Kristoffer K. Wickstrøm

Anna Hedström, Philine Bommer, Kristoffer K. Wickstrøm et al.

One of the unsolved challenges in the field of Explainable AI (XAI) is determining how to most reliably estimate the quality of an explanation method in the absence of ground truth explanation labels. Resolving this issue is of utmost importance as the evaluation outcomes generated by competing evaluation methods (or ''quality estimators''), which aim at measuring the same property of an explanation method, frequently present conflicting rankings. Such disagreements can be challenging for practitioners to interpret, thereby complicating their ability to select the best-performing explanation method. We address this problem through a meta-evaluation of different quality estimators in XAI, which we define as ''the process of evaluating the evaluation method''. Our novel framework, MetaQuantus, analyses two complementary performance characteristics of a quality estimator: its resilience to noise and reactivity to randomness, thus circumventing the need for ground truth labels. We demonstrate the effectiveness of our framework through a series of experiments, targeting various open questions in XAI such as the selection and hyperparameter optimisation of quality estimators. Our work is released under an open-source license (https://github.com/annahedstroem/MetaQuantus) to serve as a development tool for XAI- and Machine Learning (ML) practitioners to verify and benchmark newly constructed quality estimators in a given explainability context. With this work, we provide the community with clear and theoretically-grounded guidance for identifying reliable evaluation methods, thus facilitating reproducibility in the field.

Eirik A. Østmo, Kristoffer K. Wickstrøm, Keyur Radiya et al.

Deep learning has the potential to revolutionize medical practice by automating and performing important tasks like detecting and delineating the size and locations of cancers in medical images. However, most deep learning models rely on augmentation techniques that treat medical images as natural images. For contrast-enhanced Computed Tomography (CT) images in particular, the signals producing the voxel intensities have physical meaning, which is lost during preprocessing and augmentation when treating such images as natural images. To address this, we propose a novel preprocessing and intensity augmentation scheme inspired by how radiologists leverage multiple viewing windows when evaluating CT images. Our proposed method, window shifting, randomly places the viewing windows around the region of interest during training. This approach improves liver lesion segmentation performance and robustness on images with poorly timed contrast agent. Our method outperforms classical intensity augmentations as well as the intensity augmentation pipeline of the popular nn-UNet on multiple datasets.

Lars Uebbing, Harald L. Joakimsen, Siyan Chen et al.

Most dimensionality reduction methods treat data as discrete point clouds, ignoring the continuous domain structure inherent to many real-world processes. To bridge this gap, we introduce Neural Operator Function Embedding (NOFE), a domain-aware framework for continuous dimensionality reduction. NOFE learns function-to-function mappings via a Graph Kernel Operator, enabling mesh-free evaluation at arbitrary query locations independent of input discretization. We establish NOFE as approximation of sheaf-to-sheaf mappings, generalizing Sheaf Neural Networks to continuous domains. We evaluate NOFE across different datasets, comparing it against PCA, t-SNE, and UMAP. Our results demonstrate that NOFE significantly outperforms baselines in local structure preservation, achieving a local Stress of 0.111 compared to 0.398 for PCA, 0.773 for t-SNE, and 0.791 for UMAP for the ERA5 climate reanalysis dataset. NOFE also exhibits robust sampling independence, reducing the Patch Stitching Error by up to $20.0\times$ relative to UMAP (59.0 vs. 267.6 under regional normalization) and ensuring consistency across disjoint domain patches. While maintaining competitive global structure preservation (Stress-1: 0.379 vs. PCA's 0.268), NOFE resolves fine-grained structures and produces smooth, consistent embeddings that generalize across varying sample densities, addressing key limitations of discrete reduction methods.

Thea Brüsch, Kristoffer K. Wickstrøm, Mikkel N. Schmidt et al.

State-of-the-art methods for explaining predictions from time series involve learning an instance-wise saliency mask for each time step; however, many types of time series are difficult to interpret in the time domain, due to the inherently complex nature of the data. Instead, we propose to view time series explainability as saliency maps over interpretable parts, leaning on established signal processing methodology on signal decomposition. Specifically, we propose a new method called FLEXtime that uses a bank of bandpass filters to split the time series into frequency bands. Then, we learn the combination of these bands that optimally explains the model's prediction. Our extensive evaluation shows that, on average, FLEXtime outperforms state-of-the-art explainability methods across a range of datasets. FLEXtime fills an important gap in the current time series explainability methodology and is a valuable tool for a wide range of time series such as EEG and audio. Code is available at https://github.com/theabrusch/FLEXtime.

Christian Salomonsen, Kristoffer K. Wickstrøm, Samuel Kuttner et al.

Kinetic modeling enables \textit{in vivo} quantification of tracer uptake and glucose metabolism in [${}^{18}$F]Fluorodeoxyglucose ([${}^{18}$F]FDG) dynamic positron emission tomography (dPET) imaging of mice. However, kinetic modeling requires the accurate determination of the arterial input function (AIF) during imaging, which is time-consuming and invasive. Recent studies have shown the efficacy of using deep learning to directly predict the input function, surpassing established methods such as the image-derived input function (IDIF). In this work, we trained a physics-informed deep learning-based input function prediction model (PIDLIF) to estimate the AIF directly from the PET images, incorporating a kinetic modeling loss during training. The proposed method uses a two-tissue compartment model over two regions, the myocardium and brain of the mice, and is trained on a dataset of 70 [${}^{18}$F]FDG dPET images of mice accompanied by the measured AIF during imaging. The proposed method had comparable performance to the network without a physics-informed loss, and when sudden movement causing blurring in the images was simulated, the PIDLIF model maintained high performance in severe cases of image degradation. The proposed physics-informed method exhibits an improved robustness that is promoted by physically constraining the problem, enforcing consistency for out-of-distribution samples. In conclusion, the PIDLIF model offers insight into the effects of leveraging physiological distribution mechanics in mice to guide a deep learning-based AIF prediction network in images with severe degradation as a result of blurring due to movement during imaging.

