A Guide to Feature Importance Methods for Scientific Inference

While machine learning (ML) models are increasingly used due to their high predictive power, their use in understanding the data-generating process (DGP) is limited. Understanding the DGP requires insights into feature-target associations, which many ML models cannot directly provide, due to their opaque internal mechanisms. Feature importance (FI) methods provide useful insights into the DGP under certain conditions. Since the results of different FI methods have different interpretations, selecting the correct FI method for a concrete use case is crucial and still requires expert knowledge. This paper serves as a comprehensive guide to help understand the different interpretations of FI methods. Through an extensive review of FI methods and providing new proofs regarding their interpretation, we facilitate a thorough understanding of these methods and formulate concrete recommendations for scientific inference. We conclude by discussing options for FI uncertainty estimation and point to directions for future research aiming at full statistical inference from black-box ML models.

Toward Understanding the Disagreement Problem in Neural Network Feature Attribution

In recent years, neural networks have demonstrated their remarkable ability to discern intricate patterns and relationships from raw data. However, understanding the inner workings of these black box models remains challenging, yet crucial for high-stake decisions. Among the prominent approaches for explaining these black boxes are feature attribution methods, which assign relevance or contribution scores to each input variable for a model prediction. Despite the plethora of proposed techniques, ranging from gradient-based to backpropagation-based methods, a significant debate persists about which method to use. Various evaluation metrics have been proposed to assess the trustworthiness or robustness of their results. However, current research highlights disagreement among state-of-the-art methods in their explanations. Our work addresses this confusion by investigating the explanations' fundamental and distributional behavior. Additionally, through a comprehensive simulation study, we illustrate the impact of common scaling and encoding techniques on the explanation quality, assess their efficacy across different effect sizes, and demonstrate the origin of inconsistency in rank-based evaluation metrics.

Interpretable Machine Learning for Survival Analysis

With the spread and rapid advancement of black box machine learning models, the field of interpretable machine learning (IML) or explainable artificial intelligence (XAI) has become increasingly important over the last decade. This is particularly relevant for survival analysis, where the adoption of IML techniques promotes transparency, accountability and fairness in sensitive areas, such as clinical decision making processes, the development of targeted therapies, interventions or in other medical or healthcare related contexts. More specifically, explainability can uncover a survival model's potential biases and limitations and provide more mathematically sound ways to understand how and which features are influential for prediction or constitute risk factors. However, the lack of readily available IML methods may have deterred medical practitioners and policy makers in public health from leveraging the full potential of machine learning for predicting time-to-event data. We present a comprehensive review of the limited existing amount of work on IML methods for survival analysis within the context of the general IML taxonomy. In addition, we formally detail how commonly used IML methods, such as such as individual conditional expectation (ICE), partial dependence plots (PDP), accumulated local effects (ALE), different feature importance measures or Friedman's H-interaction statistics can be adapted to survival outcomes. An application of several IML methods to real data on data on under-5 year mortality of Ghanaian children from the Demographic and Health Surveys (DHS) Program serves as a tutorial or guide for researchers, on how to utilize the techniques in practice to facilitate understanding of model decisions or predictions.

arfpy: A python package for density estimation and generative modeling with adversarial random forests

This paper introduces $\textit{arfpy}$, a python implementation of Adversarial Random Forests (ARF) (Watson et al., 2023), which is a lightweight procedure for synthesizing new data that resembles some given data. The software $\textit{arfpy}$ equips practitioners with straightforward functionalities for both density estimation and generative modeling. The method is particularly useful for tabular data and its competitive performance is demonstrated in previous literature. As a major advantage over the mostly deep learning based alternatives, $\textit{arfpy}$ combines the method's reduced requirements in tuning efforts and computational resources with a user-friendly python interface. This supplies audiences across scientific fields with software to generate data effortlessly.

survex: an R package for explaining machine learning survival models

Due to their flexibility and superior performance, machine learning models frequently complement and outperform traditional statistical survival models. However, their widespread adoption is hindered by a lack of user-friendly tools to explain their internal operations and prediction rationales. To tackle this issue, we introduce the survex R package, which provides a cohesive framework for explaining any survival model by applying explainable artificial intelligence techniques. The capabilities of the proposed software encompass understanding and diagnosing survival models, which can lead to their improvement. By revealing insights into the decision-making process, such as variable effects and importances, survex enables the assessment of model reliability and the detection of biases. Thus, transparency and responsibility may be promoted in sensitive areas, such as biomedical research and healthcare applications.

