Graph Neural Networks (GNNs) have emerged as the predominant approach for learning over graph-structured data. However, most GNNs operate as black-box models and require post-hoc explanations, which may not suffice in high-stakes scenarios where transparency is crucial. In this paper, we present a GNN that is interpretable by design. Our model, Graph Neural Additive Network (GNAN), is a novel extension of the interpretable class of Generalized Additive Models, and can be visualized and fully understood by humans. GNAN is designed to be fully interpretable, offering both global and local explanations at the feature and graph levels through direct visualization of the model. These visualizations describe exactly how the model uses the relationships between the target variable, the features, and the graph. We demonstrate the intelligibility of GNANs in a series of examples on different tasks and datasets. In addition, we show that the accuracy of GNAN is on par with black-box GNNs, making it suitable for critical applications where transparency is essential, alongside high accuracy.
While analyzing the importance of features has become ubiquitous in interpretable machine learning, the joint signal from a group of related features is sometimes overlooked or inadvertently excluded. Neglecting the joint signal could bypass a critical insight: in many instances, the most significant predictors are not isolated features, but rather the combined effect of groups of features. This can be especially problematic for datasets that contain natural groupings of features, including multimodal datasets. This paper introduces a novel approach to determine the importance of a group of features for Generalized Additive Models (GAMs) that is efficient, requires no model retraining, allows defining groups posthoc, permits overlapping groups, and remains meaningful in high-dimensional settings. Moreover, this definition offers a parallel with explained variation in statistics. We showcase properties of our method on three synthetic experiments that illustrate the behavior of group importance across various data regimes. We then demonstrate the importance of groups of features in identifying depressive symptoms from a multimodal neuroscience dataset, and study the importance of social determinants of health after total hip arthroplasty. These two case studies reveal that analyzing group importance offers a more accurate, holistic view of the medical issues compared to a single-feature analysis.
Bandeira et al. (2022) introduced the Franz-Parisi (FP) criterion for characterizing the computational hard phases in statistical detection problems. The FP criterion, based on an annealed version of the celebrated Franz-Parisi potential from statistical physics, was shown to be equivalent to low-degree polynomial (LDP) lower bounds for Gaussian additive models, thereby connecting two distinct approaches to understanding the computational hardness in statistical inference. In this paper, we propose a refined FP criterion that aims to better capture the geometric ``overlap" structure of statistical models. Our main result establishes that this optimized FP criterion is equivalent to Statistical Query (SQ) lower bounds -- another foundational framework in computational complexity of statistical inference. Crucially, this equivalence holds under a mild, verifiable assumption satisfied by a broad class of statistical models, including Gaussian additive models, planted sparse models, as well as non-Gaussian component analysis (NGCA), single-index (SI) models, and convex truncation detection settings. For instance, in the case of convex truncation tasks, the assumption is equivalent with the Gaussian correlation inequality (Royen, 2014) from convex geometry. In addition to the above, our equivalence not only unifies and simplifies the derivation of several known SQ lower bounds -- such as for the NGCA model (Diakonikolas et al., 2017) and the SI model (Damian et al., 2024) -- but also yields new SQ lower bounds of independent interest, including for the computational gaps in mixed sparse linear regression (Arpino et al., 2023) and convex truncation (De et al., 2023).
Estimating causal effects of joint interventions on multiple variables is crucial in many domains, but obtaining data from such simultaneous interventions can be challenging. Our study explores how to learn joint interventional effects using only observational data and single-variable interventions. We present an identifiability result for this problem, showing that for a class of nonlinear additive outcome mechanisms, joint effects can be inferred without access to joint interventional data. We propose a practical estimator that decomposes the causal effect into confounded and unconfounded contributions for each intervention variable. Experiments on synthetic data demonstrate that our method achieves performance comparable to models trained directly on joint interventional data, outperforming a purely observational estimator.
