Stefan Haufe

Rick Wilming, Leo Kieslich, Benedict Clark et al.

In recent years, the community of 'explainable artificial intelligence' (XAI) has created a vast body of methods to bridge a perceived gap between model 'complexity' and 'interpretability'. However, a concrete problem to be solved by XAI methods has not yet been formally stated. As a result, XAI methods are lacking theoretical and empirical evidence for the 'correctness' of their explanations, limiting their potential use for quality-control and transparency purposes. At the same time, Haufe et al. (2014) showed, using simple toy examples, that even standard interpretations of linear models can be highly misleading. Specifically, high importance may be attributed to so-called suppressor variables lacking any statistical relation to the prediction target. This behavior has been confirmed empirically for a large array of XAI methods in Wilming et al. (2022). Here, we go one step further by deriving analytical expressions for the behavior of a variety of popular XAI methods on a simple two-dimensional binary classification problem involving Gaussian class-conditional distributions. We show that the majority of the studied approaches will attribute non-zero importance to a non-class-related suppressor feature in the presence of correlated noise. This poses important limitations on the interpretations and conclusions that the outputs of these XAI methods can afford.

Benedict Clark, Rick Wilming, Stefan Haufe

The field of 'explainable' artificial intelligence (XAI) has produced highly cited methods that seek to make the decisions of complex machine learning (ML) methods 'understandable' to humans, for example by attributing 'importance' scores to input features. Yet, a lack of formal underpinning leaves it unclear as to what conclusions can safely be drawn from the results of a given XAI method and has also so far hindered the theoretical verification and empirical validation of XAI methods. This means that challenging non-linear problems, typically solved by deep neural networks, presently lack appropriate remedies. Here, we craft benchmark datasets for three different non-linear classification scenarios, in which the important class-conditional features are known by design, serving as ground truth explanations. Using novel quantitative metrics, we benchmark the explanation performance of a wide set of XAI methods across three deep learning model architectures. We show that popular XAI methods are often unable to significantly outperform random performance baselines and edge detection methods. Moreover, we demonstrate that explanations derived from different model architectures can be vastly different; thus, prone to misinterpretation even under controlled conditions.

Marta Oliveira, Rick Wilming, Benedict Clark et al.

Convolutional Neural Networks (CNNs) are frequently and successfully used in medical prediction tasks. They are often used in combination with transfer learning, leading to improved performance when training data for the task are scarce. The resulting models are highly complex and typically do not provide any insight into their predictive mechanisms, motivating the field of "explainable" artificial intelligence (XAI). However, previous studies have rarely quantitatively evaluated the "explanation performance" of XAI methods against ground-truth data, and transfer learning and its influence on objective measures of explanation performance has not been investigated. Here, we propose a benchmark dataset that allows for quantifying explanation performance in a realistic magnetic resonance imaging (MRI) classification task. We employ this benchmark to understand the influence of transfer learning on the quality of explanations. Experimental results show that popular XAI methods applied to the same underlying model differ vastly in performance, even when considering only correctly classified examples. We further observe that explanation performance strongly depends on the task used for pre-training and the number of CNN layers pre-trained. These results hold after correcting for a substantial correlation between explanation and classification performance.

Stefan Haufe, Rick Wilming, Benedict Clark et al.

The field of "explainable artificial intelligence" (XAI) seemingly addresses the desire that decisions of machine learning systems should be human-understandable. However, in its current state, XAI itself needs scrutiny. Popular methods cannot reliably answer relevant questions about ML models, their training data, or test inputs, because they systematically attribute importance to input features that are independent of the prediction target. This limits the utility of XAI for diagnosing and correcting data and models, for scientific discovery, and for identifying intervention targets. The fundamental reason for this is that current XAI methods do not address well-defined problems and are not evaluated against targeted criteria of explanation correctness. Researchers should formally define the problems they intend to solve and design methods accordingly. This will lead to diverse use-case-dependent notions of explanation correctness and objective metrics of explanation performance that can be used to validate XAI algorithms.

