Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be represented by many different decision trees. The presence of models with identical decision boundaries but different evaluation processes makes model selection challenging. The models will have different variable importance and behave differently in the presence of missing values, but most optimization procedures will arbitrarily choose one such model to return. We present a boolean logical representation of decision trees that does not exhibit predictive equivalence and is faithful to the underlying decision boundary. We apply our representation to several downstream machine learning tasks. Using our representation, we show that decision trees are surprisingly robust to test-time missingness of feature values; we address predictive equivalence's impact on quantifying variable importance; and we present an algorithm to optimize the cost of reaching predictions.
The use of appropriate methods of Interpretable Machine Learning (IML) and eXplainable Artificial Intelligence (XAI) is essential for adopting black-box predictive models in fields where model and prediction explainability is required. As a novel tool for interpreting black-box models, we introduce the R package midr, which implements Maximum Interpretation Decomposition (MID). MID is a functional decomposition approach that derives a low-order additive representation of a black-box model by minimizing the squared error between the model's prediction function and this additive representation. midr enables learning from black-box models by constructing a global surrogate model with advanced analytical capabilities. After reviewing related work and the theoretical foundation of MID, we demonstrate the package's usage and discuss some of its key features.
Evolving Fuzzy Systems (eFS) have gained significant attention due to their ability to adaptively update their structure in response to data dynamics while maintaining interpretability. However, the lack of publicly available implementations of these models limits their accessibility and widespread adoption. To address this gap, we present evolvingfuzzysystems, a Python library that provides implementations of several well-established eFS models, including ePL-KRLS-DISCO, ePL+, eMG, ePL, exTS, Simpl\_eTS, and eTS. The library facilitates model evaluation and comparison by offering built-in tools for training, visualization, and performance assessment. The models are evaluated using the fetch\_california\_housing dataset, with performance measured in terms of normalized root-mean-square error (NRMSE), non-dimensional error index (NDEI), and mean absolute percentage error (MAPE). Additionally, computational complexity is analyzed by measuring execution times and rule evolution during training and testing phases. The results highlight ePL as a simple yet efficient model that balances accuracy and computational cost, making it particularly suitable for real-world applications. By making these models publicly available, evolvingfuzzysystems aims to foster research and practical applications in adaptive and interpretable machine learning.
Association Rule Mining (ARM) is the task of mining patterns among data features in the form of logical rules, with applications across a myriad of domains. However, high-dimensional datasets often result in an excessive number of rules, increasing execution time and negatively impacting downstream task performance. Managing this rule explosion remains a central challenge in ARM research. To address this, we introduce Aerial+, a novel neurosymbolic ARM method. Aerial+ leverages an under-complete autoencoder to create a neural representation of the data, capturing associations between features. It extracts rules from this neural representation by exploiting the model's reconstruction mechanism. Extensive evaluations on five datasets against seven baselines demonstrate that Aerial+ achieves state-of-the-art results by learning more concise, high-quality rule sets with full data coverage. When integrated into rule-based interpretable machine learning models, Aerial+ significantly reduces execution time while maintaining or improving accuracy.
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data through learning Riemannian geometry algorithms can achieve improved performance and interpretability in tasks like clustering, dimensionality reduction, and interpolation. In particular, learned pullback geometry has recently undergone transformative developments that now make it scalable to learn and scalable to evaluate, which further opens the door for principled non-linear data analysis and interpretable machine learning. However, there are still steps to be taken when considering real-world multi-modal data. This work focuses on addressing distortions and modeling errors that can arise in the multi-modal setting and proposes to alleviate both challenges through isometrizing the learned Riemannian structure and balancing regularity and expressivity of the diffeomorphism parametrization. We showcase the effectiveness of the synergy of the proposed approaches in several numerical experiments with both synthetic and real data.
Modeling path loss in indoor LoRaWAN technology deployments is inherently challenging due to structural obstructions, occupant density and activities, and fluctuating environmental conditions. This study proposes a two-stage approach to capture and analyze these complexities using an extensive dataset of 1,328,334 field measurements collected over six months in a single-floor office at the University of Siegen's Hoelderlinstrasse Campus, Germany. First, we implement a multiple linear regression model that includes traditional propagation metrics (distance, structural walls) and an extension with proposed environmental variables (relative humidity, temperature, carbon dioxide, particulate matter, and barometric pressure). Using analysis of variance, we demonstrate that adding these environmental factors can reduce unexplained variance by 42.32 percent. Secondly, we examine residual distributions by fitting five candidate probability distributions: Normal, Skew-Normal, Cauchy, Student's t, and Gaussian Mixture Models (GMMs) with 2 to 5 components. Our results show that a four-component Gaussian Mixture Model captures the residual heterogeneity of indoor signal propagation most accurately, significantly outperforming single-distribution approaches. Given the push toward ultra-reliable, context-aware communications in 6G networks, our analysis shows that environment-aware modeling can substantially improve LoRaWAN network design in dynamic indoor IoT deployments.
