Improving the Sampling Strategy in KernelSHAP

Shapley values are a popular model-agnostic explanation framework for explaining predictions made by complex machine learning models. The framework provides feature contribution scores that sum to the predicted response and represent each feature's importance. The computation of exact Shapley values is computationally expensive due to estimating an exponential amount of non-trivial conditional expectations. The KernelSHAP framework enables us to approximate the Shapley values using a sampled subset of weighted conditional expectations. We propose three main novel contributions: a stabilizing technique to reduce the variance of the weights in the current state-of-the-art strategy, a novel weighing scheme that corrects the Shapley kernel weights based on sampled subsets, and a straightforward strategy that includes the important subsets and integrates them with the corrected Shapley kernel weights. We compare these new approximation strategies against existing ones by evaluating their Shapley value accuracy as a function of the number of subsets. The results demonstrate that our sampling strategies significantly enhance the accuracy of the approximated Shapley value explanations, making them more reliable in practical applications. This work provides valuable insights and practical recommendations for researchers and practitioners seeking to implement Shapley value-based explainability of their models.

Finding Money Launderers Using Heterogeneous Graph Neural Networks

Current anti-money laundering (AML) systems, predominantly rule-based, exhibit notable shortcomings in efficiently and precisely detecting instances of money laundering. As a result, there has been a recent surge toward exploring alternative approaches, particularly those utilizing machine learning. Since criminals often collaborate in their money laundering endeavors, accounting for diverse types of customer relations and links becomes crucial. In line with this, the present paper introduces a graph neural network (GNN) approach to identify money laundering activities within a large heterogeneous network constructed from real-world bank transactions and business role data belonging to DNB, Norway's largest bank. Specifically, we extend the homogeneous GNN method known as the Message Passing Neural Network (MPNN) to operate effectively on a heterogeneous graph. As part of this procedure, we propose a novel method for aggregating messages across different edges of the graph. Our findings highlight the importance of using an appropriate GNN architecture when combining information in heterogeneous graphs. The performance results of our model demonstrate great potential in enhancing the quality of electronic surveillance systems employed by banks to detect instances of money laundering. To the best of our knowledge, this is the first published work applying GNN on a large real-world heterogeneous network for anti-money laundering purposes.

A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Them

Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several algorithmic approaches for computing different versions of Shapley value explanations. Here, we focus on conditional Shapley values for predictive models fitted to tabular data. Estimating precise conditional Shapley values is difficult as they require the estimation of non-trivial conditional expectations. In this article, we develop new methods, extend earlier proposed approaches, and systematize the new refined and existing methods into different method classes for comparison and evaluation. The method classes use either Monte Carlo integration or regression to model the conditional expectations. We conduct extensive simulation studies to evaluate how precisely the different method classes estimate the conditional expectations, and thereby the conditional Shapley values, for different setups. We also apply the methods to several real-world data experiments and provide recommendations for when to use the different method classes and approaches. Roughly speaking, we recommend using parametric methods when we can specify the data distribution almost correctly, as they generally produce the most accurate Shapley value explanations. When the distribution is unknown, both generative methods and regression models with a similar form as the underlying predictive model are good and stable options. Regression-based methods are often slow to train but produce the Shapley value explanations quickly once trained. The vice versa is true for Monte Carlo-based methods, making the different methods appropriate in different practical situations.

Using Shapley Values and Variational Autoencoders to Explain Predictive Models with Dependent Mixed Features

Shapley values are today extensively used as a model-agnostic explanation framework to explain complex predictive machine learning models. Shapley values have desirable theoretical properties and a sound mathematical foundation. Precise Shapley value estimates for dependent data rely on accurate modeling of the dependencies between all feature combinations. In this paper, we use a variational autoencoder with arbitrary conditioning (VAEAC) to model all feature dependencies simultaneously. We demonstrate through comprehensive simulation studies that VAEAC outperforms the state-of-the-art methods for a wide range of settings for both continuous and mixed dependent features. Finally, we apply VAEAC to the Abalone data set from the UCI Machine Learning Repository.

