Giuseppe Casalicchio

Julia Herbinger, Marvin N. Wright, Thomas Nagler et al.

Global feature effect methods, such as partial dependence plots, provide an intelligible visualization of the expected marginal feature effect. However, such global feature effect methods can be misleading, as they do not represent local feature effects of single observations well when feature interactions are present. We formally introduce generalized additive decomposition of global effects (GADGET), which is a new framework based on recursive partitioning to find interpretable regions in the feature space such that the interaction-related heterogeneity of local feature effects is minimized. We provide a mathematical foundation of the framework and show that it is applicable to the most popular methods to visualize marginal feature effects, namely partial dependence, accumulated local effects, and Shapley additive explanations (SHAP) dependence. Furthermore, we introduce and validate a new permutation-based interaction detection procedure that is applicable to any feature effect method that fits into our proposed framework. We empirically evaluate the theoretical characteristics of the proposed methods based on various feature effect methods in different experimental settings. Moreover, we apply our introduced methodology to three real-world examples to showcase their usefulness.

Julia Moosbauer, Giuseppe Casalicchio, Marius Lindauer et al.

Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces trust in HPO, and thus hinders its broad adoption. Here, we study the combination of HPO with interpretable machine learning (IML) methods such as partial dependence plots. These techniques are more and more used to explain the marginal effect of hyperparameters on the black-box cost function or to quantify the importance of hyperparameters. However, if such methods are naively applied to the experimental data of the HPO process in a post-hoc manner, the underlying sampling bias of the optimizer can distort interpretations. We propose a modified HPO method which efficiently balances the search for the global optimum w.r.t. predictive performance \emph{and} the reliable estimation of IML explanations of an underlying black-box function by coupling Bayesian optimization and Bayesian Algorithm Execution. On benchmark cases of both synthetic objectives and HPO of a neural network, we demonstrate that our method returns more reliable explanations of the underlying black-box without a loss of optimization performance.

Susanne Dandl, Andreas Hofheinz, Martin Binder et al.

Counterfactual explanation methods provide information on how feature values of individual observations must be changed to obtain a desired prediction. Despite the increasing amount of proposed methods in research, only a few implementations exist whose interfaces and requirements vary widely. In this work, we introduce the counterfactuals R package, which provides a modular and unified R6-based interface for counterfactual explanation methods. We implemented three existing counterfactual explanation methods and propose some optional methodological extensions to generalize these methods to different scenarios and to make them more comparable. We explain the structure and workflow of the package using real use cases and show how to integrate additional counterfactual explanation methods into the package. In addition, we compared the implemented methods for a variety of models and datasets with regard to the quality of their counterfactual explanations and their runtime behavior.

Enrique Valero-Leal, Bernd Bischl, Pedro Larrañaga et al.

Group counterfactual explanations find a set of counterfactual instances to explain a group of input instances contrastively. However, existing methods either (i) optimize counterfactuals only for a fixed group and do not generalize to new group members, (ii) strictly rely on strong model assumptions (e.g., linearity) for tractability or/and (iii) poorly control the counterfactual group geometry distortion. We instead learn an explicit optimal transport map that sends any group instance to its counterfactual without re-optimization, minimizing the group's total transport cost. This enables generalization with fewer parameters, making it easier to interpret the common actionable recourse. For linear classifiers, we prove that functions representing group counterfactuals are derived via mathematical optimization, identifying the underlying convex optimization type (QP, QCQP, ...). Experiments show that they accurately generalize, preserve group geometry and incur only negligible additional transport cost compared to baseline methods. If model linearity cannot be exploited, our approach also significantly outperforms the baselines.

Holger Löwe, Christian A. Scholbeck, Christian Heumann et al.

Forward marginal effects have recently been introduced as a versatile and effective model-agnostic interpretation method particularly suited for non-linear and non-parametric prediction models. They provide comprehensible model explanations of the form: if we change feature values by a pre-specified step size, what is the change in the predicted outcome? We present the R package fmeffects, the first software implementation of the theory surrounding forward marginal effects. The relevant theoretical background, package functionality and handling, as well as the software design and options for future extensions are discussed in this paper.

Fiona Katharina Ewald, Martin Binder, Matthias Feurer et al.

