefore, is to propose a formalized, data-driven and powerful method. To this end, we explore the discretization of continuous variables through the binning of spline functions, which allows for capturing non-linear effects in the predictor variables and yields highly interpretable predictors taking only a small number of discrete values. Moreover, we extend upon the weight-of-evidence approach and propose to estimate the proportions using shrinkage estimators. Together, this offers an improved ability to exploit both non-linear and categorical predictors for achieving increased classification precision, while maintaining interpretability of the resulting model and decreasing the risk of overfitting. We present the results of a series of experiments in a fraud detection setting, which illustrate the effectiveness of the presented approach. We facilitate reproduction of the presented results and adoption of the proposed approaches by providing both the dataset and the code for implementing the experiments and the presented approach.

stat.ML↗

arXiv2021

Noise robustness of persistent homology on greyscale images, across filtrations and signatures

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image noise, and quantify the loss of performance in classifying the MNIST handwritten digits when noise is added to the data. The results show that the sensitivity to noise of PH is influenced by the choice of filtrations and persistence signatures (respectively the input and output of PH), and in particular, that PH features are often not robust to noise in a classification task.

math.AT↗

arXiv2021

Computational Efficient Approximations of the Concordance Probability in a Big Data Setting

Performance measurement is an essential task once a statistical model is created. The Area Under the receiving operating characteristics Curve (AUC) is the most popular measure for evaluating the quality of a binary classifier. In this case, AUC is equal to the concordance probability, a frequently used measure to evaluate the discriminatory power of the model. Contrary to AUC, the concordance probability can also be extended to the situation with a continuous response variable. Due to the staggering size of data sets nowadays, determining this discriminatory measure requires a tremendous amount of costly computations and is hence immensely time consuming, certainly in case of a continuous response variable. Therefore, we propose two estimation methods that calculate the concordance probability in a fast and accurate way and that can be applied to both the discrete and continuous setting. Extensive simulation studies show the excellent performance and fast computing times of both estimators. Finally, experiments on two real-life data sets confirm the conclusions of the artificial simulations.

stat.CO↗

arXiv2020

Sparse dimension reduction based on energy and ball statistics

As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which rely on minimal to no model assumptions. These are defined according to an optimization criterion that maximizes a nonparametric measure of association. The original estimators are nonsparse, which means that all variables contribute to the model. However, in many practical applications, an SDR technique may be called for that is sparse and as such, intrinsically performs sufficient variable selection (SVS). This paper examines how such a sparse SDR estimator can be constructed. Three variants are investigated, depending on different measures of association: distance covariance, martingale difference divergence and ball covariance. A simulation study shows that each of these estimators can achieve correct variable selection in highly nonlinear contexts, yet are sensitive to outliers and computationally intensive. The study sheds light on the subtle differences between the methods. Two examples illustrate how these new estimators can be applied in practice, with a slight preference for the option based on martingale difference divergence in the bioinformatics example.

stat.ME↗

arXiv2020

direpack: A Python 3 package for state-of-the-art statistical dimension reduction methods

The direpack package aims to establish a set of modern statistical dimension reduction techniques into the Python universe as a single, consistent package. The dimension reduction methods included resort into three categories: projection pursuit based dimension reduction, sufficient dimension reduction, and robust M estimators for dimension reduction. As a corollary, regularized regression estimators based on these reduced dimension spaces are provided as well, ranging from classical principal component regression up to sparse partial robust M regression. The package also contains a set of classical and robust pre-processing utilities, including generalized spatial signs, as well as dedicated plotting functionality and cross-validation utilities. Finally, direpack has been written consistent with the scikit-learn API, such that the estimators can flawlessly be included into (statistical and/or machine) learning pipelines in that framework.

stat.CO↗

arXiv2020

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.

stat.AP↗

arXiv2020

robROSE: A robust approach for dealing with imbalanced data in fraud detection

A major challenge when trying to detect fraud is that the fraudulent activities form a minority class which make up a very small proportion of the data set. In most data sets, fraud occurs in typically less than 0.5% of the cases. Detecting fraud in such a highly imbalanced data set typically leads to predictions that favor the majority group, causing fraud to remain undetected. We discuss some popular oversampling techniques that solve the problem of imbalanced data by creating synthetic samples that mimic the minority class. A frequent problem when analyzing real data is the presence of anomalies or outliers. When such atypical observations are present in the data, most oversampling techniques are prone to create synthetic samples that distort the detection algorithm and spoil the resulting analysis. A useful tool for anomaly detection is robust statistics, which aims to find the outliers by first fitting the majority of the data and then flagging data observations that deviate from it. In this paper, we present a robust version of ROSE, called robROSE, which combines several promising approaches to cope simultaneously with the problem of imbalanced data and the presence of outliers. The proposed method achieves to enhance the presence of the fraud cases while ignoring anomalies. The good performance of our new sampling technique is illustrated on simulated and real data sets and it is shown that robROSE can provide better insight in the structure of the data. The source code of the robROSE algorithm is made freely available.

