Clustering in high-dimensional settings with severe feature noise remains challenging, especially when only a small subset of dimensions is informative and the final number of clusters is not specified in advance. In such regimes, partition recovery, feature relevance learning, and structural adaptation are tightly coupled, and standard likelihood-based methods can become unstable or overly sensitive to noisy dimensions. We propose DIVI, a data-informed variational clustering framework that combines global feature gating with split-based adaptive structure growth. DIVI uses informative prior initialization to stabilize optimization, learns feature relevance in a differentiable manner, and expands model complexity only when local diagnostics indicate underfit. Beyond clustering performance, we also examine runtime scalability and parameter sensitivity in order to clarify the computational and practical behavior of the framework. Empirically, we find that DIVI performs competitively under severe feature noise, remains computationally feasible, and yields interpretable feature-gating behavior, while also exhibiting conservative growth and identifiable failure regimes in challenging settings. Overall, DIVI is best viewed as a practical variational clustering framework for noisy high-dimensional data rather than as a fully Bayesian generative solution.

Random forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods based on Shapley values have been introduced to refine the analysis of feature relevance in tree-based models to a local (per instance) level. In this context, we first show that the global Mean Decrease of Impurity (MDI) variable importance scores correspond to Shapley values under some conditions. Then, we derive a local MDI importance measure of variable relevance, which has a very natural connection with the global MDI measure and can be related to a new notion of local feature relevance. We further link local MDI importances with Shapley values and discuss them in the light of related measures from the literature. The measures are illustrated through experiments on several classification and regression problems.

Clustering algorithms often assume all features contribute equally to the data structure, an assumption that usually fails in high-dimensional or noisy settings. Feature weighting methods can address this, but most require additional parameter tuning. We propose SHARK (Shapley Reweighted $k$-means), a feature-weighted clustering algorithm motivated by the use of Shapley values from cooperative game theory to quantify feature relevance, which requires no additional parameters beyond those in $k$-means. We prove that the $k$-means objective can be decomposed into a sum of per-feature Shapley values, providing an axiomatic foundation for unsupervised feature relevance and reducing Shapley computation from exponential to polynomial time. SHARK iteratively re-weights features by the inverse of their Shapley contribution, emphasising informative dimensions and down-weighting irrelevant ones. Experiments on synthetic and real-world data sets show that SHARK consistently matches or outperforms existing methods, achieving superior robustness and accuracy, particularly in scenarios where noise may be present. Software: https://github.com/rickfawley/shark.

There have been several attempts to develop Feature Selection (FS) algorithms capable of identifying features that are relevant in a dataset. Although in certain applications the FS algorithms can be seen to be successful, they have similar basic limitations. In all cases, the global feature selection algorithms seek to select features that are relevant and common to all classes of the dataset. This is a major limitation since there could be features that are specifically useful for a particular class while irrelevant for other classes, and full explanation of the relationship at class level therefore cannot be determined. While the inclusion of such features for all classes could cause improved predictive ability for the relevant class, the same features could be problematic for other classes. In this paper, we examine this issue and also develop a class-level feature selection method called the Feature Weighted Growing Self-Organising Map (FWGSOM). The proposed method carries out feature analysis at class level which enhances its ability to identify relevant features for each class. Results from experiments indicate that our method performs better than other methods, gives explainable results at class level, and has a low computational footprint when compared to other methods.

Random forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods based on Shapley values have been introduced to refine the analysis of feature relevance in tree-based models to a local (per instance) level. In this context, we first show that the global Mean Decrease of Impurity (MDI) variable importance scores correspond to Shapley values under some conditions. Then, we derive a local MDI importance measure of variable relevance, which has a very natural connection with the global MDI measure and can be related to a new notion of local feature relevance. We further link local MDI importances with Shapley values and discuss them in the light of related measures from the literature. The measures are illustrated through experiments on several classification and regression problems.

Brain-computer interface (BCI) systems facilitate unique communication between humans and computers, benefiting severely disabled individuals. Despite decades of research, BCIs are not fully integrated into clinical and commercial settings. It's crucial to assess and explain BCI performance, offering clear explanations for potential users to avoid frustration when it doesn't work as expected. This work investigates the efficacy of different deep learning and Riemannian geometry-based classification models in the context of motor imagery (MI) based BCI using electroencephalography (EEG). We then propose an optimal transport theory-based approach using earth mover's distance (EMD) to quantify the comparison of the feature relevance map with the domain knowledge of neuroscience. For this, we utilized explainable AI (XAI) techniques for generating feature relevance in the spatial domain to identify important channels for model outcomes. Three state-of-the-art models are implemented - 1) Riemannian geometry-based classifier, 2) EEGNet, and 3) EEG Conformer, and the observed trend in the model's accuracy across different architectures on the dataset correlates with the proposed feature relevance metrics. The models with diverse architectures perform significantly better when trained on channels relevant to motor imagery than data-driven channel selection. This work focuses attention on the necessity for interpretability and incorporating metrics beyond accuracy, underscores the value of combining domain knowledge and quantifying model interpretations with data-driven approaches in creating reliable and robust Brain-Computer Interfaces (BCIs).