Interpreting Deep Neural Networks with the Package innsight

The R package innsight offers a general toolbox for revealing variable-wise interpretations of deep neural networks' predictions with so-called feature attribution methods. Aside from the unified and user-friendly framework, the package stands out in three ways: It is generally the first R package implementing feature attribution methods for neural networks. Secondly, it operates independently of the deep learning library allowing the interpretation of models from any R package, including keras, torch, neuralnet, and even custom models. Despite its flexibility, innsight benefits internally from the torch package's fast and efficient array calculations, which builds on LibTorch $-$ PyTorch's C++ backend $-$ without a Python dependency. Finally, it offers a variety of visualization tools for tabular, signal, image data or a combination of these. Additionally, the plots can be rendered interactively using the plotly package.

Conditional Feature Importance for Mixed Data

Despite the popularity of feature importance measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analyzing a variable's importance before and after adjusting for covariates - i.e., between marginal and conditional measures. Our work draws attention to this rarely acknowledged, yet crucial distinction and showcases its implications. Further, we reveal that for testing conditional feature importance (CFI), only few methods are available and practitioners have hitherto been severely restricted in method application due to mismatching data requirements. Most real-world data exhibits complex feature dependencies and incorporates both continuous and categorical data (mixed data). Both properties are oftentimes neglected by CFI measures. To fill this gap, we propose to combine the conditional predictive impact (CPI) framework (arXiv:1901.09917) with sequential knockoff sampling (arXiv:2010.14026). The CPI enables CFI measurement that controls for any feature dependencies by sampling valid knockoffs - hence, generating synthetic data with similar statistical properties - for the data to be analyzed. Sequential knockoffs were deliberately designed to handle mixed data and thus allow us to extend the CPI approach to such datasets. We demonstrate through numerous simulations and a real-world example that our proposed workflow controls type I error, achieves high power and is in line with results given by other CFI measures, whereas marginal feature importance metrics result in misleading interpretations. Our findings highlight the necessity of developing statistically adequate, specialized methods for mixed data.

Unifying local and global model explanations by functional decomposition of low dimensional structures

We consider a global explanation of a regression or classification function by decomposing it into the sum of main components and interaction components of arbitrary order. When adding an identification constraint that is motivated by a causal interpretation, we find q-interaction SHAP to be the unique solution to that constraint. Here, q denotes the highest order of interaction present in the decomposition. Our result provides a new perspective on SHAP values with various practical and theoretical implications: If SHAP values are decomposed into main and all interaction effects, they provide a global explanation with causal interpretation. In principle, the decomposition can be applied to any machine learning model. However, since the number of possible interactions grows exponentially with the number of features, exact calculation is only feasible for methods that fit low dimensional structures or ensembles of those. We provide an algorithm and efficient implementation for gradient boosted trees (xgboost and random planted forests that calculates this decomposition. Conducted experiments suggest that our method provides meaningful explanations and reveals interactions of higher orders. We also investigate further potential of our new insights by utilizing the global explanation for motivating a new measure of feature importance, and for reducing direct and indirect bias by post-hoc component removal.

Smooth densities and generative modeling with unsupervised random forests

Density estimation is a fundamental problem in statistics, and any attempt to do so in high dimensions typically requires strong assumptions or complex deep learning architectures. An important application for density estimators is synthetic data generation, an area currently dominated by neural networks that often demand enormous training datasets and extensive tuning. We propose a new method based on unsupervised random forests for estimating smooth densities in arbitrary dimensions without parametric constraints, as well as generating realistic synthetic data. We prove the consistency of our approach and demonstrate its advantages over existing tree-based density estimators, which generally rely on ill-chosen split criteria and do not scale well with data dimensionality. Experiments illustrate that our algorithm compares favorably to state-of-the-art deep learning generative models, achieving superior performance in a range of benchmark trials while executing about two orders of magnitude faster on average. Our method is implemented in easy-to-use $\texttt{R}$ and Python packages.

Relating the Partial Dependence Plot and Permutation Feature Importance to the Data Generating Process

Scientists and practitioners increasingly rely on machine learning to model data and draw conclusions. Compared to statistical modeling approaches, machine learning makes fewer explicit assumptions about data structures, such as linearity. However, their model parameters usually cannot be easily related to the data generating process. To learn about the modeled relationships, partial dependence (PD) plots and permutation feature importance (PFI) are often used as interpretation methods. However, PD and PFI lack a theory that relates them to the data generating process. We formalize PD and PFI as statistical estimators of ground truth estimands rooted in the data generating process. We show that PD and PFI estimates deviate from this ground truth due to statistical biases, model variance and Monte Carlo approximation errors. To account for model variance in PD and PFI estimation, we propose the learner-PD and the learner-PFI based on model refits, and propose corrected variance and confidence interval estimators.