arXiv subjects

Sabine Müller

Publications and source records attributed to Sabine Müller.

8 recordsLinked to original sources

arXiv2026

Persistence Probability of Fractional Brownian Motion with Random Hurst Exponent

We study the persistence properties of a fractional Brownian motion whose Hurst exponent is a random variable instead of a fixed constant. For each fixed $H \in (0,1)$, it is well known that the persistence probability of an FBM below a constant barrier decays like $T^{-(1-H)+o(1)}$, as $T$ tends to infinity, cf. Molchan (1999). Our object of interest is the persistence probability of the process resulting from first randomly selecting $H\in (0,1)$ and then considering a fractional Brownian motion with this value of $H$ as a Hurst exponent, a process that is referred to as a fractional Brownian motion with random exponent. We prove that its persistence probability decays as $T^{-(1-H_0)+o(1)}$, as $T$ tends to infinity, where $H_0$ is the essential supremum of the distribution of the random Hurst exponent.

math.PR↗

arXiv2025

Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning

Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people's lives. This leads to explainable AI (XAI) manifesting itself as an important research field that helps humans to better comprehend ML systems. In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services. QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in the form of quantum-classical hybrid algorithms that combine quantum and classical resources. Quantum gates constitute the building blocks of gate-based quantum hardware and form circuits that can be used for quantum computations. For QML applications, quantum circuits are typically parameterized and their parameters are optimized classically such that a suitably defined objective function is minimized. Inspired by XAI, we raise the question of the explainability of such circuits by quantifying the importance of (groups of) gates for specific goals. To this end, we apply the well-established concept of Shapley values. The resulting attributions can be interpreted as explanations for why a specific circuit works well for a given task, improving the understanding of how to construct parameterized (or variational) quantum circuits, and fostering their human interpretability in general. An experimental evaluation on simulators and two superconducting quantum hardware devices demonstrates the benefits of the proposed framework for classification, generative modeling, transpilation, and optimization. Furthermore, our results shed some light on the role of specific gates in popular QML approaches.

quant-ph↗

arXiv2024

LLM-Generated Tips Rival Expert-Created Tips in Helping Students Answer Quantum-Computing Questions

Individual teaching is among the most successful ways to impart knowledge. Yet, this method is not always feasible due to large numbers of students per educator. Quantum computing serves as a prime example facing this issue, due to the hype surrounding it. Alleviating high workloads for teachers, often accompanied with individual teaching, is crucial for continuous high quality education. Therefore, leveraging Large Language Models (LLMs) such as GPT-4 to generate educational content can be valuable. We conducted two complementary studies exploring the feasibility of using GPT-4 to automatically generate tips for students. In the first one students (N=46) solved four multiple-choice quantum computing questions with either the help of expert-created or LLM-generated tips. To correct for possible biases towards LLMs, we introduced two additional conditions, making some participants believe that they were given expert-created tips, when they were given LLM-generated tips and vice versa. Our second study (N=23) aimed to directly compare the LLM-generated and expert-created tips, evaluating their quality, correctness and helpfulness, with both experienced educators and students participating. Participants in our second study found that the LLM-generated tips were significantly more helpful and pointed better towards relevant concepts than the expert-created tips, while being more prone to be giving away the answer. While participants in the first study performed significantly better in answering the quantum computing questions when given tips labeled as LLM-generated, even if they were created by an expert. This phenomenon could be a placebo effect induced by the participants' biases for LLM-generated content. Ultimately, we find that LLM-generated tips are good enough to be used instead of expert tips in the context of quantum computing basics.

cs.HC↗

arXiv2023

Feature Selection on Quantum Computers

In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higherquality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark datasets. We observe competitive performance.

quant-ph↗

arXiv2020

Robustness of Brain Tumor Segmentation

Purpose: The segmentation of brain tumors is one of the most active areas of medical image analysis. While current methods perform superhuman on benchmark data sets, their applicability in daily clinical practice has not been evaluated. In our work we investigate the generalization behavior of deep neural networks in this scenario. Approach: We evaluate the performance of three state-of-the-art methods, a basic U-net architecture and a cascadic Mumford-Shah approach. We also propose two simple modifications (which do not change the topology) to improve generalization performance. Results: In our experiments we show that a well-trained U-network shows the best generalization behavior and is sufficient to solve this segmentation problem. We illustrate why extensions of this model in a realistic scenario can be not only pointless but even harmful. Conclusions: We conclude from our experiments that the generalization performance of deep neural networks is severely limited in medical image analysis especially in the area of brain tumor segmentation. In our opinion, current topologies are optimized for the actual benchmark data set, but are not directly applicable in daily clinical practice.

eess.IV↗

arXiv2020

Object Segmentation Tracking from Generic Video Cues

We propose a light-weight variational framework for online tracking of object segmentations in videos based on optical flow and image boundaries. While high-end computer vision methods on this task rely on sequence specific training of dedicated CNN architectures, we show the potential of a variational model, based on generic video information from motion and color. Such cues are usually required for tasks such as robot navigation or grasp estimation. We leverage them directly for video object segmentation and thus provide accurate segmentations at potentially very low extra cost. Our simple method can provide competitive results compared to the costly CNN-based methods with parameter tuning. Furthermore, we show that our approach can be combined with state-of-the-art CNN-based segmentations in order to improve over their respective results. We evaluate our method on the datasets DAVIS 16,17 and SegTrack v2.

cs.CV↗

arXiv2020

Scalable Hyperparameter Optimization with Lazy Gaussian Processes

Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious manual (try and error) tuning of these parameters. Due to its very high sample efficiency, Bayesian Optimization over a Gaussian Processes modeling of the parameter space has become the method of choice. Unfortunately, this approach suffers from a cubic compute complexity due to underlying Cholesky factorization, which makes it very hard to be scaled beyond a small number of sampling steps. In this paper, we present a novel, highly accurate approximation of the underlying Gaussian Process. Reducing its computational complexity from cubic to quadratic allows an efficient strong scaling of Bayesian Optimization while outperforming the previous approach regarding optimization accuracy. The first experiments show speedups of a factor of 162 in single node and further speed up by a factor of 5 in a parallel environment.

cs.LG↗

arXiv2015

Prediction of Search Targets From Fixations in Open-World Settings

Previous work on predicting the target of visual search from human fixations only considered closed-world settings in which training labels are available and predictions are performed for a known set of potential targets. In this work we go beyond the state of the art by studying search target prediction in an open-world setting in which we no longer assume that we have fixation data to train for the search targets. We present a dataset containing fixation data of 18 users searching for natural images from three image categories within synthesised image collages of about 80 images. In a closed-world baseline experiment we show that we can predict the correct target image out of a candidate set of five images. We then present a new problem formulation for search target prediction in the open-world setting that is based on learning compatibilities between fixations and potential targets.

cs.CV↗