We introduce and investigate the iterated application of Generalized Matrix Learning Vector Quantizaton for the analysis of feature relevances in classification problems, as well as for the construction of class-discriminative subspaces. The suggested Iterated Relevance Matrix Analysis (IRMA) identifies a linear subspace representing the classification specific information of the considered data sets using Generalized Matrix Learning Vector Quantization (GMLVQ). By iteratively determining a new discriminative subspace while projecting out all previously identified ones, a combined subspace carrying all class-specific information can be found. This facilitates a detailed analysis of feature relevances, and enables improved low-dimensional representations and visualizations of labeled data sets. Additionally, the IRMA-based classdiscriminative subspace can be used for dimensionality reduction and the training of robust classifiers with potentially improved performance. Preprint submitted to Neurocomputing January 24, 2024 1. Introduction Prototype-based systems such as Learning Vector Quantization (LVQ) [1, 2, 3, 4] can serve as genuinely interpretable and transparent classification tools [5].

As ChatGPT et al. conquer the world, the optimal liability framework for AI systems remains an unsolved problem across the globe. In a much-anticipated move, the European Commission advanced two proposals outlining the European approach to AI liability in September 2022: a novel AI Liability Directive and a revision of the Product Liability Directive. They constitute the final cornerstone of EU AI regulation. Crucially, the liability proposals and the EU AI Act are inherently intertwined: the latter does not contain any individual rights of affected persons, and the former lack specific, substantive rules on AI development and deployment. Taken together, these acts may well trigger a Brussels Effect in AI regulation, with significant consequences for the US and beyond. This paper makes three novel contributions. First, it examines in detail the Commission proposals and shows that, while making steps in the right direction, they ultimately represent a half-hearted approach: if enacted as foreseen, AI liability in the EU will primarily rest on disclosure of evidence mechanisms and a set of narrowly defined presumptions concerning fault, defectiveness and causality. Hence, second, the article suggests amendments, which are collected in an Annex at the end of the paper. Third, based on an analysis of the key risks AI poses, the final part of the paper maps out a road for the future of AI liability and regulation, in the EU and beyond. This includes: a comprehensive framework for AI liability; provisions to support innovation; an extension to non-discrimination/algorithmic fairness, as well as explainable AI; and sustainability. I propose to jump-start sustainable AI regulation via sustainability impact assessments in the AI Act and sustainable design defects in the liability regime. In this way, the law may help spur not only fair AI and XAI, but potentially also sustainable AI (SAI).

Neural classifiers are non linear systems providing decisions on the classes of patterns, for a given problem they have learned. The output computed by a classifier for each pattern constitutes an approximation of the output of some unknown function, mapping pattern data to their respective classes. The lack of knowledge of such a function along with the complexity of neural classifiers, especially when these are deep learning architectures, do not permit to obtain information on how specific predictions have been made. Hence, these powerful learning systems are considered as black boxes and in critical applications their use tends to be considered inappropriate. Gaining insight on such a black box operation constitutes a one way approach in interpreting operation of neural classifiers and assessing the validity of their decisions. In this paper we tackle this problem introducing a novel methodology for discovering which features are considered relevant by a trained neural classifier and how they affect the classifier's output, thus obtaining an explanation on its decision. Although, feature relevance has received much attention in the machine learning literature here we reconsider it in terms of nonlinear parameter estimation targeted by a set membership approach which is based on interval analysis. Hence, the proposed methodology builds on sound mathematical approaches and the results obtained constitute a reliable estimation of the classifier's decision premises.

This article studies how to detect and explain concept drift. Human activity recognition is used as a case study together with a online batch learning situation where the quality of the labels used in the model updating process starts to decrease. Drift detection is based on identifying a set of features having the largest relevance difference between the drifting model and a model that is known to be accurate and monitoring how the relevance of these features changes over time. As a main result of this article, it is shown that feature relevance analysis cannot only be used to detect the concept drift but also to explain the reason for the drift when a limited number of typical reasons for the concept drift are predefined. To explain the reason for the concept drift, it is studied how these predefined reasons effect to feature relevance. In fact, it is shown that each of these has an unique effect to features relevance and these can be used to explain the reason for concept drift.