Machine learning and high-throughput experimentation have greatly accelerated the discovery of mixed metal oxide catalysts by leveraging their compositional flexibility. However, the lack of established synthesis routes for solid-state materials remains a significant challenge in inorganic chemistry. An interpretable machine learning model is therefore essential, as it provides insights into the key factors governing phase formation. Here, we focus on the formation of single-phase Fe$_2$(ZnCo)O$_4$, synthesized via a high-throughput co-precipitation method. We combined a kernel classification model with a novel application of global SHAP analysis to pinpoint the experimental features most critical to single phase synthesizability by interpreting the contributions of each feature. Global SHAP analysis reveals that precursor and precipitating agent contributions to single-phase spinel formation align closely with established crystal growth theories. These results not only underscore the importance of interpretable machine learning in refining synthesis protocols but also establish a framework for data-informed experimental design in inorganic synthesis.
Mental health issues among college students have reached critical levels, significantly impacting academic performance and overall wellbeing. Predicting and understanding mental health status among college students is challenging due to three main factors: the necessity for large-scale longitudinal datasets, the prevalence of black-box machine learning models lacking transparency, and the tendency of existing approaches to provide aggregated insights at the population level rather than individualized understanding. To tackle these challenges, this paper presents I-HOPE, the first Interpretable Hierarchical mOdel for Personalized mEntal health prediction. I-HOPE is a two-stage hierarchical model that connects raw behavioral features to mental health status through five defined behavioral categories as interaction labels. We evaluate I-HOPE on the College Experience Study, the longest longitudinal mobile sensing dataset. This dataset spans five years and captures data from both pre-pandemic periods and the COVID-19 pandemic. I-HOPE achieves a prediction accuracy of 91%, significantly surpassing the 60-70% accuracy of baseline methods. In addition, I-HOPE distills complex patterns into interpretable and individualized insights, enabling the future development of tailored interventions and improving mental health support. The code is available at https://github.com/roycmeghna/I-HOPE.
Virus-like particles (VLPs) are valuable for vaccine development due to their immune-triggering properties. Understanding their stoichiometry, the number of protein subunits to form a VLP, is critical for vaccine optimisation. However, current experimental methods to determine stoichiometry are time-consuming and require highly purified proteins. To efficiently classify stoichiometry classes in proteins, we curate a new dataset and propose an interpretable, data-driven pipeline leveraging linear machine learning models. We also explore the impact of feature encoding on model performance and interpretability, as well as methods to identify key protein sequence features influencing classification. The evaluation of our pipeline demonstrates that it can classify stoichiometry while revealing protein features that possibly influence VLP assembly. The data and code used in this work are publicly available at https://github.com/Shef-AIRE/StoicIML.
Health outcomes depend on complex environmental and sociodemographic factors whose effects change over location and time. Only recently has fine-grained spatial and temporal data become available to study these effects, namely the MEDSAT dataset of English health, environmental, and sociodemographic information. Leveraging this new resource, we use a variety of variable importance techniques to robustly identify the most informative predictors across multiple health outcomes. We then develop an interpretable machine learning framework based on Generalized Additive Models (GAMs) and Multiscale Geographically Weighted Regression (MGWR) to analyze both local and global spatial dependencies of each variable on various health outcomes. Our findings identify NO2 as a global predictor for asthma, hypertension, and anxiety, alongside other outcome-specific predictors related to occupation, marriage, and vegetation. Regional analyses reveal local variations with air pollution and solar radiation, with notable shifts during COVID. This comprehensive approach provides actionable insights for addressing health disparities, and advocates for the integration of interpretable machine learning in public health.
