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Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high‐dimensional time‐series data are challenging tasks in study of real‐world complex systems, which demand interpretable data representations to facilitate comprehension of both spatial and temporal information within the original data space. This study proposes a general and analytical ultralow‐dimensionality reduction method for dynamical systems named spatial‐temporal principal component analysis (stPCA) to fully represent the dynamics of a high‐dimensional time‐series by only a single latent variable without distortion, which transforms high‐dimensional spatial information into one‐dimensional temporal information based on nonlinear delay‐embedding theory. The dynamics of this single variable is analytically solved and theoretically preserves the temporal property of original high‐dimensional time‐series, thereby accurately and reliably identifying the tipping point before an upcoming critical transition. Its applications to real‐world datasets such as individual‐specific heterogeneous ICU records demonstrate the effectiveness of stPCA, which quantitatively and robustly provides the early‐warning signals of the critical/tipping state on each patient. The proposed spatial‐temporal principal component analysis (stPCA) method analytically reduces high‐dimensional time‐series data to a single latent variable by transforming spatial information into temporal dynamics. By preserving the temporal properties of the original data, stPCA effectively identifies critical transitions and tipping points. It provides robust early‐warning signals, demonstrating effectiveness on both simulation and real‐world datasets.

Interpretable representations are the backbone of many explainers that target black-box predictive systems based on artificial intelligence and machine learning algorithms. They translate the low-level data representation necessary for good predictive performance into high-level human-intelligible concepts used to convey the explanatory insights. Notably, the explanation type and its cognitive complexity are directly controlled by the interpretable representation, tweaking which allows to target a particular audience and use case. However, many explainers built upon interpretable representations overlook their merit and fall back on default solutions that often carry implicit assumptions, thereby degrading the explanatory power and reliability of such techniques. To address this problem, we study properties of interpretable representations that encode presence and absence of human-comprehensible concepts. We demonstrate how they are operationalised for tabular, image and text data; discuss their assumptions, strengths and weaknesses; identify their core building blocks; and scrutinise their configuration and parameterisation. In particular, this in-depth analysis allows us to pinpoint their explanatory properties, desiderata and scope for (malicious) manipulation in the context of tabular data where a linear model is used to quantify the influence of interpretable concepts on a black-box prediction. Our findings lead to a range of recommendations for designing trustworthy interpretable representations; specifically, the benefits of class-aware (supervised) discretisation of tabular data, e.g., with decision trees, and sensitivity of image interpretable representations to segmentation granularity and occlusion colour.

We investigate the applicability of machine learning technologies to the development of parsimonious, interpretable, catchment‐scale hydrologic models using directed‐graph architectures based on the mass‐conserving perceptron (MCP) as the fundamental computational unit. Here, we focus on architectural complexity (depth) at a single location, rather than universal applicability (breadth) across large samples of catchments. The goal is to discover a minimal representation (numbers of cell‐states and flow paths) that represents the dominant processes that can explain the input‐state‐output behaviors of a given catchment, with particular emphasis given to simulating the full range (high, medium, and low) of flow dynamics. We find that a “HyMod Like” architecture with three cell‐states and two major flow pathways achieves such a representation at our study location, but that the additional incorporation of an input‐bypass mechanism significantly improves the timing and shape of the hydrograph, while the inclusion of bi‐directional groundwater mass exchanges significantly enhances the simulation of baseflow. Overall, our results demonstrate the importance of using multiple diagnostic metrics for model evaluation, while highlighting the need for properly selecting and designing the training metrics based on information‐theoretic foundations that are better suited to extracting information across the full range of flow dynamics. This study sets the stage for interpretable regional‐scale MCP‐based hydrological modeling (using large sample data) by using neural architecture search to determine appropriate minimal representations for catchments in different hydroclimatic regimes. Plain Language Summary We show that conventional machine learning technologies can be used to develop parsimonious, interpretable, catchment‐scale hydrologic models using the mass‐conserving perceptron (MCP) as a fundamental computational unit. Using data from the Leaf River Basin, we test a variety of minimal, dominant process, representations that can explain the input‐state‐output dynamics of the catchment. Our results demonstrate the importance of using multiple diagnostic metrics for evaluation and comparison of different model architectures, and highlight the importance of choosing (or designing) objective functions for model training that are properly suited to the task of extracting information across the full range of flow dynamics. This depth‐focus study sets the stage for interpretable regional‐scale MCP‐based hydrological modeling (using large sample data) by using neural architecture search to determine appropriate minimal representations for catchments in different hydroclimatic regimes. Key Points We utilize mass‐conserving perceptron (MCP) directed‐graph architectures to develop concise, interpretable catchment‐scale hydrologic models We focus on model complexity (depth) at a single location, rather than universal applicability (breadth) across large samples of catchments This study set the stage for interpretable MCP‐based modeling to find minimal representations in different hydroclimatic regimes

