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We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method successfully estimates the number and locations of changepoints with a given error rate and under minimal conditions, for all sparsities of the changing subset. Moreover, our method has computational complexity linear up to logarithmic factors in both the length and number of time series, making it applicable to large data sets. Through extensive numerical studies we show that the new methodology is highly competitive in terms of both estimation accuracy and computational cost. The practical usefulness of the method is illustrated by analysing sensor data from a hydro power plant. An efficient R implementation is available.

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.

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.