Rashomon sets are model sets within one model class that perform nearly as well as a reference model from the same model class. They reveal the existence of alternative well-performing models, which may support different interpretations. This enables selecting models that match domain knowledge, hidden constraints, or user preferences. However, efficient construction methods currently exist for only a few model classes. Applied machine learning usually searches many model classes, and the best class is unknown beforehand. We therefore study Rashomon sets in the combined algorithm selection and hyperparameter optimization (CASH) setting and call them CASHomon sets. We propose TruVaRImp, a model-based active learning algorithm for level set estimation with an implicit threshold, and provide convergence guarantees. On synthetic and real-world datasets, TruVaRImp reliably identifies CASHomon sets members and matches or outperforms naive sampling, Bayesian optimization, classical and implicit level set estimation methods, and other baselines. Our analyses of predictive multiplicity and feature-importance variability across model classes question the common practice of interpreting data through a single model class.

Julia Herbinger, Susanne Dandl, Fiona K. Ewald et al.

Surrogate models play a crucial role in retrospectively interpreting complex and powerful black box machine learning models via model distillation. This paper focuses on using model-based trees as surrogate models which partition the feature space into interpretable regions via decision rules. Within each region, interpretable models based on additive main effects are used to approximate the behavior of the black box model, striking for an optimal balance between interpretability and performance. Four model-based tree algorithms, namely SLIM, GUIDE, MOB, and CTree, are compared regarding their ability to generate such surrogate models. We investigate fidelity, interpretability, stability, and the algorithms' capability to capture interaction effects through appropriate splits. Based on our comprehensive analyses, we finally provide an overview of user-specific recommendations.

Christian A. Scholbeck, Henri Funk, Giuseppe Casalicchio

A clustering outcome for high-dimensional data is typically interpreted via post-processing, involving dimension reduction and subsequent visualization. This destroys the meaning of the data and obfuscates interpretations. We propose algorithm-agnostic interpretation methods to explain clustering outcomes in reduced dimensions while preserving the integrity of the data. The permutation feature importance for clustering represents a general framework based on shuffling feature values and measuring changes in cluster assignments through custom score functions. The individual conditional expectation for clustering indicates observation-wise changes in the cluster assignment due to changes in the data. The partial dependence for clustering evaluates average changes in cluster assignments for the entire feature space. All methods can be used with any clustering algorithm able to reassign instances through soft or hard labels. In contrast to common post-processing methods such as principal component analysis, the introduced methods maintain the original structure of the features.

Vasilis Gkolemis, Christos Diou, Dimitris Kyriakopoulos et al.

Effector is a Python package for interpreting machine learning (ML) models that are trained on tabular data through global and regional feature effects. Global effects, like Partial Dependence Plot (PDP) and Accumulated Local Effects (ALE), are widely used for explaining tabular ML models due to their simplicity -- each feature's average influence on the prediction is summarized by a single 1D plot. However, when features are interacting, global effects can be misleading. Regional effects address this by partitioning the input space into disjoint subregions with minimal interactions within each and computing a separate regional effect per subspace. Regional effects are then visualized by a set of 1D plots per feature. Effector provides efficient implementations of state-of-the-art global and regional feature effects methods under a unified API. The package integrates seamlessly with major ML libraries like scikit-learn and PyTorch. It is designed to be modular and extensible, and comes with comprehensive documentation and tutorials. Effector is an open-source project publicly available on Github at https://github.com/givasile/effector.

Lukas Burk, Fiona Katharina Ewald, Giuseppe Casalicchio et al.

We introduce xplainfi, an R package built on top of the mlr3 ecosystem for global, loss-based feature importance methods for machine learning models. Various feature importance methods exist in R, but significant gaps remain, particularly regarding conditional importance methods and associated statistical inference procedures. The package implements permutation feature importance, conditional feature importance, relative feature importance, leave-one-covariate-out, and generalizations thereof, and both marginal and conditional Shapley additive global importance methods. It provides a modular conditional sampling architecture based on Gaussian distributions, adversarial random forests, conditional inference trees, and knockoff-based samplers, which enable conditional importance analysis for continuous and mixed data. Statistical inference is available through multiple approaches, including variance-corrected confidence intervals and the conditional predictive impact framework. We demonstrate that xplainfi produces importance scores consistent with existing implementations across multiple simulation settings and learner types, while offering competitive runtime performance. The package is available on CRAN and provides researchers and practitioners with a comprehensive toolkit for feature importance analysis and model interpretation in R.

Timo Heiß, Coco Bögel, Bernd Bischl et al.