In this paper we introduce a new class of software tools engaged in delivering successful explanations of complex processes on top of basic Explainable AI (XAI) software systems. These tools, that we call cumulatively Explanatory AI (YAI) systems, enhance the quality of the basic output of a XAI by adopting a user-centred approach to explanation that can cater to the individual needs of the explainees with measurable improvements in usability. Our approach is based on Achinstein’s theory of explanations, where explaining is an illocutionary (i.e., broad yet pertinent and deliberate) act of pragmatically answering a question. Accordingly, user-centrality enters in the equation by considering that the overall amount of information generated by answering all questions can rapidly become overwhelming and that individual users may perceive the need to explore just a few of them. In this paper, we give the theoretical foundations of YAI, formally defining a user-centred explanatory tool and the space of all possible explanations, or explanatory space, generated by it. To this end, we frame the explanatory space as an hypergraph of knowledge and we identify a set of heuristics and properties that can help approximating a decomposition of it into a tree-like representation for efficient and user-centred explanation retrieval. Finally, we provide some old and new empirical results to support our theory, showing that explanations are more than textual or visual presentations of the sole information provided by a XAI.

The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. Prior research has mostly focused on improving the accuracy and efficiency of classifiers, with interpretability being somewhat neglected. This aspect of classifiers has become critical for many application domains and the introduction of the EU GDPR legislation in 2018 is likely to further emphasize the importance of interpretable learning algorithms. Currently, state-of-the-art classification accuracy is achieved with very complex models based on large ensembles (COTE) or deep neural networks (FCN). These approaches are not efficient with regard to either time or space, are difficult to interpret and cannot be applied to variable-length time series, requiring pre-processing of the original series to a set fixed-length. In this paper we propose new time series classification algorithms to address these gaps. Our approach is based on symbolic representations of time series, efficient sequence mining algorithms and linear classification models. Our linear models are as accurate as deep learning models but are more efficient regarding running time and memory, can work with variable-length time series and can be interpreted by highlighting the discriminative symbolic features on the original time series. We advance the state-of-the-art in time series classification by proposing new algorithms built using the following three key ideas: (1) Multiple resolutions of symbolic representations: we combine symbolic representations obtained using different parameters, rather than one fixed representation (e.g., multiple SAX representations); (2) Multiple domain representations: we combine symbolic representations in time (e.g., SAX) and frequency (e.g., SFA) domains, to be more robust across problem types; (3) Efficient navigation in a huge symbolic-words space: we extend a symbolic sequence classifier (SEQL) to work with multiple symbolic representations and use its greedy feature selection strategy to effectively filter the best features for each representation. We show that our multi-resolution multi-domain linear classifier (mtSS-SEQL+LR) achieves a similar accuracy to the state-of-the-art COTE ensemble, and to recent deep learning methods (FCN, ResNet), but uses a fraction of the time and memory required by either COTE or deep models. To further analyse the interpretability of our classifier, we present a case study on a human motion dataset collected by the authors. We discuss the accuracy, efficiency and interpretability of our proposed algorithms and release all the results, source code and data to encourage reproducibility.

