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.
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.
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.
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.
Many important datasets contain samples that are missing one or more feature values. Maintaining the interpretability of machine learning models in the presence of such missing data is challenging. Singly or multiply imputing missing values complicates the model's mapping from features to labels. On the other hand, reasoning on indicator variables that represent missingness introduces a potentially large number of additional terms, sacrificing sparsity. We solve these problems with M-GAM, a sparse, generalized, additive modeling approach that incorporates missingness indicators and their interaction terms while maintaining sparsity through l0 regularization. We show that M-GAM provides similar or superior accuracy to prior methods while significantly improving sparsity relative to either imputation or naive inclusion of indicator variables.
Survival analysis is a classic problem in statistics with important applications in healthcare. Most machine learning models for survival analysis are black-box models, limiting their use in healthcare settings where interpretability is paramount. More recently, glass-box machine learning models have been introduced for survival analysis, with both strong predictive performance and interpretability. Still, several gaps remain, as no prior glass-box survival model can produce calibrated shape functions with enough flexibility to capture the complex patterns often found in real data. To fill this gap, we introduce a new glass-box machine learning model for survival analysis called DNAMite. DNAMite uses feature discretization and kernel smoothing in its embedding module, making it possible to learn shape functions with a flexible balance of smoothness and jaggedness. Further, DNAMite produces calibrated shape functions that can be directly interpreted as contributions to the cumulative incidence function. Our experiments show that DNAMite generates shape functions closer to true shape functions on synthetic data, while making predictions with comparable predictive performance and better calibration than previous glass-box and black-box models.
Transparent models, which are machine learning models that produce inherently interpretable predictions, are receiving significant attention in high-stakes domains. However, despite much real-world data being collected as time series, there is a lack of studies on transparent time series models. To address this gap, we propose a novel transparent neural network model for time series called Generalized Additive Time Series Model (GATSM). GATSM consists of two parts: 1) independent feature networks to learn feature representations, and 2) a transparent temporal module to learn temporal patterns across different time steps using the feature representations. This structure allows GATSM to effectively capture temporal patterns and handle dynamic-length time series while preserving transparency. Empirical experiments show that GATSM significantly outperforms existing generalized additive models and achieves comparable performance to black-box time series models, such as recurrent neural networks and Transformer. In addition, we demonstrate that GATSM finds interesting patterns in time series. The source code is available at https://github.com/gim4855744/GATSM.
Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A significant challenge in this integration is maintaining the interpretability of the additive model component. Inspired by large-scale biomechanics datasets, this paper explores extending SSNs to functional data. Existing methods in functional data analysis are promising but often not expressive enough to account for all interactions and non-linearities and do not scale well to large datasets. Although the SSN approach presents a compelling potential solution, its adaptation to functional data remains complex. In this work, we propose a functional SSN method that retains the advantageous properties of classical functional regression approaches while also improving scalability. Our numerical experiments demonstrate that this approach accurately recovers underlying signals, enhances predictive performance, and performs favorably compared to competing methods.
Generalized additive models (GAMs) have long been a powerful white-box tool for the intelligible analysis of tabular data, revealing the influence of each feature on the model predictions. Despite the success of neural networks (NNs) in various domains, their application as NN-based GAMs in tabular data analysis remains suboptimal compared to tree-based ones, and the opacity of encoders in NN-GAMs also prevents users from understanding how networks learn the functions. In this work, we propose a new deep tabular learning method, termed Prototypical Neural Additive Model (ProtoNAM), which introduces prototypes into neural networks in the framework of GAMs. With the introduced prototype-based feature activation, ProtoNAM can flexibly model the irregular mapping from tabular features to the outputs while maintaining the explainability of the final prediction. We also propose a gradient-boosting inspired hierarchical shape function modeling method, facilitating the discovery of complex feature patterns and bringing transparency into the learning process of each network layer. Our empirical evaluations demonstrate that ProtoNAM outperforms all existing NN-based GAMs, while providing additional insights into the shape function learned for each feature. The source code of ProtoNAM is available at \url{https://github.com/Teddy-XiongGZ/ProtoNAM}.
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.
Interpretable clustering algorithms aim to group similar data points while explaining the obtained groups to support knowledge discovery and pattern recognition tasks. While most approaches to interpretable clustering construct clusters using decision trees, the interpretability of trees often deteriorates on complex problems where large trees are required. In this work, we introduce the Neural Clustering Additive Model (NeurCAM), a novel approach to the interpretable clustering problem that leverages neural generalized additive models to provide fuzzy cluster membership with additive explanations of the obtained clusters. To promote sparsity in our model's explanations, we introduce selection gates that explicitly limit the number of features and pairwise interactions leveraged. Additionally, we demonstrate the capacity of our model to perform text clustering that considers the contextual representation of the texts while providing explanations for the obtained clusters based on uni- or bi-word terms. Extensive experiments show that NeurCAM achieves performance comparable to black-box methods on tabular datasets while remaining interpretable. Additionally, our approach significantly outperforms other interpretable clustering approaches when clustering on text data.