Global feature effects such as PD and ALE plots are widely used to interpret black-box models. However, they are only estimates of true underlying effects, and their reliability depends on multiple sources of error. Despite the popularity of global feature effects, these error sources are largely unexplored. In particular, the practically relevant question of whether to use training or holdout data to estimate feature effects remains unanswered. We address this gap by providing a systematic, estimator-level analysis that disentangles sources of bias and variance for PD and ALE. To this end, we derive a mean-squared-error decomposition that separates model bias, estimation bias, model variance, and estimation variance, and analyze their dependence on model characteristics, data selection, and sample size. We validate our theoretical findings through an extensive simulation study across multiple data-generating processes, learners, estimation strategies (training data, validation data, and cross-validation), and sample sizes. Our results reveal that, while using holdout data is theoretically the cleanest, potential biases arising from the training data are empirically negligible and dominated by the impact of the usually higher sample size. The estimation variance depends on both the presence of interactions and the sample size, with ALE being particularly sensitive to the latter. Cross-validation-based estimation is a promising approach that reduces the model variance component, particularly for overfitting models. Our analysis provides a principled explanation of the sources of error in feature effect estimates and offers concrete guidance on choosing estimation strategies when interpreting machine learning models.

Vasilis Gkolemis, Loukas Kavouras, Dimitrios Kyriakopoulos et al.

Generalized additive models (GAMs) offer interpretability through independent univariate feature effects but underfit when interactions are present in data. GA$^2$Ms add selected pairwise interactions which improves accuracy, but sacrifices interpretability and limits model auditing. We propose \emph{Conditionally Additive Local Models} (CALMs), a new model class, that balances the interpretability of GAMs with the accuracy of GA$^2$Ms. CALMs allow multiple univariate shape functions per feature, each active in different regions of the input space. These regions are defined independently for each feature as simple logical conditions (thresholds) on the features it interacts with. As a result, effects remain locally additive while varying across subregions to capture interactions. We further propose a principled distillation-based training pipeline that identifies homogeneous regions with limited interactions and fits interpretable shape functions via region-aware backfitting. Experiments on diverse classification and regression tasks show that CALMs consistently outperform GAMs and achieve accuracy comparable with GA$^2$Ms. Overall, CALMs offer a compelling trade-off between predictive accuracy and interpretability.

Ludwig Bothmann, Sven Strickroth, Giuseppe Casalicchio et al.

Education should not be a privilege but a common good. It should be openly accessible to everyone, with as few barriers as possible; even more so for key technologies such as Machine Learning (ML) and Data Science (DS). Open Educational Resources (OER) are a crucial factor for greater educational equity. In this paper, we describe the specific requirements for OER in ML and DS and argue that it is especially important for these fields to make source files publicly available, leading to Open Source Educational Resources (OSER). We present our view on the collaborative development of OSER, the challenges this poses, and first steps towards their solutions. We outline how OSER can be used for blended learning scenarios and share our experiences in university education. Finally, we discuss additional challenges such as credit assignment or granting certificates.

Christoph Molnar, Giuseppe Casalicchio, Bernd Bischl

We present a brief history of the field of interpretable machine learning (IML), give an overview of state-of-the-art interpretation methods, and discuss challenges. Research in IML has boomed in recent years. As young as the field is, it has over 200 years old roots in regression modeling and rule-based machine learning, starting in the 1960s. Recently, many new IML methods have been proposed, many of them model-agnostic, but also interpretation techniques specific to deep learning and tree-based ensembles. IML methods either directly analyze model components, study sensitivity to input perturbations, or analyze local or global surrogate approximations of the ML model. The field approaches a state of readiness and stability, with many methods not only proposed in research, but also implemented in open-source software. But many important challenges remain for IML, such as dealing with dependent features, causal interpretation, and uncertainty estimation, which need to be resolved for its successful application to scientific problems. A further challenge is a missing rigorous definition of interpretability, which is accepted by the community. To address the challenges and advance the field, we urge to recall our roots of interpretable, data-driven modeling in statistics and (rule-based) ML, but also to consider other areas such as sensitivity analysis, causal inference, and the social sciences.

Moritz Herrmann, F. Julian D. Lange, Katharina Eggensperger et al.

We warn against a common but incomplete understanding of empirical research in machine learning that leads to non-replicable results, makes findings unreliable, and threatens to undermine progress in the field. To overcome this alarming situation, we call for more awareness of the plurality of ways of gaining knowledge experimentally but also of some epistemic limitations. In particular, we argue most current empirical machine learning research is fashioned as confirmatory research while it should rather be considered exploratory.