Nowadays, Neural Networks are considered one of the most effective methods for various tasks such as anomaly detection, computer-aided disease detection, or natural language processing. However, these networks suffer from the ``black-box'' problem which makes it difficult to understand how they make decisions. In order to solve this issue, an R package called neuralGAM is introduced. This package implements a Neural Network topology based on Generalized Additive Models, allowing to fit an independent Neural Network to estimate the contribution of each feature to the output variable, yielding a highly accurate and interpretable Deep Learning model. The neuralGAM package provides a flexible framework for training Generalized Additive Neural Networks, which does not impose any restrictions on the Neural Network architecture. We illustrate the use of the neuralGAM package in both synthetic and real data examples.
The Rashomon effect describes the observation that in machine learning (ML) multiple models often achieve similar predictive performance while explaining the underlying relationships in different ways. This observation holds even for intrinsically interpretable models, such as Generalized Additive Models (GAMs), which offer users valuable insights into the model's behavior. Given the existence of multiple GAM configurations with similar predictive performance, a natural question is whether we can personalize these configurations based on users' needs for interpretability. In our study, we developed an approach to personalize models based on contextual bandits. In an online experiment with 108 users in a personalized treatment and a non-personalized control group, we found that personalization led to individualized rather than one-size-fits-all configurations. Despite these individual adjustments, the interpretability remained high across both groups, with users reporting a strong understanding of the models. Our research offers initial insights into the potential for personalizing interpretable ML.
Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers limited physical interpretability. The objective of this paper is to develop a real-time parameter estimation algorithm aimed at identifying time-varying dynamics within an interpretable model structure. An additive model structure is adopted for this purpose, which offers enhanced parsimony and is shown to be particularly suitable for mechanical systems. The proposed approach integrates the recursive simplified refined instrumental variable method with block-coordinate descent to minimize an exponentially-weighted output error cost function. This novel recursive identification method delivers parametric continuous-time additive models and is applicable in both open-loop and closed-loop controlled systems. Its efficacy is shown using numerical simulations and is further validated using experimental data to detect the time-varying resonance dynamics of a flexible beam system. These results demonstrate the effectiveness of the proposed approach for online and interpretable estimation for advanced monitoring and control applications.
We review generalized additive models as a type of ``transparent'' model that has recently seen renewed interest in the deep learning community as neural additive models. We highlight multiple types of nonidentifiability in this model class and discuss challenges in interpretability, arguing for restraint when claiming ``interpretability'' or ``suitability for safety-critical applications'' of such models.
Longitudinal biomedical studies monitor individuals over time to capture dynamics in brain development, disease progression, and treatment effects. However, estimating trajectories of brain biomarkers is challenging due to biological variability, inconsistencies in measurement protocols (e.g., differences in MRI scanners), scarcity, and irregularity in longitudinal measurements. Herein, we introduce a novel personalized deep kernel regression framework for forecasting brain biomarkers, with application to regional volumetric measurements. Our approach integrates two key components: a population model that captures brain trajectories from a large and diverse cohort, and a subject-specific model that captures individual trajectories. To optimally combine these, we propose Adaptive Shrinkage Estimation, which effectively balances population and subject-specific models. We assess our model's performance through predictive accuracy metrics, uncertainty quantification, and validation against external clinical studies. Benchmarking against state-of-the-art statistical and machine learning models -- including linear mixed effects models, generalized additive models, and deep learning methods -- demonstrates the superior predictive performance of our approach. Additionally, we apply our method to predict trajectories of composite neuroimaging biomarkers, which highlights the versatility of our approach in modeling the progression of longitudinal neuroimaging biomarkers. Furthermore, validation on three external neuroimaging studies confirms the robustness of our method across different clinical contexts. We make the code available at https://github.com/vatass/AdaptiveShrinkageDKGP.