As an emerging interpretable technique, Generalized Additive Models (GAMs) adopt neural networks to individually learn non-linear functions for each feature, which are then combined through a linear model for final predictions. Although GAMs can explain deep neural networks (DNNs) at the feature level, they require large numbers of model parameters and are prone to overfitting, making them hard to train and scale. Additionally, in real-world datasets with many features, the interpretability of feature-based explanations diminishes for humans. To tackle these issues, recent research has shifted towards concept-based interpretable methods. These approaches try to integrate concept learning as an intermediate step before making predictions, explaining the predictions in terms of human-understandable concepts. However, these methods require domain experts to extensively label concepts with relevant names and their ground-truth values. In response, we propose CAT, a novel interpretable Concept-bAsed Taylor additive model to simply this process. CAT does not have to require domain experts to annotate concepts and their ground-truth values. Instead, it only requires users to simply categorize input features into broad groups, which can be easily accomplished through a quick metadata review. Specifically, CAT first embeds each group of input features into one-dimensional high-level concept representation, and then feeds the concept representations into a new white-box Taylor Neural Network (TaylorNet). The TaylorNet aims to learn the non-linear relationship between the inputs and outputs using polynomials. Evaluation results across multiple benchmarks demonstrate that CAT can outperform or compete with the baselines while reducing the need of extensive model parameters. Importantly, it can explain model predictions through high-level concepts that human can understand.
The primary challenge in Federated Learning (FL) is to model non-IID distributions across clients, whose fine-grained structure is important to improve knowledge sharing. For example, some knowledge is globally shared across all clients, some is only transferable within a subgroup of clients, and some are client-specific. To capture and exploit this structure, we train models organized in a multi-level structure, called ``Multi-level Additive Models (MAM)'', for better knowledge-sharing across heterogeneous clients and their personalization. In federated MAM (FeMAM), each client is assigned to at most one model per level and its personalized prediction sums up the outputs of models assigned to it across all levels. For the top level, FeMAM trains one global model shared by all clients as FedAvg. For every mid-level, it learns multiple models each assigned to a subgroup of clients, as clustered FL. Every bottom-level model is trained for one client only. In the training objective, each model aims to minimize the residual of the additive predictions by the other models assigned to each client. To approximate the arbitrary structure of non-IID across clients, FeMAM introduces more flexibility and adaptivity to FL by incrementally adding new models to the prediction of each client and reassigning another if necessary, automatically optimizing the knowledge-sharing structure. Extensive experiments show that FeMAM surpasses existing clustered FL and personalized FL methods in various non-IID settings. Our code is available at https://github.com/shutong043/FeMAM.
Accurate mid-term (weeks to one year) hourly electricity load forecasts are essential for strategic decision-making in power plant operation, ensuring supply security and grid stability, planning and building energy storage systems, and energy trading. While numerous models effectively predict short-term (hours to a few days) hourly load, mid-term forecasting solutions remain scarce. In mid-term load forecasting, capturing the multifaceted characteristics of load, including daily, weekly and annual seasonal patterns, as well as autoregressive effects, weather and holiday impacts, and socio-economic non-stationarities, presents significant modeling challenges. To address these challenges, we propose a novel forecasting method using Generalized Additive Models (GAMs) built from interpretable P-splines that is enhanced with autoregressive post-processing. This model incorporates smoothed temperatures, Error-Trend-Seasonal (ETS) modeled and persistently forecasted non-stationary socio-economic states, a nuanced representation of effects from vacation periods, fixed date and weekday holidays, and seasonal information as inputs. The proposed model is evaluated using load data from 24 European countries over more than 9 years (2015-2024). This analysis demonstrates that the model not only has significantly enhanced forecasting accuracy compared to state-of-the-art methods but also offers valuable insights into the influence of individual components on predicted load, given its full interpretability. Achieving performance akin to day-ahead Transmission System Operator (TSO) forecasts, with computation times of just a few seconds for several years of hourly data, underscores the potential of the model for practical application in the power system industry.
We address the critical challenge of applying feature attribution methods to the transformer architecture, which dominates current applications in natural language processing and beyond. Traditional attribution methods to explainable AI (XAI) explicitly or implicitly rely on linear or additive surrogate models to quantify the impact of input features on a model's output. In this work, we formally prove an alarming incompatibility: transformers are structurally incapable of representing linear or additive surrogate models used for feature attribution, undermining the grounding of these conventional explanation methodologies. To address this discrepancy, we introduce the Softmax-Linked Additive Log Odds Model (SLALOM), a novel surrogate model specifically designed to align with the transformer framework. SLALOM demonstrates the capacity to deliver a range of insightful explanations with both synthetic and real-world datasets. We highlight SLALOM's unique efficiency-quality curve by showing that SLALOM can produce explanations with substantially higher fidelity than competing surrogate models or provide explanations of comparable quality at a fraction of their computational costs. We release code for SLALOM as an open-source project online at https://github.com/tleemann/slalom_explanations.