MCCE: Monte Carlo sampling of realistic counterfactual explanations

In this paper we introduce MCCE: Monte Carlo sampling of realistic Counterfactual Explanations, a model-based method that generates counterfactual explanations by producing a set of feasible examples using conditional inference trees. Unlike algorithmic-based counterfactual methods that have to solve complex optimization problems or other model based methods that model the data distribution using heavy machine learning models, MCCE is made up of only two light-weight steps (generation and post-processing). MCCE is also straightforward for the end user to understand and implement, handles any type of predictive model and type of feature, takes into account actionability constraints when generating the counterfactual explanations, and generates as many counterfactual explanations as needed. In this paper we introduce MCCE and give a comprehensive list of performance metrics that can be used to compare counterfactual explanations. We also compare MCCE with a range of state-of-the-art methods and a new baseline method on benchmark data sets. MCCE outperforms all model-based methods and most algorithmic-based methods when also taking into account validity (i.e., a correctly changed prediction) and actionability constraints. Finally, we show that MCCE has the strength of performing almost as well when given just a small subset of the training data.

groupShapley: Efficient prediction explanation with Shapley values for feature groups

Shapley values has established itself as one of the most appropriate and theoretically sound frameworks for explaining predictions from complex machine learning models. The popularity of Shapley values in the explanation setting is probably due to its unique theoretical properties. The main drawback with Shapley values, however, is that its computational complexity grows exponentially in the number of input features, making it unfeasible in many real world situations where there could be hundreds or thousands of features. Furthermore, with many (dependent) features, presenting/visualizing and interpreting the computed Shapley values also becomes challenging. The present paper introduces groupShapley: a conceptually simple approach for dealing with the aforementioned bottlenecks. The idea is to group the features, for example by type or dependence, and then compute and present Shapley values for these groups instead of for all individual features. Reducing hundreds or thousands of features to half a dozen or so, makes precise computations practically feasible and the presentation and knowledge extraction greatly simplified. We prove that under certain conditions, groupShapley is equivalent to summing the feature-wise Shapley values within each feature group. Moreover, we provide a simulation study exemplifying the differences when these conditions are not met. We illustrate the usability of the approach in a real world car insurance example, where groupShapley is used to provide simple and intuitive explanations.

Statistical embedding: Beyond principal components

There has been an intense recent activity in embedding of very high dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part we cover nonlinear methods such as principal curves, multidimensional scaling, local linear methods, ISOMAP, graph based methods and kernel based methods. The second part is concerned with topological embedding methods, in particular mapping topological properties into persistence diagrams. Another type of data sets with a tremendous growth is very high-dimensional network data. The task considered in part three is how to embed such data in a vector space of moderate dimension to make the data amenable to traditional techniques such as cluster and classification techniques. The final part of the survey deals with embedding in $\mathbb{R}^2$, which is visualization. Three methods are presented: $t$-SNE, UMAP and LargeVis based on methods in parts one, two and three, respectively. The methods are illustrated and compared on two simulated data sets; one consisting of a triple of noisy Ranunculoid curves, and one consisting of networks of increasing complexity and with two types of nodes.

Explaining predictive models using Shapley values and non-parametric vine copulas

The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence, there have recently been attempts of appropriately modelling/estimating the dependence between the features. Although the proposed methods clearly outperform the traditional approach assuming independence, they have their weaknesses. In this paper we propose two new approaches for modelling the dependence between the features. Both approaches are based on vine copulas, which are flexible tools for modelling multivariate non-Gaussian distributions able to characterise a wide range of complex dependencies. The performance of the proposed methods is evaluated on simulated data sets and a real data set. The experiments demonstrate that the vine copula approaches give more accurate approximations to the true Shapley values than its competitors.

Explaining predictive models with mixed features using Shapley values and conditional inference trees

It is becoming increasingly important to explain complex, black-box machine learning models. Although there is an expanding literature on this topic, Shapley values stand out as a sound method to explain predictions from any type of machine learning model. The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. This methodology was then extended to explain dependent features with an underlying continuous distribution. In this paper, we propose a method to explain mixed (i.e. continuous, discrete, ordinal, and categorical) dependent features by modeling the dependence structure of the features using conditional inference trees. We demonstrate our proposed method against the current industry standards in various simulation studies and find that our method often outperforms the other approaches. Finally, we apply our method to a real financial data set used in the 2018 FICO Explainable Machine Learning Challenge and show how our explanations compare to the FICO challenge Recognition Award winning team.

Explaining individual predictions when features are dependent: More accurate approximations to Shapley values

Explaining complex or seemingly simple machine learning models is a practical and ethical question, as well as a legal issue. Can I trust the model? Is it biased? Can I explain it to others? We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Of existing work on interpreting complex models, Shapley values is the only method with a solid theoretical foundation. Kernel SHAP is a computationally efficient approximation to Shapley values in higher dimensions. Like most other existing methods, this approach assumes independent features, which may give very wrong explanations. This is the case even if a simple linear model is used for predictions. We extend the Kernel SHAP method to handle dependent features. We provide several examples of linear and non-linear models with linear and non-linear feature dependence, where our method gives more accurate approximations to the true Shapley values. We also propose a method for aggregating individual Shapley values, such that the prediction can be explained by groups of dependent variables.