GNNs are powerful models based on node representation learning that perform particularly well in many machine learning problems related to graphs. The major obstacle to the deployment of GNNs is mostly a problem of societal acceptability and trustworthiness, properties which require making explicit the internal functioning of such models. Here, we propose to mine activation rules in the hidden layers to understand how the GNNs perceive the world. The problem is not to discover activation rules that are individually highly discriminating for an output of the model. Instead, the challenge is to provide a small set of rules that cover all input graphs. To this end, we introduce the subjective activation pattern domain. We define an effective and principled algorithm to enumerate activations rules in each hidden layer. The proposed approach for quantifying the interest of these rules is rooted in information theory and is able to account for background knowledge on the input graph data. The activation rules can then be redescribed thanks to pattern languages involving interpretable features. We show that the activation rules provide insights on the characteristics used by the GNN to classify the graphs. Especially, this allows to identify the hidden features built by the GNN through its different layers. Also, these rules can subsequently be used for explaining GNN decisions. Experiments on both synthetic and real-life datasets show highly competitive performance, with up to 200% improvement in fidelity on explaining graph classification over the SOTA methods.

Machine learning (ML) methods, such as artificial neural networks (ANN), k-nearest neighbors (kNN), random forests (RF), support vector machines (SVM), and boosted decision trees (DTs), may offer stronger predictive performance than more traditional, parametric methods, such as linear regression, multiple linear regression, and logistic regression (LR), for specific mapping and modeling tasks. However, this increased performance is often accompanied by increased model complexity and decreased interpretability, resulting in critiques of their “black box” nature, which highlights the need for algorithms that can offer both strong predictive performance and interpretability. This is especially true when the global model and predictions for specific data points need to be explainable in order for the model to be of use. Explainable boosting machines (EBM), an augmentation and refinement of generalize additive models (GAMs), has been proposed as an empirical modeling method that offers both interpretable results and strong predictive performance. The trained model can be graphically summarized as a set of functions relating each predictor variable to the dependent variable along with heat maps representing interactions between selected pairs of predictor variables. In this study, we assess EBMs for predicting the likelihood or probability of slope failure occurrence based on digital terrain characteristics in four separate Major Land Resource Areas (MLRAs) in the state of West Virginia, USA and compare the results to those obtained with LR, kNN, RF, and SVM. EBM provided predictive accuracies comparable to RF and SVM and better than LR and kNN. The generated functions and visualizations for each predictor variable and included interactions between pairs of predictor variables, estimation of variable importance based on average mean absolute scores, and provided scores for each predictor variable for new predictions add interpretability, but additional work is needed to quantify how these outputs may be impacted by variable correlation, inclusion of interaction terms, and large feature spaces. Further exploration of EBM is merited for geohazard mapping and modeling in particular and spatial predictive mapping and modeling in general, especially when the value or use of the resulting predictions would be greatly enhanced by improved interpretability globally and availability of prediction explanations at each cell or aggregating unit within the mapped or modeled extent.