Symbolic regression has excelled in uncovering equations from physics, chemistry, biology, and related disciplines. However, its effectiveness becomes less certain when applied to experimental data lacking inherent closed-form expressions. Empirically derived relationships, such as entire stress-strain curves, may defy concise closed-form representation, compelling us to explore more adaptive modeling approaches that balance flexibility with interpretability. In our pursuit, we turn to Generalized Additive Models (GAMs), a widely used class of models known for their versatility across various domains. Although GAMs can capture non-linear relationships between variables and targets, they cannot capture intricate feature interactions. In this work, we investigate both of these challenges and propose a novel class of models, Shape Arithmetic Expressions (SHAREs), that fuses GAM's flexible shape functions with the complex feature interactions found in mathematical expressions. SHAREs also provide a unifying framework for both of these approaches. We also design a set of rules for constructing SHAREs that guarantee transparency of the found expressions beyond the standard constraints based on the model's size.
Feature selection is a critical component in predictive analytics that significantly affects the prediction accuracy and interpretability of models. Intrinsic methods for feature selection are built directly into model learning, providing a fast and attractive option for large amounts of data. Machine learning algorithms, such as penalized regression models (e.g., lasso) are the most common choice when it comes to in-built feature selection. However, they fail to capture non-linear relationships, which ultimately affects their ability to predict outcomes in intricate datasets. In this paper, we propose IGANN Sparse, a novel machine learning model from the family of generalized additive models, which promotes sparsity through a non-linear feature selection process during training. This ensures interpretability through improved model sparsity without sacrificing predictive performance. Moreover, IGANN Sparse serves as an exploratory tool for information systems researchers to unveil important non-linear relationships in domains that are characterized by complex patterns. Our ongoing research is directed at a thorough evaluation of the IGANN Sparse model, including user studies that allow to assess how well users of the model can benefit from the reduced number of features. This will allow for a deeper understanding of the interactions between linear vs. non-linear modeling, number of selected features, and predictive performance.
Recent years have seen important advances in the building of interpretable models, machine learning models that are designed to be easily understood by humans. In this work, we show that large language models (LLMs) are remarkably good at working with interpretable models, too. In particular, we show that LLMs can describe, interpret, and debug Generalized Additive Models (GAMs). Combining the flexibility of LLMs with the breadth of statistical patterns accurately described by GAMs enables dataset summarization, question answering, and model critique. LLMs can also improve the interaction between domain experts and interpretable models, and generate hypotheses about the underlying phenomenon. We release \url{https://github.com/interpretml/TalkToEBM} as an open-source LLM-GAM interface.
Deep neural networks have revolutionized many fields, but their black-box nature also occasionally prevents their wider adoption in fields such as healthcare and finance, where interpretable and explainable models are required. The recent development of Neural Additive Models (NAMs) is a significant step in the direction of interpretable deep learning for tabular datasets. In this paper, we propose a new subclass of NAMs that use a single-layer neural network construction of the Gaussian process via random Fourier features, which we call Gaussian Process Neural Additive Models (GP-NAM). GP-NAMs have the advantage of a convex objective function and number of trainable parameters that grows linearly with feature dimensionality. It suffers no loss in performance compared to deeper NAM approaches because GPs are well-suited for learning complex non-parametric univariate functions. We demonstrate the performance of GP-NAM on several tabular datasets, showing that it achieves comparable or better performance in both classification and regression tasks with a large reduction in the number of parameters.
Dynamic networks offer an insight of how relational systems evolve. However, modeling these networks efficiently remains a challenge, primarily due to computational constraints, especially as the number of observed events grows. This paper addresses this issue by introducing the Deep Relational Event Additive Model (DREAM) as a solution to the computational challenges presented by modeling non-linear effects in Relational Event Models (REMs). DREAM relies on Neural Additive Models to model non-linear effects, allowing each effect to be captured by an independent neural network. By strategically trading computational complexity for improved memory management and leveraging the computational capabilities of Graphic Processor Units (GPUs), DREAM efficiently captures complex non-linear relationships within data. This approach demonstrates the capability of DREAM in modeling dynamic networks and scaling to larger networks. Comparisons with traditional REM approaches showcase DREAM superior computational efficiency. The model potential is further demonstrated by an examination of the patent citation network, which contains nearly 8 million nodes and 100 million events.