We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive structure and satisfies a higher-order smoothness property, characterized by the H\"older family of functions. The additive model for H\"older classes of functions is well-studied in the literature on nonparametric function estimation, where it is shown that such a model benefits from a substantial improvement of the estimation accuracy compared to the H\"older model without additive structure. We study this established framework in the context of gradient-free optimization. We propose a randomized gradient estimator that, when plugged into a gradient descent algorithm, allows one to achieve minimax optimal optimization error of the order $dT^{-(\beta-1)/\beta}$, where $d$ is the dimension of the problem, $T$ is the number of queries and $\beta\ge 2$ is the H\"older degree of smoothness. We conclude that, in contrast to nonparametric estimation problems, no substantial gain of accuracy can be achieved when using additive models in gradient-free optimization.
Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main objective of this paper is to develop a parametric identification strategy that delivers accurate and physically relevant models of multivariable systems using time-domain data. The introduced approach adopts an additive model structure, offering a parsimonious and interpretable representation of many physical systems, and employs a refined instrumental variable-based estimation algorithm. The developed identification method enables the estimation of parametric continuous-time additive models and is applicable to both open and closed-loop controlled systems. The performance of the estimator is demonstrated through numerical simulations and experimentally validated on a flexible beam system.
Electricity demand forecasting is key to ensuring that supply meets demand lest the grid would blackout. Reliable short-term forecasts may be obtained by combining a Generalized Additive Models (GAM) with a State-Space model (Obst et al., 2021), leading to an adaptive (or online) model. A GAM is an over-parameterized linear model defined by a formula and a state-space model involves hyperparameters. Both the formula and adaptation parameters have to be fixed before model training and have a huge impact on the model's predictive performance. We propose optimizing them using the DRAGON package of Keisler (2025), originally designed for neural architecture search. This work generalizes it for automated online generalized additive model selection by defining an efficient modeling of the search space (namely, the space of the GAM formulae and adaptation parameters). Its application to short-term French electricity demand forecasting demonstrates the relevance of the approach
Enhancing the accuracy and efficiency of machine learning algorithms employed in neural interface systems is crucial for advancing next-generation intelligent therapeutic devices. However, current systems often utilize basic machine learning models that do not fully exploit the natural structure of brain signals. Additionally, existing learning models used for neural signal processing often demonstrate low speed and efficiency during inference. To address these challenges, this study introduces Micro Tree-based NAM (MT-NAM), a distilled model based on the recently proposed Neural Additive Models (NAM). The MT-NAM achieves a remarkable 100$\times$ improvement in inference speed compared to standard NAM, without compromising accuracy. We evaluate our approach on the CHB-MIT scalp EEG dataset, which includes recordings from 24 patients with varying numbers of sessions and seizures. NAM achieves an 85.3\% window-based sensitivity and 95\% specificity. Interestingly, our proposed MT-NAM shows only a 2\% reduction in sensitivity compared to the original NAM. To regain this sensitivity, we utilize a test-time template adjuster (T3A) as an update mechanism, enabling our model to achieve higher sensitivity during test time by accommodating transient shifts in neural signals. With this online update approach, MT-NAM achieves the same sensitivity as the standard NAM while achieving approximately 50$\times$ acceleration in inference speed.
In recent years, the Shapley value and SHAP explanations have emerged as one of the most dominant paradigms for providing post-hoc explanations of black-box models. Despite their well-founded theoretical properties, many recent works have focused on the limitations in both their computational efficiency and their representation power. The underlying connection with additive models, however, is left critically under-emphasized in the current literature. In this work, we find that a variational perspective linking GAM models and SHAP explanations is able to provide deep insights into nearly all recent developments. In light of this connection, we borrow in the other direction to develop a new method to train interpretable GAM models which are automatically purified to compute the Shapley value in a single forward pass. Finally, we provide theoretical results showing the limited representation power of GAM models is the same Achilles' heel existing in SHAP and discuss the implications for SHAP's modern usage in CV and NLP.
Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such as generalized additive models and hierarchical forecasting. In this paper, we propose a unified framework for integrating and combining linear constraints in time series forecasting. Within this framework, we show that the exact minimizer of the constrained empirical risk can be computed efficiently using linear algebra alone. This approach allows for highly scalable implementations optimized for GPUs. We validate the proposed methodology through extensive benchmarking on real-world tasks, including electricity demand forecasting and tourism forecasting, achieving state-of-the-art performance.