cs.LG↗

arXiv2020

Cellwise Robust M Regression

The cellwise robust M regression estimator is introduced as the first estimator of its kind that intrinsically yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust against vertical outliers and leverage points. As a by-product, the method yields a weighted and imputed data set that contains estimates of what the values in cellwise outliers would need to amount to if they had fit the model. The method is illustrated to be equally robust as its casewise counterpart, MM regression. The cellwise regression method discards less information than any casewise robust estimator. Therefore, predictive power can be expected to be at least as good as casewise alternatives. These results are corroborated in a simulation study. Moreover, while the simulations show that predictive performance is at least on par with casewise methods if not better, an application to a data set consisting of compositions of Swiss nutrients, shows that in individual cases, CRM can achieve a significantly higher predictive accuracy compared to MM regression.

stat.ME↗

arXiv2019

Concordance probability in a big data setting: application in non-life insurance

The concordance probability or C-index is a popular measure to capture the discriminatory ability of a regression model. In this article, the definition of this measure is adapted to the specific needs of the frequency and severity model, typically used during the technical pricing of a non-life insurance product. Due to the typical large sample size of the frequency data in particular, two different adaptations of the estimation procedure of the concordance probability are presented. Note that the latter procedures can be applied to all different versions of the concordance probability.

math.AP↗

arXiv2018

The Minimum Regularized Covariance Determinant estimator

The Minimum Covariance Determinant (MCD) approach robustly estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension exceeds the subset size. We propose the Minimum Regularized Covariance Determinant (MRCD) approach, which differs from the MCD in that the scatter matrix is a convex combination of a target matrix and the sample covariance matrix of the subset. A data-driven procedure sets the weight of the target matrix, so that the regularization is only used when needed. The MRCD estimator is defined in any dimension, is well-conditioned by construction and preserves the good robustness properties of the MCD. We prove that so-called concentration steps can be performed to reduce the MRCD objective function, and we exploit this fact to construct a fast algorithm. We verify the accuracy and robustness of the MRCD estimator in a simulation study and illustrate its practical use for outlier detection and regression analysis on real-life high-dimensional data sets in chemistry and criminology.

stat.ME↗

arXiv2018

Multivariate Constrained Robust M-Regression for Shaping Forward Curves in Electricity Markets

In this paper, a multivariate constrained robust M-regression (MCRM) method is developed to estimate shaping coefficients for electricity forward prices. An important benefit of the new method is that model arbitrage can be ruled out at an elementary level, as all shaping coefficients are treated simultaneously. Moreover, the new method is robust to outliers, such that the provided results are stable and not sensitive to isolated sparks or dips in the market. An efficient algorithm is presented to estimate all shaping coefficients at a low computational cost. To illustrate its good performance, the method is applied to German electricity prices.

stat.AP↗

arXiv2017

Profit Driven Decision Trees for Churn Prediction

Customer retention campaigns increasingly rely on predictive models to detect potential churners in a vast customer base. From the perspective of machine learning, the task of predicting customer churn can be presented as a binary classification problem. Using data on historic behavior, classification algorithms are built with the purpose of accurately predicting the probability of a customer defecting. The predictive churn models are then commonly selected based on accuracy related performance measures such as the area under the ROC curve (AUC). However, these models are often not well aligned with the core business requirement of profit maximization, in the sense that, the models fail to take into account not only misclassification costs, but also the benefits originating from a correct classification. Therefore, the aim is to construct churn prediction models that are profitable and preferably interpretable too. The recently developed expected maximum profit measure for customer churn (EMPC) has been proposed in order to select the most profitable churn model. We present a new classifier that integrates the EMPC metric directly into the model construction. Our technique, called ProfTree, uses an evolutionary algorithm for learning profit driven decision trees. In a benchmark study with real-life data sets from various telecommunication service providers, we show that ProfTree achieves significant profit improvements compared to classic accuracy driven tree-based methods.

stat.ML↗