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Anselm Hudde

Publications and source records attributed to Anselm Hudde.

6 recordsLinked to original sources

Backdoor attacks on DNN and GBDT -- A Case Study from the insurance domain

Machine learning (ML) will likely play a large role in many processes in the future, also for insurance companies. However, ML models are at risk of being attacked and manipulated. In this work, the robustness of Gradient Boosted Decision Tree (GBDT) models and Deep Neural Networks (DNN) within an insurance context will be evaluated. Therefore, two GBDT models and two DNNs are trained on two different tabular datasets from an insurance context. Past research in this domain mainly used homogenous data and there are comparably few insights regarding heterogenous tabular data. The ML tasks performed on the datasets are claim prediction (regression) and fraud detection (binary classification). For the backdoor attacks different samples containing a specific pattern were crafted and added to the training data. It is shown, that this type of attack can be highly successful, even with a few added samples. The backdoor attacks worked well on the models trained on one dataset but poorly on the models trained on the other. In real-world scenarios the attacker will have to face several obstacles but as attacks can work with very few added samples this risk should be evaluated.

cs.LG

Training Gradient Boosted Decision Trees on Tabular Data Containing Label Noise for Classification Tasks

Label noise, which refers to the mislabeling of instances in a dataset, can significantly impair classifier performance, increase model complexity, and affect feature selection. While most research has concentrated on deep neural networks for image and text data, this study explores the impact of label noise on gradient-boosted decision trees (GBDTs), the leading algorithm for tabular data. This research fills a gap by examining the robustness of GBDTs to label noise, focusing on adapting two noise detection methods from deep learning for use with GBDTs and introducing a new detection method called Gradients. Additionally, we extend a method initially designed for GBDTs to incorporate relabeling. By using diverse datasets such as Covertype and Breast Cancer, we systematically introduce varying levels of label noise and evaluate the effectiveness of early stopping and noise detection methods in maintaining model performance. Our noise detection methods achieve state-of-the-art results, with a noise detection accuracy above 99% on the Adult dataset across all noise levels. This work enhances the understanding of label noise in GBDTs and provides a foundation for future research in noise detection and correction methods.

cs.LG

On the Itô-Alekseev-Gröbner formula for stochastic differential equations

In this article we establish a new formula for the difference of a test function of the solution of a stochastic differential equation and of the test function of an Itô process. The introduced formula essentially generalizes both the classical Alekseev-Gröbner formula from the literature on deterministic differential equations as well as the classical Itô formula from stochastic analysis. The proposed Itô-Alekseev-Gröbner formula is a powerful tool for deriving strong approximation rates for perturbations and approximations of stochastic ordinary and partial differential equations.

math.PR

European and Asian Greeks for exponential Lévy processes

In this paper we give easy-to-implement closed-form expressions for European and Asian Greeks for general L2-payoff functions and underlying assets in an exponential Lévy process model with nonvanishing Brownian motion part. The results are based on Hilbert space valued Malliavin Calculus and extend previous results from the literature. Numerical experiments suggest, that in the case of a continuous payoff function, a combination of Malliavin Monte Carlo Greeks and the finite difference method has a better convergence behavior, whereas in the case of discontinuous payoff functions, the Malliavin Monte Carlo method clearly is the superior method compared to the finite difference approach, for first- and second order Greeks. Reduction arguments from the literature based on measure change imply that the expressions for the Greeks in this paper also hold true for generalized Asian options in particular for fixed and floating strike Asian options.

math.PR

On moments and strong local Hölder regularity of solutions of stochastic differential equations and of their spatial derivative processes

Spatial differentiability of solutions of stochastic differential equations (SDEs) is a classical question in stochastic analysis. The case of coefficients with globally Lipschitz continuous derivatives is well understood in the literature. Counterexamples with smooth and bounded coefficients demonstrate that the non-globally Lipschitz case is more subtle. In this article we establish conditions, including a suitable local monotonicity property, which provide existence of continuously differentiable solutions of SDEs, moment estimates and strong local Hölder regularity.

math.PR

A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations

There are numerous applications of the classical (deterministic) Gronwall inequality. Recently, Michael Scheutzow discovered a stochastic Gronwall inequality which provides upper bounds for $p$-th moments, $p\in(0,1)$, of the supremum of nonnegative scalar continuous processes which satisfy a linear integral inequality. In this article we complement this with upper bounds for $p$-th moments, $p\in[2,\infty)$, of the supremum of general Itô processes which satisfy a suitable one-sided affine-linear growth condition. As example applications, we improve known results on strong local Lipschitz continuity in the starting point of solutions of stochastic differential equations (SDEs), on (exponential) moment estimates for SDEs, on strong completeness of SDEs, and on perturbation estimates for SDEs.

math.PR