Fiona Katharina Ewald, Ludwig Bothmann, Marvin N. Wright et al.

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 global 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.

Julian Rodemann, Federico Croppi, Philipp Arens et al.

Bayesian optimization (BO) with Gaussian processes (GP) has become an indispensable algorithm for black box optimization problems. Not without a dash of irony, BO is often considered a black box itself, lacking ways to provide reasons as to why certain parameters are proposed to be evaluated. This is particularly relevant in human-in-the-loop applications of BO, such as in robotics. We address this issue by proposing ShapleyBO, a framework for interpreting BO's proposals by game-theoretic Shapley values.They quantify each parameter's contribution to BO's acquisition function. Exploiting the linearity of Shapley values, we are further able to identify how strongly each parameter drives BO's exploration and exploitation for additive acquisition functions like the confidence bound. We also show that ShapleyBO can disentangle the contributions to exploration into those that explore aleatoric and epistemic uncertainty. Moreover, our method gives rise to a ShapleyBO-assisted human machine interface (HMI), allowing users to interfere with BO in case proposals do not align with human reasoning. We demonstrate this HMI's benefits for the use case of personalizing wearable robotic devices (assistive back exosuits) by human-in-the-loop BO. Results suggest human-BO teams with access to ShapleyBO can achieve lower regret than teams without.

Ludwig Bothmann, Philip A. Boustani, Jose M. Alvarez et al.

Bias-transforming methods of fairness-aware machine learning aim to correct a non-neutral status quo with respect to a protected attribute (PA). Current methods, however, lack an explicit formulation of what drives non-neutrality. We introduce privilege scores (PS) to measure PA-related privilege by comparing the model predictions in the real world with those in a fair world in which the influence of the PA is removed. At the individual level, PS can identify individuals who qualify for affirmative action; at the global level, PS can inform bias-transforming policies. After presenting estimation methods for PS, we propose privilege score contributions (PSCs), an interpretation method that attributes the origin of privilege to mediating features and direct effects. We provide confidence intervals for both PS and PSCs. Experiments on simulated and real-world data demonstrate the broad applicability of our methods and provide novel insights into gender and racial privilege in mortgage and college admissions applications.

Hubert Baniecki, Giuseppe Casalicchio, Bernd Bischl et al.

We discover a theoretical connection between explanation estimation and distribution compression that significantly improves the approximation of feature attributions, importance, and effects. While the exact computation of various machine learning explanations requires numerous model inferences and becomes impractical, the computational cost of approximation increases with an ever-increasing size of data and model parameters. We show that the standard i.i.d. sampling used in a broad spectrum of algorithms for post-hoc explanation leads to an approximation error worthy of improvement. To this end, we introduce Compress Then Explain (CTE), a new paradigm of sample-efficient explainability. It relies on distribution compression through kernel thinning to obtain a data sample that best approximates its marginal distribution. CTE significantly improves the accuracy and stability of explanation estimation with negligible computational overhead. It often achieves an on-par explanation approximation error 2-3x faster by using fewer samples, i.e. requiring 2-3x fewer model evaluations. CTE is a simple, yet powerful, plug-in for any explanation method that now relies on i.i.d. sampling.

Hubert Baniecki, Giuseppe Casalicchio, Bernd Bischl et al.

We study the robustness of global post-hoc explanations for predictive models trained on tabular data. Effects of predictor features in black-box supervised learning are an essential diagnostic tool for model debugging and scientific discovery in applied sciences. However, how vulnerable they are to data and model perturbations remains an open research question. We introduce several theoretical bounds for evaluating the robustness of partial dependence plots and accumulated local effects. Our experimental results with synthetic and real-world datasets quantify the gap between the best and worst-case scenarios of (mis)interpreting machine learning predictions globally.

Susanne Dandl, Marc Becker, Bernd Bischl et al.

This work introduces a novel R package for concise, informative summaries of machine learning models. We take inspiration from the summary function for (generalized) linear models in R, but extend it in several directions: First, our summary function is model-agnostic and provides a unified summary output also for non-parametric machine learning models; Second, the summary output is more extensive and customizable -- it comprises information on the dataset, model performance, model complexity, model's estimated feature importances, feature effects, and fairness metrics; Third, models are evaluated based on resampling strategies for unbiased estimates of model performances, feature importances, etc. Overall, the clear, structured output should help to enhance and expedite the model selection process, making it a helpful tool for practitioners and researchers alike.