Marco Morik, Ali Hashemi, Klaus-Robert Müller et al.

Reconstructing brain sources is a fundamental challenge in neuroscience, crucial for understanding brain function and dysfunction. Electroencephalography (EEG) signals have a high temporal resolution. However, identifying the correct spatial location of brain sources from these signals remains difficult due to the ill-posed structure of the problem. Traditional methods predominantly rely on manually crafted priors, missing the flexibility of data-driven learning, while recent deep learning approaches focus on end-to-end learning, typically using the physical information of the forward model only for generating training data. We propose the novel hybrid method 3D-PIUNet for EEG source localization that effectively integrates the strengths of traditional and deep learning techniques. 3D-PIUNet starts from an initial physics-informed estimate by using the pseudo inverse to map from measurements to source space. Secondly, by viewing the brain as a 3D volume, we use a 3D convolutional U-Net to capture spatial dependencies and refine the solution according to the learned data prior. Training the model relies on simulated pseudo-realistic brain source data, covering different source distributions. Trained on this data, our model significantly improves spatial accuracy, demonstrating superior performance over both traditional and end-to-end data-driven methods. Additionally, we validate our findings with real EEG data from a visual task, where 3D-PIUNet successfully identifies the visual cortex and reconstructs the expected temporal behavior, thereby showcasing its practical applicability.

Benedict Clark, Rick Wilming, Artur Dox et al.

The evolving landscape of explainable artificial intelligence (XAI) aims to improve the interpretability of intricate machine learning (ML) models, yet faces challenges in formalisation and empirical validation, being an inherently unsupervised process. In this paper, we bring together various benchmark datasets and novel performance metrics in an initial benchmarking platform, the Explainable AI Comparison Toolkit (EXACT), providing a standardised foundation for evaluating XAI methods. Our datasets incorporate ground truth explanations for class-conditional features, and leveraging novel quantitative metrics, this platform assesses the performance of post-hoc XAI methods in the quality of the explanations they produce. Our recent findings have highlighted the limitations of popular XAI methods, as they often struggle to surpass random baselines, attributing significance to irrelevant features. Moreover, we show the variability in explanations derived from different equally performing model architectures. This initial benchmarking platform therefore aims to allow XAI researchers to test and assure the high quality of their newly developed methods.

Rick Wilming, Artur Dox, Hjalmar Schulz et al.

Large pre-trained language models have become a crucial backbone for many downstream tasks in natural language processing (NLP), and while they are trained on a plethora of data containing a variety of biases, such as gender biases, it has been shown that they can also inherit such biases in their weights, potentially affecting their prediction behavior. However, it is unclear to what extent these biases also affect feature attributions generated by applying "explainable artificial intelligence" (XAI) techniques, possibly in unfavorable ways. To systematically study this question, we create a gender-controlled text dataset, GECO, in which the alteration of grammatical gender forms induces class-specific words and provides ground truth feature attributions for gender classification tasks. This enables an objective evaluation of the correctness of XAI methods. We apply this dataset to the pre-trained BERT model, which we fine-tune to different degrees, to quantitatively measure how pre-training induces undesirable bias in feature attributions and to what extent fine-tuning can mitigate such explanation bias. To this extent, we provide GECOBench, a rigorous quantitative evaluation framework for benchmarking popular XAI methods. We show a clear dependency between explanation performance and the number of fine-tuned layers, where XAI methods are observed to benefit particularly from fine-tuning or complete retraining of embedding layers.

Céline Budding, Fabian Eitel, Kerstin Ritter et al.

Over the last years, many 'explainable artificial intelligence' (xAI) approaches have been developed, but these have not always been objectively evaluated. To evaluate the quality of heatmaps generated by various saliency methods, we developed a framework to generate artificial data with synthetic lesions and a known ground truth map. Using this framework, we evaluated two data sets with different backgrounds, Perlin noise and 2D brain MRI slices, and found that the heatmaps vary strongly between saliency methods and backgrounds. We strongly encourage further evaluation of saliency maps and xAI methods using this framework before applying these in clinical or other safety-critical settings.