The goal of this work is to develop principled techniques to extract information from high dimensional data sets with complex dependencies in areas such as medicine that can provide insight into individual as well as population level variation. We develop $\texttt{LucidAtlas}$, an approach that can represent spatially varying information, and can capture the influence of covariates as well as population uncertainty. As a versatile atlas representation, $\texttt{LucidAtlas}$ offers robust capabilities for covariate interpretation, individualized prediction, population trend analysis, and uncertainty estimation, with the flexibility to incorporate prior knowledge. Additionally, we discuss the trustworthiness and potential risks of neural additive models for analyzing dependent covariates and then introduce a marginalization approach to explain the dependence of an individual predictor on the models' response (the atlas). To validate our method, we demonstrate its generalizability on two medical datasets. Our findings underscore the critical role of by-construction interpretable models in advancing scientific discovery. Our code will be publicly available upon acceptance.
Cerebral perfusion plays a crucial role in maintaining brain function and is tightly coupled with neuronal activity. While previous studies have examined cerebral perfusion trajectories across development and aging, precise characterization of its lifespan dynamics has been limited by small sample sizes and methodological inconsistencies. In this study, we construct the first comprehensive normative model of cerebral perfusion across the human lifespan (birth to 85 years) using a large multi-site dataset of over 12,000 high-quality arterial spin labeling (ASL) MRI scans. Leveraging generalized additive models for location, scale, and shape (GAMLSS), we mapped nonlinear growth trajectories of cerebral perfusion at global, network, and regional levels. We observed a rapid postnatal increase in cerebral perfusion, peaking at approximately 7.1 years, followed by a gradual decline into adulthood. Sex differences were evident, with distinct regional maturation patterns rather than uniform differences across all brain regions. Beyond normative modeling, we quantified individual deviations from expected CBF patterns in neurodegenerative and psychiatric conditions, identifying disease-specific perfusion abnormalities across four brain disorders. Using longitudinal data, we established typical and atypical cerebral perfusion trajectories, highlighting the prognostic value of perfusion-based biomarkers for detecting disease progression. Our findings provide a robust normative framework for cerebral perfusion, facilitating precise characterization of brain health across the lifespan and enhancing the early identification of neurovascular dysfunction in clinical populations.
Causal additive models have been employed as tractable yet expressive frameworks for causal discovery involving hidden variables. State-of-the-art methodologies suggest that determining the causal relationship between a pair of variables is infeasible in the presence of an unobserved backdoor or an unobserved causal path. Contrary to this assumption, we theoretically show that resolving the causal direction is feasible in certain scenarios by incorporating two novel components into the theory. The first component introduces a novel characterization of regression sets within independence between regression residuals. The second component leverages conditional independence among the observed variables. We also provide a search algorithm that integrates these innovations and demonstrate its competitive performance against existing methods.
Many problems within personalized medicine and digital health rely on the analysis of continuous-time functional biomarkers and other complex data structures emerging from high-resolution patient monitoring. In this context, this work proposes new optimization-based variable selection methods for multivariate, functional, and even more general outcomes in metrics spaces based on best-subset selection. Our framework applies to several types of regression models, including linear, quantile, or non parametric additive models, and to a broad range of random responses, such as univariate, multivariate Euclidean data, functional, and even random graphs. Our analysis demonstrates that our proposed methodology outperforms state-of-the-art methods in accuracy and, especially, in speed-achieving several orders of magnitude improvement over competitors across various type of statistical responses as the case of mathematical functions. While our framework is general and is not designed for a specific regression and scientific problem, the article is self-contained and focuses on biomedical applications. In the clinical areas, serves as a valuable resource for professionals in biostatistics, statistics, and artificial intelligence interested in variable selection problem in this new technological AI-era.
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.