Christian A. Scholbeck, Julia Moosbauer, Giuseppe Casalicchio et al.

We argue that interpretations of machine learning (ML) models or the model-building process can be seen as a form of sensitivity analysis (SA), a general methodology used to explain complex systems in many fields such as environmental modeling, engineering, or economics. We address both researchers and practitioners, calling attention to the benefits of a unified SA-based view of explanations in ML and the necessity to fully credit related work. We bridge the gap between both fields by formally describing how (a) the ML process is a system suitable for SA, (b) how existing ML interpretation methods relate to this perspective, and (c) how other SA techniques could be applied to ML.

Susanne Dandl, Giuseppe Casalicchio, Bernd Bischl et al.

This work introduces interpretable regional descriptors, or IRDs, for local, model-agnostic interpretations. IRDs are hyperboxes that describe how an observation's feature values can be changed without affecting its prediction. They justify a prediction by providing a set of "even if" arguments (semi-factual explanations), and they indicate which features affect a prediction and whether pointwise biases or implausibilities exist. A concrete use case shows that this is valuable for both machine learning modelers and persons subject to a decision. We formalize the search for IRDs as an optimization problem and introduce a unifying framework for computing IRDs that covers desiderata, initialization techniques, and a post-processing method. We show how existing hyperbox methods can be adapted to fit into this unified framework. A benchmark study compares the methods based on several quality measures and identifies two strategies to improve IRDs.

Julia Herbinger, Bernd Bischl, Giuseppe Casalicchio

Machine learning models can automatically learn complex relationships, such as non-linear and interaction effects. Interpretable machine learning methods such as partial dependence plots visualize marginal feature effects but may lead to misleading interpretations when feature interactions are present. Hence, employing additional methods that can detect and measure the strength of interactions is paramount to better understand the inner workings of machine learning models. We demonstrate several drawbacks of existing global interaction detection approaches, characterize them theoretically, and evaluate them empirically. Furthermore, we introduce regional effect plots with implicit interaction detection, a novel framework to detect interactions between a feature of interest and other features. The framework also quantifies the strength of interactions and provides interpretable and distinct regions in which feature effects can be interpreted more reliably, as they are less confounded by interactions. We prove the theoretical eligibility of our method and show its applicability on various simulation and real-world examples.

Christian A. Scholbeck, Giuseppe Casalicchio, Christoph Molnar et al.

Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a direct feature effect on the predicted outcome. Hence, marginal effects are typically used as approximations for feature effects, either in the shape of derivatives of the prediction function or forward differences in prediction due to a change in a feature value. While marginal effects are commonly used in many scientific fields, they have not yet been adopted as a model-agnostic interpretation method for machine learning models. This may stem from their inflexibility as a univariate feature effect and their inability to deal with the non-linearities found in black box models. We introduce a new class of marginal effects termed forward marginal effects. We argue to abandon derivatives in favor of better-interpretable forward differences. Furthermore, we generalize marginal effects based on forward differences to multivariate changes in feature values. To account for the non-linearity of prediction functions, we introduce a non-linearity measure for marginal effects. We argue against summarizing feature effects of a non-linear prediction function in a single metric such as the average marginal effect. Instead, we propose to partition the feature space to compute conditional average marginal effects on feature subspaces, which serve as conditional feature effect estimates.

Julia Moosbauer, Julia Herbinger, Giuseppe Casalicchio et al.

Automated hyperparameter optimization (HPO) can support practitioners to obtain peak performance in machine learning models. However, there is often a lack of valuable insights into the effects of different hyperparameters on the final model performance. This lack of explainability makes it difficult to trust and understand the automated HPO process and its results. We suggest using interpretable machine learning (IML) to gain insights from the experimental data obtained during HPO with Bayesian optimization (BO). BO tends to focus on promising regions with potential high-performance configurations and thus induces a sampling bias. Hence, many IML techniques, such as the partial dependence plot (PDP), carry the risk of generating biased interpretations. By leveraging the posterior uncertainty of the BO surrogate model, we introduce a variant of the PDP with estimated confidence bands. We propose to partition the hyperparameter space to obtain more confident and reliable PDPs in relevant sub-regions. In an experimental study, we provide quantitative evidence for the increased quality of the PDPs within sub-regions.

