In many machine learning problems, understanding variable importance is a central concern. Two common approaches are Permute-and-Predict (PaP), which randomly permutes a feature in a validation set, and Leave-One-Covariate-Out (LOCO), which retrains models after permuting a training feature. Both methods deem a variable important if predictions with the original data substantially outperform those with permutations. In linear regression, empirical studies have linked PaP to regression coefficients and LOCO to $t$-statistics, but a formal theory has been lacking. We derive closed-form expressions for both measures, expressed using square-root transformations. PaP is shown to be proportional to the coefficient and predictor variability: $\text{PaP}_i = β_i \sqrt{2\operatorname{Var}(\mathbf{x}^v_i)}$, while LOCO is proportional to the coefficient but dampened by collinearity (captured by $Δ$): $\text{LOCO}_i = β_i (1 -Δ)\sqrt{1 + c}$. These derivations explain why PaP is largely unaffected by multicollinearity, whereas LOCO is highly sensitive to it. Monte Carlo simulations confirm these findings across varying levels of collinearity. Although derived for linear regression, we also show that these results provide reasonable approximations for models like Random Forests. Overall, this work establishes a theoretical basis for two widely used importance measures, helping analysts understand how they are affected by the true coefficients, dimension, and covariance structure. This work bridges empirical evidence and theory, enhancing the interpretability and application of variable importance measures.

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce \textit{Stochastic Parameter Decomposition} (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd/tree/spd-paper.

Ensuring consistent product quality in modern manufacturing is crucial, particularly in safety-critical applications. Conventional quality control approaches, reliant on manually defined thresholds and features, lack adaptability to the complexity and variability inherent in production data and necessitate extensive domain expertise. Conversely, data-driven methods, such as machine learning, demonstrate high detection performance but typically function as black-box models, thereby limiting their acceptance in industrial environments where interpretability is paramount. This paper introduces a methodology for industrial fault detection, which is both data-driven and transparent. The approach integrates a supervised machine learning model for multi-class fault classification, Shapley Additive Explanations for post-hoc interpretability, and a do-main-specific visualisation technique that maps model explanations to operator-interpretable features. Furthermore, the study proposes an evaluation methodology that assesses model explanations through quantitative perturbation analysis and evaluates visualisations by qualitative expert assessment. The approach was applied to the crimping process, a safety-critical joining technique, using a dataset of univariate, discrete time series. The system achieves a fault detection accuracy of 95.9 %, and both quantitative selectivity analysis and qualitative expert evaluations confirmed the relevance and inter-pretability of the generated explanations. This human-centric approach is designed to enhance trust and interpretability in data-driven fault detection, thereby contributing to applied system design in industrial quality control.

Explainability is necessary for many tasks in biomedical research. Recent explainability methods have focused on attention, gradient, and Shapley value. These do not handle data with strong associated prior knowledge and fail to constrain explainability results based on known relationships between predictive features. We propose GraphPINE, a graph neural network (GNN) architecture leveraging domain-specific prior knowledge to initialize node importance optimized during training for drug response prediction. Typically, a manual post-prediction step examines literature (i.e., prior knowledge) to understand returned predictive features. While node importance can be obtained for gradient and attention after prediction, node importance from these methods lacks complementary prior knowledge; GraphPINE seeks to overcome this limitation. GraphPINE differs from other GNN gating methods by utilizing an LSTM-like sequential format. We introduce an importance propagation layer that unifies 1) updates for feature matrix and node importance and 2) uses GNN-based graph propagation of feature values. This initialization and updating mechanism allows for informed feature learning and improved graph representation. We apply GraphPINE to cancer drug response prediction using drug screening and gene data collected for over 5,000 gene nodes included in a gene-gene graph with a drug-target interaction (DTI) graph for initial importance. The gene-gene graph and DTIs were obtained from curated sources and weighted by article count discussing relationships between drugs and genes. GraphPINE achieves a PR-AUC of 0.894 and ROC-AUC of 0.796 across 952 drugs. Code is available at https://anonymous.4open.science/r/GraphPINE-40DE.

Node importance estimation, a classical problem in network analysis, underpins various web applications. Previous methods either exploit intrinsic topological characteristics, e.g., graph centrality, or leverage additional information, e.g., data heterogeneity, for node feature enhancement. However, these methods follow the supervised learning setting, overlooking the fact that ground-truth node-importance data are usually partially labeled in practice. In this work, we propose the first semi-supervised node importance estimation framework, i.e., EASING, to improve learning quality for unlabeled data in heterogeneous graphs. Different from previous approaches, EASING explicitly captures uncertainty to reflect the confidence of model predictions. To jointly estimate the importance values and uncertainties, EASING incorporates DJE, a deep encoder-decoder neural architecture. DJE introduces distribution modeling for graph nodes, where the distribution representations derive both importance and uncertainty estimates. Additionally, DJE facilitates effective pseudo-label generation for the unlabeled data to enrich the training samples. Based on labeled and pseudo-labeled data, EASING develops effective semi-supervised heteroscedastic learning with varying node uncertainty regularization. Extensive experiments on three real-world datasets highlight the superior performance of EASING compared to competing methods. Codes are available via https://github.com/yankai-chen/EASING.

Machine learning (ML) models serve as powerful tools for threat detection and mitigation; however, they also introduce potential new risks. Adversarial input can exploit these models through standard interfaces, thus creating new attack pathways that threaten critical network operations. As ML advancements progress, adversarial strategies become more advanced, and conventional defenses such as adversarial training are costly in computational terms and often fail to provide real-time detection. These methods typically require a balance between robustness and model performance, which presents challenges for applications that demand instant response. To further investigate this vulnerability, we suggest a novel strategy for detecting and mitigating adversarial attacks using eXplainable Artificial Intelligence (XAI). This approach is evaluated in real time within intrusion detection systems (IDS), leading to the development of a zero-touch mitigation strategy. Additionally, we explore various scenarios in the Radio Resource Control (RRC) layer within the Open Radio Access Network (O-RAN) framework, emphasizing the critical need for enhanced mitigation techniques to strengthen IDS defenses against advanced threats and implement a zero-touch mitigation solution. Extensive testing across different scenarios in the RRC layer of the O-RAN infrastructure validates the ability of the framework to detect and counteract integrated RRC-layer attacks when paired with adversarial strategies, emphasizing the essential need for robust defensive mechanisms to strengthen IDS against complex threats.

While XAI focuses on providing AI explanations to humans, can the reverse - humans explaining their judgments to AI - foster richer, synergistic human-AI systems? This paper explores various forms of human inputs to AI and examines how human explanations can guide machine learning models toward automated judgments and explanations that align more closely with human concepts.

Sensor-based Human Activity Recognition (HAR) in smart home environments is crucial for several applications, especially in the healthcare domain. The majority of the existing approaches leverage deep learning models. While these approaches are effective, the rationale behind their outputs is opaque. Recently, eXplainable Artificial Intelligence (XAI) approaches emerged to provide intuitive explanations to the output of HAR models. To the best of our knowledge, these approaches leverage classic deep models like CNNs or RNNs. Recently, Graph Neural Networks (GNNs) proved to be effective for sensor-based HAR. However, existing approaches are not designed with explainability in mind. In this work, we propose the first explainable Graph Neural Network explicitly designed for smart home HAR. Our results on two public datasets show that this approach provides better explanations than state-of-the-art methods while also slightly improving the recognition rate.