Rick Wilming, Céline Budding, Klaus-Robert Müller et al.

Machine learning (ML) is increasingly often used to inform high-stakes decisions. As complex ML models (e.g., deep neural networks) are often considered black boxes, a wealth of procedures has been developed to shed light on their inner workings and the ways in which their predictions come about, defining the field of 'explainable AI' (XAI). Saliency methods rank input features according to some measure of 'importance'. Such methods are difficult to validate since a formal definition of feature importance is, thus far, lacking. It has been demonstrated that some saliency methods can highlight features that have no statistical association with the prediction target (suppressor variables). To avoid misinterpretations due to such behavior, we propose the actual presence of such an association as a necessary condition and objective preliminary definition for feature importance. We carefully crafted a ground-truth dataset in which all statistical dependencies are well-defined and linear, serving as a benchmark to study the problem of suppressor variables. We evaluate common explanation methods including LRP, DTD, PatternNet, PatternAttribution, LIME, Anchors, SHAP, and permutation-based methods with respect to our objective definition. We show that most of these methods are unable to distinguish important features from suppressors in this setting.

Ali Hashemi, Yijing Gao, Chang Cai et al.

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate science. In these domains, both the model parameters to be inferred and the measurement noise may exhibit a complex spatio-temporal structure. Existing work either neglects the temporal structure or leads to computationally demanding inference schemes. Overcoming these limitations, we devise a novel flexible hierarchical Bayesian framework within which the spatio-temporal dynamics of model parameters and noise are modeled to have Kronecker product covariance structure. Inference in our framework is based on majorization-minimization optimization and has guaranteed convergence properties. Our highly efficient algorithms exploit the intrinsic Riemannian geometry of temporal autocovariance matrices. For stationary dynamics described by Toeplitz matrices, the theory of circulant embeddings is employed. We prove convex bounding properties and derive update rules of the resulting algorithms. On both synthetic and real neural data from M/EEG, we demonstrate that our methods lead to improved performance.

Lucas C. Parra, Stefan Haufe, Jacek P. Dmochowski

How does one find dimensions in multivariate data that are reliably expressed across repetitions? For example, in a brain imaging study one may want to identify combinations of neural signals that are reliably expressed across multiple trials or subjects. For a behavioral assessment with multiple ratings, one may want to identify an aggregate score that is reliably reproduced across raters. Correlated Components Analysis (CorrCA) addresses this problem by identifying components that are maximally correlated between repetitions (e.g. trials, subjects, raters). Here we formalize this as the maximization of the ratio of between-repetition to within-repetition covariance. We show that this criterion maximizes repeat-reliability, defined as mean over variance across repeats, and that it leads to CorrCA or to multi-set Canonical Correlation Analysis, depending on the constraints. Surprisingly, we also find that CorrCA is equivalent to Linear Discriminant Analysis for zero-mean signals, which provides an unexpected link between classic concepts of multivariate analysis. We present an exact parametric test of statistical significance based on the F-statistic for normally distributed independent samples, and present and validate shuffle statistics for the case of dependent samples. Regularization and extension to non-linear mappings using kernels are also presented. The algorithms are demonstrated on a series of data analysis applications, and we provide all code and data required to reproduce the results.

Irene Winkler, Danny Panknin, Daniel Bartz et al.

Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-reversed data. They show that this procedure, time-reversed Granger causality (TRGC), robustly rejects causal interpretations on mixtures of independent signals. While promising results have been achieved in simulations, it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction. Here we prove that, for linear finite-order autoregressive processes with unidirectional information flow, the application of time reversal for testing Granger causality indeed leads to correct estimates of information flow and its directionality. Using simulations, we further show that TRGC is able to infer correct directionality with similar statistical power as the net Granger causality between two variables, while being much more robust to the presence of measurement noise.