Decision trees are widely used in machine learning due to their simplicity and interpretability, but they often lack robustness to adversarial attacks and data perturbations. The paper proposes a novel island-based coevolutionary algorithm (ICoEvoRDF) for constructing robust decision tree ensembles. The algorithm operates on multiple islands, each containing populations of decision trees and adversarial perturbations. The populations on each island evolve independently, with periodic migration of top-performing decision trees between islands. This approach fosters diversity and enhances the exploration of the solution space, leading to more robust and accurate decision tree ensembles. ICoEvoRDF utilizes a popular game theory concept of mixed Nash equilibrium for ensemble weighting, which further leads to improvement in results. ICoEvoRDF is evaluated on 20 benchmark datasets, demonstrating its superior performance compared to state-of-the-art methods in optimizing both adversarial accuracy and minimax regret. The flexibility of ICoEvoRDF allows for the integration of decision trees from various existing methods, providing a unified framework for combining diverse solutions. Our approach offers a promising direction for developing robust and interpretable machine learning models
Recent advances in prototypical learning have shown remarkable potential to provide useful decision interpretations associating activation maps and predictions with class-specific training prototypes. Such prototypical learning has been well-studied for various single-label diseases, but for quite relevant and more challenging multi-label diagnosis, where multiple diseases are often concurrent within an image, existing prototypical learning models struggle to obtain meaningful activation maps and effective class prototypes due to the entanglement of the multiple diseases. In this paper, we present a novel Cross- and Intra-image Prototypical Learning (CIPL) framework, for accurate multi-label disease diagnosis and interpretation from medical images. CIPL takes advantage of common cross-image semantics to disentangle the multiple diseases when learning the prototypes, allowing a comprehensive understanding of complicated pathological lesions. Furthermore, we propose a new two-level alignment-based regularisation strategy that effectively leverages consistent intra-image information to enhance interpretation robustness and predictive performance. Extensive experiments show that our CIPL attains the state-of-the-art (SOTA) classification accuracy in two public multi-label benchmarks of disease diagnosis: thoracic radiography and fundus images. Quantitative interpretability results show that CIPL also has superiority in weakly-supervised thoracic disease localisation over other leading saliency- and prototype-based explanation methods.
Our proposed framework attempts to break the trade-off between performance and explainability by introducing an explainable-by-design convolutional neural network (CNN) based on the lateral inhibition mechanism. The ExplaiNet model consists of the predictor, that is a high-accuracy CNN with residual or dense skip connections, and the explainer probabilistic graph that expresses the spatial interactions of the network neurons. The value on each graph node is a local discrete feature (LDF) vector, a patch descriptor that represents the indices of antagonistic neurons ordered by the strength of their activations, which are learned with gradient descent. Using LDFs as sequences we can increase the conciseness of explanations by repurposing EXTREME, an EM-based sequence motif discovery method that is typically used in molecular biology. Having a discrete feature motif matrix for each one of intermediate image representations, instead of a continuous activation tensor, allows us to leverage the inherent explainability of Bayesian networks. By collecting observations and directly calculating probabilities, we can explain causal relationships between motifs of adjacent levels and attribute the model's output to global motifs. Moreover, experiments on various tiny image benchmark datasets confirm that our predictor ensures the same level of performance as the baseline architecture for a given count of parameters and/or layers. Our novel method shows promise to exceed this performance while providing an additional stream of explanations. In the solved MNIST classification task, it reaches a comparable to the state-of-the-art performance for single models, using standard training setup and 0.75 million parameters.
Graph learning is naturally well suited for use in symbolic, object-centric planning due to its ability to exploit relational structures exhibited in planning domains and to take as input planning instances with arbitrary numbers of objects. Numeric planning is an extension of symbolic planning in which states may now also exhibit numeric variables. In this work, we propose data-efficient and interpretable machine learning models for learning to solve numeric planning tasks. This involves constructing a new graph kernel for graphs with both continuous and categorical attributes, as well as new optimisation methods for learning heuristic functions for numeric planning. Experiments show that our graph kernels are vastly more efficient and generalise better than graph neural networks for numeric planning, and also yield competitive coverage performance compared to domain-independent numeric planners. Code is available at https://github.com/DillonZChen/goose
Banzhaf values offer a simple and interpretable alternative to the widely-used Shapley values. We introduce Kernel Banzhaf, a novel algorithm inspired by KernelSHAP, that leverages an elegant connection between Banzhaf values and linear regression. Through extensive experiments on feature attribution tasks, we demonstrate that Kernel Banzhaf substantially outperforms other algorithms for estimating Banzhaf values in both sample efficiency and robustness to noise. Furthermore, we prove theoretical guarantees on the algorithm's performance, establishing Kernel Banzhaf as a valuable tool for interpretable machine learning.
