Ingrid K. Glad

Lars Henry Berge Olsen, Ingrid Kristine Glad, Martin Jullum et al.

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.

Lars Henry Berge Olsen, Ingrid Kristine Glad, Martin Jullum et al.

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 in the field of cooperative game theory. 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 our VAEAC approach to Shapley value estimation outperforms the state-of-the-art methods for a wide range of settings for both continuous and mixed dependent features. For high-dimensional settings, our VAEAC approach with a non-uniform masking scheme significantly outperforms competing methods. Finally, we apply our VAEAC approach to estimate Shapley value explanations for the Abalone data set from the UCI Machine Learning Repository.

Clara Bertinelli Salucci, Azzeddine Bakdi, Ingrid K. Glad et al.

Longevity and safety of lithium-ion batteries are facilitated by efficient monitoring and adjustment of the battery operating conditions. Hence, it is crucial to implement fast and accurate algorithms for State of Health (SoH) monitoring on the Battery Management System. The task is challenging due to the complexity and multitude of the factors contributing to the battery degradation, especially because the different degradation processes occur at various timescales and their interactions play an important role. Data-driven methods bypass this issue by approximating the complex processes with statistical or machine learning models. This paper proposes a data-driven approach which is understudied in the context of battery degradation, despite its simplicity and ease of computation: the Multivariable Fractional Polynomial (MFP) regression. Models are trained from historical data of one exhausted cell and used to predict the SoH of other cells. The data are characterised by varying loads simulating dynamic operating conditions. Two hypothetical scenarios are considered: one assumes that a recent capacity measurement is known, the other is based only on the nominal capacity. It was shown that the degradation behaviour of the batteries under examination is influenced by their historical data, as supported by the low prediction errors achieved (root mean squared errors from 1.2% to 7.22% when considering data up to the battery End of Life). Moreover, we offer a multi-factor perspective where the degree of impact of each different factor is analysed. Finally, we compare with a Long Short-Term Memory Neural Network and other works from the literature on the same dataset. We conclude that the MFP regression is effective and competitive with contemporary works, and provides several additional advantages e.g. in terms of interpretability, generalisability, and implementability.

Andreas Brandsæter, Ingrid K. Glad

This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the predictions are useful. The paper proposes a novel approach to quantify how different data-clusters of the training data affect a prediction. The quantification is based on Shapley values, a concept which originates from coalitional game theory, developed to fairly distribute the payout among a set of cooperating players. A player's Shapley value is a measure of that player's contribution. Shapley values are often used to quantify feature importance, ie. how features affect a prediction. This paper extends this to cluster importance, letting clusters of the training data act as players in a game where the predictions are the payouts. The novel methodology proposed in this paper lets us explore and investigate how different clusters of the training data affect the predictions made by any black-box model, allowing new aspects of the reasoning and inner workings of a prediction model to be conveyed to the users. The methodology is fundamentally different from existing explanation methods, providing insight which would not be available otherwise, and should complement existing explanation methods, including explanations based on feature importance.

Martin Tveten, Ingrid K. Glad

When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying projections are often the most important ones. In this article, we present a novel method that automatically tailors the choice of projections to monitor for sparse changes in the mean and/or covariance matrix of high-dimensional data. A subset of the least varying projections is almost always selected based on a criteria of the projection's sensitivity to changes. Our focus is on online/sequential change detection, where the aim is to detect changes as quickly as possible, while controlling false alarms at a specified level. A combination of tailored PCA and a generalized log-likelihood monitoring procedure displays high efficiency in detecting even very sparse changes in the mean, variance and correlation. We demonstrate on real data that tailored PCA monitoring is efficient for sparse change detection also when the data streams are highly auto-correlated and non-normal. Notably, error control is achieved without a large validation set, which is needed in most existing methods.