Accumulated Local Effects (ALE) is a model-agnostic approach for global explanations of the results of black-box machine learning (ML) algorithms. There are at least three challenges with conducting statistical inference based on ALE: ensuring the reliability of ALE analyses, especially in the context of small datasets; intuitively characterizing a variable's overall effect in ML; and making robust inferences from ML data analysis. In response, we introduce innovative tools and techniques for statistical inference using ALE, establishing bootstrapped confidence intervals tailored to dataset size and introducing ALE effect size measures that intuitively indicate effects on both the outcome variable scale and a normalized scale. Furthermore, we demonstrate how to use these tools to draw reliable statistical inferences, reflecting the flexible patterns ALE adeptly highlights, with implementations available in the 'ale' package in R. This work propels the discourse on ALE and its applicability in ML and statistical analysis forward, offering practical solutions to prevailing challenges in the field.

Interpreting complex nonlinear machine-learning models is an inherently difficult task. A common approach is the post-hoc analysis of black-box models for dataset-level interpretation (Murdoch et al. 2019) using model-agnostic techniques such as the permutation-based variable importance, and graphical displays such as partial dependence plots that visualize main effects while integrating over the remaining dimensions (Molnar, Casalicchio, and Bischl 2020). These tools are so far limited to displaying the relationship between the response and one (or sometimes two) predictor(s), while attempting to control for the influence of the other predictors. This can be rather unsatisfactory when dealing with a large number of highly correlated predictors, which are often semantically grouped. While the literature on explainable machine learning has often focused on dealing with dependencies affecting individual features, e.g. by introducing conditional diagnostics (Strobl et al. 2008; Molnar, König, Bischl, et al. 2020), no practical solutions are available yet for dealing with model interpretation in highdimensional feature spaces with strongly dependent features (Molnar, Casalicchio, and Bischl 2020; Molnar, König, Herbinger, et al. 2020). These situations routinely occur in environmental remote sensing and other geographical and ecological analyses (Landgrebe 2002; Zortea, Haertel, and Clarke 2007), which motivated the present proposal to enhance existing model interpretation tools by offering a new, transformed perspective. For example, vegetation'greenness' as a measure of photosynthetic activity is often used to classify landcover or land use from satellite imagery acquired at multiple time points throughout the growing season (Peña and Brenning 2015; Peña, Liao, and Brenning 2017). Spectral reflectances of equivalent spectral bands (the features) are usually strongly correlated within the same phenological stage since vegetation characteristics vary gradually.

Model explainability is one of the most important problems in machine learning today. It's often the case that certain "black box" models such as deep neural networks are deployed to production and are running critical systems from everything in your workplace security cameras to your smartphone. It's a scary thought that not even the developers of these algorithms understand why exactly the algorithms make the decisions they do -- or even worse, how to prevent an adversary from exploiting them. While there are many challenges facing the designer of a "black box" algorithm, it's not completely hopeless. There are actually many different ways to illuminate the decisions a model makes.

Model explainability is one of the most important problems in machine learning today. It's often the case that certain "black box" models such as deep neural networks are deployed to production and are running critical systems from everything in your workplace security cameras to your smartphone. It's a scary thought that not even the developers of these algorithms understand why exactly the algorithms make the decisions they do -- or even worse, how to prevent an adversary from exploiting them. While there are many challenges facing the designer of a "black box" algorithm, it's not completely hopeless. There are actually many different ways to illuminate the decisions a model makes.

Interpreting a nonparametric regression model with many predictors is known to be a challenging problem. There has been renewed interest in this topic due to the extensive use of machine learning algorithms and the difficulty in understanding and explaining their input-output relationships. This paper develops a unified framework using a derivative-based approach for existing tools in the literature, including the partial-dependence plots, marginal plots and accumulated effects plots. It proposes a new interpretation technique called the accumulated total derivative effects plot and demonstrates how its components can be used to develop extensive insights in complex regression models with correlated predictors. The techniques are illustrated through simulation results.