Best practice standards aim to standardize care and improve outcomes. However, variation in clinical practice exists, and not all deviations are inappropriate. Measuring adherence to best practice standards remains challenging due to limitations in representation methods and data fidelity. This scoping review aims to survey and synthesize the existing literature on the computable representation of guideline recommendations and to explore methods for detecting and quantifying deviations from best practice standards. We followed the Arksey and O'Malley framework and PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews) guidelines. Five databases (Ovid Medline, EMBASE, IEEE Xplore, Web of Science, and Scopus) were searched in November 2025. Studies were included if they either (1) described a computer representation of best practice standards or (2) assessed adherence to such standards using patient data, including patient data derived from electronic medical records or event logs. Screening was done using Covidence (Veritas Health Innovation). Data were extracted on representation, clinical context, data sources, adherence metrics, and modeling techniques. A narrative synthesis was conducted to identify themes. Twenty-four studies were included. Most studies were published as conference proceedings (13/24, 54%). Fourteen studies (14/24, 58%) included measurement of adherence to best practice standards. Cardiovascular conditions were the most common focus (13/24, 54%). Data sources included Health Level Seven (HL7) messages, structured electronic medical record data, event logs, and Fast Healthcare Interoperability Resources (FHIR)-transformed data. Best practice standards were formalized using Business Process Model and Notation (BPMN; 6/24, 25%), ontologies (7/24, 29%), FHIR (4/24, 17%), or hybrid approaches (4/24, 17%). The most common method for adherence measurement was rule-based alignment. Several studies incorporated weighted scoring to differentiate the severity of deviations. Process mining was used in a subset to detect sequence and timing variations. However, most models lacked contextual sensitivity and rarely incorporated patient-specific factors, such as comorbidities, patient acuity, or clinician rationale. Consequently, although deviations can be automatically identified, determining whether they were clinically warranted remained largely unresolved. Despite promising advances, challenges persist in computer-interpretable representation and measuring adherence in a clinically meaningful way. Current approaches predominantly assess technical alignment rather than clinical relevance and are limited by data quality and standardization, thereby limiting real-world utility. This scoping review offers an innovative contribution by synthesizing evidence from 2 separate domains-the computable representation of best practice standards and the measurement of adherence. The findings emphasize the need for context-aware, standardized modeling and integration with clinical workflows to distinguish warranted from unwarranted deviations. Such advances are essential for scalable, transparent, and real-time adherence monitoring-ultimately driving safer, patient-centered care delivery.

A principled, model-agnostic framework for structural feature extraction in time series is presented, grounded in topological data analysis (TDA). The motivation stems from two gaps identified in the literature: First, compact and interpretable representations that summarise the global geometric organisation of trajectories across scales remain scarce. Second, a unified, task-agnostic protocol for evaluating structure preservation against established non-topological families is still missing. To address these gaps, time-delay embeddings are employed to reconstruct phase space, sliding windows are used to generate local point clouds, and Vietoris–Rips persistent homology (up to dimension two) is computed. The resulting persistence diagrams are summarised with three transparent descriptors—persistence entropy, maximum persistence amplitude, and feature counts—and concatenated across delays and window sizes to yield a multiscale representation designed to complement temporal and spectral features while remaining computationally tractable. A unified experimental design is specified in which heterogeneous, regularly sampled financial series are preprocessed on native calendars and contrasted with competitive baselines spanning lagged, calendar-driven, difference/change, STL-based, delay-embedding PCA, price-based statistical, signature (FRUITS), and network-derived (NetF) features. Structure preservation is assessed through complementary criteria that probe spectral similarity, variance-scaled reconstruction fidelity, and the conservation of distributional shape (location, scale, asymmetry, tails). The study is positioned as an evaluation of representations, rather than a forecasting benchmark, emphasising interpretability, comparability, and methodological transparency while outlining avenues for adaptive hyperparameter selection and alternative filtrations.

Knowledge Graphs represent real-world facts and are used in several applications; however, they are often incomplete and have many missing facts. Link prediction is the task of completing these missing facts from existing ones. Embedding models based on Tensor Factorization attain state-of-the-art results in link prediction. Nevertheless, the embeddings they produce can not be easily interpreted. Inspired by previous work on word embeddings, we propose inducing sparsity in the bilinear tensor factorization model, RESCAL, to build interpretable Knowledge Graph embeddings. To overcome the difficulties that stochastic gradient descent has when producing sparse solutions, we add l 1 regularization to the learning objective by using the generalized Regularized Dual Averaging online optimization algorithm. The proposed method substantially improves the interpretability of the learned embeddings while maintaining competitive performance in the standard metrics.