Christoph Molnar, Timo Freiesleben, Gunnar König et al.

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.

Gunnar König, Timo Freiesleben, Bernd Bischl et al.

Global model-agnostic feature importance measures either quantify whether features are directly used for a model's predictions (direct importance) or whether they contain prediction-relevant information (associative importance). Direct importance provides causal insight into the model's mechanism, yet it fails to expose the leakage of information from associated but not directly used variables. In contrast, associative importance exposes information leakage but does not provide causal insight into the model's mechanism. We introduce DEDACT - a framework to decompose well-established direct and associative importance measures into their respective associative and direct components. DEDACT provides insight into both the sources of prediction-relevant information in the data and the direct and indirect feature pathways by which the information enters the model. We demonstrate the method's usefulness on simulated examples.

Quay Au, Julia Herbinger, Clemens Stachl et al.

Interpretable machine learning has become a very active area of research due to the rising popularity of machine learning algorithms and their inherently challenging interpretability. Most work in this area has been focused on the interpretation of single features in a model. However, for researchers and practitioners, it is often equally important to quantify the importance or visualize the effect of feature groups. To address this research gap, we provide a comprehensive overview of how existing model-agnostic techniques can be defined for feature groups to assess the grouped feature importance, focusing on permutation-based, refitting, and Shapley-based methods. We also introduce an importance-based sequential procedure that identifies a stable and well-performing combination of features in the grouped feature space. Furthermore, we introduce the combined features effect plot, which is a technique to visualize the effect of a group of features based on a sparse, interpretable linear combination of features. We used simulation studies and a real data example from computational psychology to analyze, compare, and discuss these methods.

Christoph Molnar, Gunnar König, Julia Herbinger et al.

An increasing number of model-agnostic interpretation techniques for machine learning (ML) models such as partial dependence plots (PDP), permutation feature importance (PFI) and Shapley values provide insightful model interpretations, but can lead to wrong conclusions if applied incorrectly. We highlight many general pitfalls of ML model interpretation, such as using interpretation techniques in the wrong context, interpreting models that do not generalize well, ignoring feature dependencies, interactions, uncertainty estimates and issues in high-dimensional settings, or making unjustified causal interpretations, and illustrate them with examples. We focus on pitfalls for global methods that describe the average model behavior, but many pitfalls also apply to local methods that explain individual predictions. Our paper addresses ML practitioners by raising awareness of pitfalls and identifying solutions for correct model interpretation, but also addresses ML researchers by discussing open issues for further research.

Christoph Molnar, Gunnar König, Bernd Bischl et al.

The interpretation of feature importance in machine learning models is challenging when features are dependent. Permutation feature importance (PFI) ignores such dependencies, which can cause misleading interpretations due to extrapolation. A possible remedy is more advanced conditional PFI approaches that enable the assessment of feature importance conditional on all other features. Due to this shift in perspective and in order to enable correct interpretations, it is therefore important that the conditioning is transparent and humanly comprehensible. In this paper, we propose a new sampling mechanism for the conditional distribution based on permutations in conditional subgroups. As these subgroups are constructed using decision trees (transformation trees), the conditioning becomes inherently interpretable. This not only provides a simple and effective estimator of conditional PFI, but also local PFI estimates within the subgroups. In addition, we apply the conditional subgroups approach to partial dependence plots (PDP), a popular method for describing feature effects that can also suffer from extrapolation when features are dependent and interactions are present in the model. We show that PFI and PDP based on conditional subgroups often outperform methods such as conditional PFI based on knockoffs, or accumulated local effect plots. Furthermore, our approach allows for a more fine-grained interpretation of feature effects and importance within the conditional subgroups.

Christian A. Scholbeck, Christoph Molnar, Christian Heumann et al.

Model-agnostic interpretation techniques allow us to explain the behavior of any predictive model. Due to different notations and terminology, it is difficult to see how they are related. A unified view on these methods has been missing. We present the generalized SIPA (sampling, intervention, prediction, aggregation) framework of work stages for model-agnostic interpretations and demonstrate how several prominent methods for feature effects can be embedded into the proposed framework. Furthermore, we extend the framework to feature importance computations by pointing out how variance-based and performance-based importance measures are based on the same work stages. The SIPA framework reduces the diverse set of model-agnostic techniques to a single methodology and establishes a common terminology to discuss them in future work.