Machine learning is permeating every conceivable domain to promote data-driven decision support. The focus is often on advanced black-box models due to their assumed performance advantages, whereas interpretable models are often associated with inferior predictive qualities. More recently, however, a new generation of generalized additive models (GAMs) has been proposed that offer promising properties for capturing complex, non-linear patterns while remaining fully interpretable. To uncover the merits and limitations of these models, this study examines the predictive performance of seven different GAMs in comparison to seven commonly used machine learning models based on a collection of twenty tabular benchmark datasets. To ensure a fair and robust model comparison, an extensive hyperparameter search combined with cross-validation was performed, resulting in 68,500 model runs. In addition, this study qualitatively examines the visual output of the models to assess their level of interpretability. Based on these results, the paper dispels the misconception that only black-box models can achieve high accuracy by demonstrating that there is no strict trade-off between predictive performance and model interpretability for tabular data. Furthermore, the paper discusses the importance of GAMs as powerful interpretable models for the field of information systems and derives implications for future work from a socio-technical perspective.
Comorbid anxiety disorders are common among patients with major depressive disorder (MDD), and numerous studies have identified an association between comorbid anxiety and resistance to pharmacological depression treatment. However, the impact of anxiety on the effectiveness of non-pharmacological interventions for MDD is not as well understood. In this study, we applied machine learning techniques to predict treatment responses in a large-scale clinical trial (n=493) of individuals with MDD, who were recruited online and randomly assigned to one of three smartphone-based interventions. Our analysis reveals that a baseline GAD-7 questionnaire score in the moderate to severe range (>10) predicts reduced probability of recovery from MDD. Our findings suggest that depressed individuals with comorbid anxiety face lower odds of substantial improvement in the context of smartphone-based therapeutic interventions for depression. Our work highlights a methodology that can identify simple, clinically useful "rules of thumb" for treatment response prediction using interpretable machine learning models.
Existing text representations such as embeddings and bag-of-words are not suitable for rule learning due to their high dimensionality and absent or questionable feature-level interpretability. This article explores whether large language models (LLMs) could address this by extracting a small number of interpretable features from text. We demonstrate this process on two datasets (CORD-19 and M17+) containing several thousand scientific articles from multiple disciplines and a target being a proxy for research impact. An evaluation based on testing for the statistically significant correlation with research impact has shown that LLama 2-generated features are semantically meaningful. We consequently used these generated features in text classification to predict the binary target variable representing the citation rate for the CORD-19 dataset and the ordinal 5-class target representing an expert-awarded grade in the M17+ dataset. Machine-learning models trained on the LLM-generated features provided similar predictive performance to the state-of-the-art embedding model SciBERT for scientific text. The LLM used only 62 features compared to 768 features in SciBERT embeddings, and these features were directly interpretable, corresponding to notions such as article methodological rigor, novelty, or grammatical correctness. As the final step, we extract a small number of well-interpretable action rules. Consistently competitive results obtained with the same LLM feature set across both thematically diverse datasets show that this approach generalizes across domains.
Local feature selection in machine learning provides instance-specific explanations by focusing on the most relevant features for each prediction, enhancing the interpretability of complex models. However, such methods tend to produce misleading explanations by encoding additional information in their selections. In this work, we attribute the problem of misleading selections by formalizing the concepts of label and feature leakage. We rigorously derive the necessary and sufficient conditions under which we can guarantee no leakage, and show existing methods do not meet these conditions. Furthermore, we propose the first local feature selection method that is proven to have no leakage called SUWR. Our experimental results indicate that SUWR is less prone to overfitting and combines state-of-the-art predictive performance with high feature-selection sparsity. Our generic and easily extendable formal approach provides a strong theoretical basis for future work on interpretability with reliable explanations.
Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave-based responses or deformation-induced property variation). This work addresses the rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and non-unique solutions. Unlike data-intensive and non-interpretable deep-learning-based methods, we propose the Random-forest-based Interpretable Generative Inverse Design (RIGID), a single-shot inverse design method for fast generation of metamaterial designs with on-demand functional behaviors. RIGID leverages the interpretability of a random forest-based "design$\rightarrow$response" forward model, eliminating the need for a more complex "response$\rightarrow$design" inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. We validate RIGID on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm-based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on-demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints.