Christoph Molnar

• Ludwig-Maximilians-Universität in Munich

To learn about real world phenomena, scientists have traditionally used models with clearly interpretable elements. However, modern machine learning (ML) models, while powerful predictors, lack this direct elementwise interpretability (e.g. neural network weights). Interpretable machine learning (IML) offers a solution by analyzing models holistica...

Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models such as 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 e...

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. Consequently, the parameters of machine learning models usually cannot be easily related to the data generatin...

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 importanc...

Understanding the spatial variation of soil properties is central to many sub-disciplines of soil science. Commonly in soil mapping studies, a soil map is constructed through prediction by a statistical or non-statistical model calibrated with measured values of the soil property and environmental covariates of which maps are available. In recent y...

Interpretable machine learning (IML) is concerned with the behavior and the properties of machine learning models. Scientists, however, are only interested in the model as a gateway to understanding the modeled phenomenon. We show how to develop IML methods such that they allow insight into relevant phenomenon properties. We argue that current IML...

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 interpret...

Explainable Artificial Intelligence (xAI) is an established field with a vibrant community that has developed a variety of very successful approaches to explain and interpret predictions of complex machine learning models such as deep neural networks. In this article, we briefly introduce a few selected methods and discuss them in a short, clear an...

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 fe...

Understanding the spatial variation of soil properties is central to many sub-disciplines of soil science. Commonly in soil mapping studies, a soil map is constructed through prediction by a statistical or non-statistical model calibrated with measured values of the soil property and environmental covariates of which maps are available. In recent y...

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 abou...

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. Rec...

Counterfactual explanations are one of the most popular methods to make predictions of black box machine learning models interpretable by providing explanations in the form of ‘what-if scenarios’. Most current approaches optimize a collapsed, weighted sum of multiple objectives, which are naturally difficult to balance a-priori. We propose the Mult...

Interpretable Machine Learning (IML) methods are used to gain insight into the relevance of a feature of interest for the performance of a model. Commonly used IML methods differ in whether they consider features of interest in isolation, e.g., Permutation Feature Importance (PFI), or in relation to all remaining feature variables, e.g., Conditiona...

Modern requirements for machine learning (ML) models include both high predictive performance and model interpretability. A growing number of techniques provide model interpretations, but can lead to wrong conclusions if applied incorrectly. We illustrate pitfalls of ML model interpretation such as bad model generalization, dependent features, feat...

Partial dependence plots and permutation feature importance are popular model-agnostic interpretation methods. Both methods are based on predicting artificially created data points. When features are dependent, both methods extrapolate to feature areas with low data density. The extrapolation can cause misleading interpretations. To overcome extrap...

Counterfactual explanations are one of the most popular methods to make predictions of black box machine learning models interpretable by providing explanations in the form of `what-if scenarios'. Current approaches can compute counterfactuals only for certain model classes or feature types, or they generate counterfactuals that are not consistent...

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 m...

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 quanti...

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 m...

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. Rece...

To obtain interpretable machine learning models, either interpretable models are constructed from the outset - e.g. shallow decision trees, rule lists, or sparse generalized linear models - or post-hoc interpretation methods - e.g. partial dependence or ALE plots - are employed. Both approaches have disadvantages. While the former can restrict the...

In recent years, a large amount of model-agnostic methods to improve the transparency, trustability, and interpretability of machine learning models have been developed. Based on a recent method for model-agnostic global feature importance, we introduce a local feature importance measure for individual observations and propose two visual tools: par...

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:...

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:...

Objectives To analyse the impact of tumour necrosis factor inhibitors (TNFis) on spinal radiographic progression in ankylosing spondylitis (AS). Methods Patients with AS in the Swiss Clinical Quality Management cohort with up to 10 years of follow-up and radiographic assessments every 2 years were included. Radiographs were scored by two readers a...

Background Whether tumor necrosis factor inhibitors (TNFi) have an influence on radiographic progression in ankylosing spondylitis (AS) remains controversial. Objectives To investigate the impact of TNFi use on spinal radiographic progression in AS. Methods Patients fulfilling the modified NY Criteria for AS (as assessed by central reading) in th...

Eine Alternative zur Nutzung von Individualdaten bei der Schätzung von Wählerwanderungen stellt die ökologische Inferenz dar. Bei dieser wird zur Schätzung nur auf die offiziellen Wahlergebnisse der betrachteten beiden Wahlen zurückgegriffen. Obwohl Daten zur Verknüpfung der beiden Wahlentscheidungen auf individueller Ebene fehlen, können durch die...

Background: Whether tumor necrosis factor inhibitors (TNFi) have an influence on radiographic progression in ankylosing spondylitis (AS) remains controversial. Objectives: To investigate the impact of TNFi use on spinal radiographic progression in AS. Methods: Patients fulfilling the modified NY Criteria for AS (as assessed by central reading) in t...

The analysis of voter transitions is an important area of electoral studies. A main strategy is to use aggregate data provided by the offices of statistics regarding districts, precincts, communities etc. and to rely on ecological inference. Ecological inference, however, is plagued by the well-known indeterminacy problem. In this article, we prese...

Background: Medical errors have recently been recognized as a relevant concern in public health, and increasing research efforts have been made to find ways of improving patient safety. In palliative care, however, studies on errors are scant. Objective: Our aim was to gather pilot data concerning experiences and attitudes of palliative care pro...