Quay Au, Daniel Schalk, Giuseppe Casalicchio et al.

Multi-output prediction deals with the prediction of several targets of possibly diverse types. One way to address this problem is the so called problem transformation method. This method is often used in multi-label learning, but can also be used for multi-output prediction due to its generality and simplicity. In this paper, we introduce an algorithm that uses the problem transformation method for multi-output prediction, while simultaneously learning the dependencies between target variables in a sparse and interpretable manner. In a first step, predictions are obtained for each target individually. Target dependencies are then learned via a component-wise boosting approach. We compare our new method with similar approaches in a benchmark using multi-label, multivariate regression and mixed-type datasets.

Christoph Molnar, Giuseppe Casalicchio, Bernd Bischl

Post-hoc model-agnostic interpretation methods such as partial dependence plots can be employed to interpret complex machine learning models. While these interpretation methods can be applied regardless of model complexity, they can produce misleading and verbose results if the model is too complex, especially w.r.t. feature interactions. To quantify the complexity of arbitrary machine learning models, we propose model-agnostic complexity measures based on functional decomposition: number of features used, interaction strength and main effect complexity. We show that post-hoc interpretation of models that minimize the three measures is more reliable and compact. Furthermore, we demonstrate the application of these measures in a multi-objective optimization approach which simultaneously minimizes loss and complexity.

Giuseppe Casalicchio, Christoph Molnar, Bernd Bischl

In recent years, a large amount of model-agnostic methods to improve the transparency, trustability and interpretability of machine learning models have been developed. We introduce local feature importance as a local version of a recent model-agnostic global feature importance method. Based on local feature importance, we propose two visual tools: partial importance (PI) and individual conditional importance (ICI) plots which visualize how changes in a feature affect the model performance on average, as well as for individual observations. Our proposed methods are related to partial dependence (PD) and individual conditional expectation (ICE) plots, but visualize the expected (conditional) feature importance instead of the expected (conditional) prediction. Furthermore, we show that averaging ICI curves across observations yields a PI curve, and integrating the PI curve with respect to the distribution of the considered feature results in the global feature importance. Another contribution of our paper is the Shapley feature importance, which fairly distributes the overall performance of a model among the features according to the marginal contributions and which can be used to compare the feature importance across different models.

Bernd Bischl, Giuseppe Casalicchio, Matthias Feurer et al.

Machine learning research depends on objectively interpretable, comparable, and reproducible algorithm benchmarks. We advocate the use of curated, comprehensive suites of machine learning tasks to standardize the setup, execution, and reporting of benchmarks. We enable this through software tools that help to create and leverage these benchmarking suites. These are seamlessly integrated into the OpenML platform, and accessible through interfaces in Python, Java, and R. OpenML benchmarking suites (a) are easy to use through standardized data formats, APIs, and client libraries; (b) come with extensive meta-information on the included datasets; and (c) allow benchmarks to be shared and reused in future studies. We then present a first, carefully curated and practical benchmarking suite for classification: the OpenML Curated Classification benchmarking suite 2018 (OpenML-CC18). Finally, we discuss use cases and applications which demonstrate the usefulness of OpenML benchmarking suites and the OpenML-CC18 in particular.

Philipp Probst, Quay Au, Giuseppe Casalicchio et al.

We implemented several multilabel classification algorithms in the machine learning package mlr. The implemented methods are binary relevance, classifier chains, nested stacking, dependent binary relevance and stacking, which can be used with any base learner that is accessible in mlr. Moreover, there is access to the multilabel classification versions of randomForestSRC and rFerns. All these methods can be easily compared by different implemented multilabel performance measures and resampling methods in the standardized mlr framework. In a benchmark experiment with several multilabel datasets, the performance of the different methods is evaluated.

Giuseppe Casalicchio, Jakob Bossek, Michel Lang et al.

OpenML is an online machine learning platform where researchers can easily share data, machine learning tasks and experiments as well as organize them online to work and collaborate more efficiently. In this paper, we present an R package to interface with the OpenML platform and illustrate its usage in combination with the machine learning R package mlr. We show how the OpenML package allows R users to easily search, download and upload data sets and machine learning tasks. Furthermore, we also show how to upload results of experiments, share them with others and download results from other users. Beyond ensuring reproducibility of results, the OpenML platform automates much of the drudge work, speeds up research, facilitates collaboration and increases the users' visibility online.