Christian Salomonsen, Luigi T Luppino, Fredrik Aspheim et al.

Dynamic positron emission tomography (PET) and kinetic modeling are pivotal in advancing tracer development research in small animal studies. Accurate kinetic modeling requires precise input function estimation, traditionally achieved via arterial blood sampling. However, arterial cannulation in small animals like mice, involves intricate, time-consuming, and terminal procedures, precluding longitudinal studies. This work proposes a non-invasive, fully convolutional deep learning-based approach (FC-DLIF) to predict input functions directly from PET imaging, potentially eliminating the need for blood sampling in dynamic small-animal PET. The proposed FC-DLIF model includes a spatial feature extractor acting on the volumetric time frames of the PET sequence, extracting spatial features. These are subsequently further processed in a temporal feature extractor that predicts the arterial input function. The proposed approach is trained and evaluated using images and arterial blood curves from [$^{18}$F]FDG data using cross validation. Further, the model applicability is evaluated on imaging data and arterial blood curves collected using two additional radiotracers ([$^{18}$F]FDOPA, and [$^{68}$Ga]PSMA). The model was further evaluated on data truncated and shifted in time, to simulate shorter, and shifted, PET scans. The proposed FC-DLIF model reliably predicts the arterial input function with respect to mean squared error and correlation. Furthermore, the FC-DLIF model is able to predict the arterial input function even from truncated and shifted samples. The model fails to predict the AIF from samples collected using different radiotracers, as these are not represented in the training data. Our deep learning-based input function offers a non-invasive and reliable alternative to arterial blood sampling, proving robust and flexible to temporal shifts and different scan durations.

Kristoffer K. Wickstrøm, Thea Brüsch, Michael C. Kampffmeyer et al.

Incorporating uncertainty is crucial to provide trustworthy explanations of deep learning models. Recent works have demonstrated how uncertainty modeling can be particularly important in the unsupervised field of representation learning explainable artificial intelligence (R-XAI). Current R-XAI methods provide uncertainty by measuring variability in the importance score. However, they fail to provide meaningful estimates of whether a pixel is certainly important or not. In this work, we propose a new R-XAI method called REPEAT that addresses the key question of whether or not a pixel is \textit{certainly} important. REPEAT leverages the stochasticity of current R-XAI methods to produce multiple estimates of importance, thus considering each pixel in an image as a Bernoulli random variable that is either important or unimportant. From these Bernoulli random variables we can directly estimate the importance of a pixel and its associated certainty, thus enabling users to determine certainty in pixel importance. Our extensive evaluation shows that REPEAT gives certainty estimates that are more intuitive, better at detecting out-of-distribution data, and more concise.

Eirik A. Østmo, Kristoffer K. Wickstrøm, Keyur Radiya et al.

Contrast-enhanced Computed Tomography (CT) is important for diagnosis and treatment planning for various medical conditions. Deep learning (DL) based segmentation models may enable automated medical image analysis for detecting and delineating tumors in CT images, thereby reducing clinicians' workload. Achieving generalization capabilities in limited data domains, such as radiology, requires modern DL models to be trained with image augmentation. However, naively applying augmentation methods developed for natural images to CT scans often disregards the nature of the CT modality, where the intensities measure Hounsfield Units (HU) and have important physical meaning. This paper challenges the use of such intensity augmentations for CT imaging and shows that they may lead to artifacts and poor generalization. To mitigate this, we propose a CT-specific augmentation technique, called Random windowing, that exploits the available HU distribution of intensities in CT images. Random windowing encourages robustness to contrast-enhancement and significantly increases model performance on challenging images with poor contrast or timing. We perform ablations and analysis of our method on multiple datasets, and compare to, and outperform, state-of-the-art alternatives, while focusing on the challenge of liver tumor segmentation.

Kristoffer K. Wickstrøm, Daniel J. Trosten, Sigurd Løkse et al.

Despite the significant improvements that representation learning via self-supervision has led to when learning from unlabeled data, no methods exist that explain what influences the learned representation. We address this need through our proposed approach, RELAX, which is the first approach for attribution-based explanations of representations. Our approach can also model the uncertainty in its explanations, which is essential to produce trustworthy explanations. RELAX explains representations by measuring similarities in the representation space between an input and masked out versions of itself, providing intuitive explanations and significantly outperforming the gradient-based baseline. We provide theoretical interpretations of RELAX and conduct a novel analysis of feature extractors trained using supervised and unsupervised learning, providing insights into different learning strategies. Finally, we illustrate the usability of RELAX in multi-view clustering and highlight that incorporating uncertainty can be essential for providing low-complexity explanations, taking a crucial step towards explaining representations.