Machine learning models often excel in the accuracy of their predictions but are opaque due to their non-linear and non-parametric structure. This makes statistical inferencechallenging and disqualifies them from many applications where model interpretability is crucial. This paper proposes the Shapley regression framework as an approach for statistical inference on non-linear or non-parametric models. Inference is performed based on the Shapley value decomposition of a model , a pay-off concept from cooperative game theory. I show that universal approximators from machine learning are estimation consistent and introduce hypothesis tests for individual variable contributions, model bias and parametric functional forms. The inference properties of state-of-the-art machine learning models - like artificial neural networks, support vector machines and random forests - are investigated using numerical simulations and real-world data. The proposed framework is unique in the sense that it is identical to the conventional case of statistical inference on a linear model if the model is linear in parameters. This makes it a well-motivated extension to more general models and strengthens the case for the use of machine learning to inform decisions .
Universal function approximators, such as artificial neural networks, can learn a large variety of target functions arbitrarily well given sufficient training data. This flexibility comes at the cost of the ability to perform parametric inference. We address this gap by proposing a generic framework based on the Shapley-Taylor decomposition of a model. A surrogate parametric regression analysis is performed in the space spanned by the Shapley value expansion of a model . This allows for the testing of standard hypotheses of interest. At the same time, the proposed approach provides novel insights into statistical learning processes themselves derived from the consistency and bias properties of the nonparametric estimators. We apply the framework to the estimation of heterogeneous treatment effects in simulated and real-world randomised experiments. We introduce an explicit treatment function based on higher-order Shapley-Taylor indices. This can be used to identify potentially complex treatment channels and help the generalisation of findings from experimental settings. More generally, the presented approach allows for a standardised use and communication of results form machine learning models .
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Machine learning models often excel in the accuracy of their predictions but are opaque due to their non-linear and non-parametric structure. This makes statistical inferencechallenging and disqualifies them from many applications where model interpretability is crucial. This paper proposes the Shapley regression framework as an approach for statistical inference on non-linear or non-parametric models. Inference is performed based on the Shapley value decomposition
Universal function approximators, such as artificial neural networks, can learn a large variety of target functions arbitrarily well given sufficient training data. This flexibility comes at the cost of the ability to perform parametric inference. We address this gap by proposing a generic framework based on the Shapley-Taylor decomposition of a model. A surrogate parametric regression analysis is performed in the space spanned by the Shapley value expansion
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, a pay-off concept from cooperative game theory. I show that universal approximators from machine learning are estimation consistent and introduce hypothesis tests for individual variable contributions, model bias and parametric functional forms. The inference properties of state-of-the-art machine learning models - like artificial neural networks, support vector machines and random forests - are investigated using numerical simulations and
. This allows for the testing of standard hypotheses of interest. At the same time, the proposed approach provides novel insights into statistical learning processes themselves derived from the consistency and bias properties of the nonparametric estimators. We apply the framework to the estimation of heterogeneous treatment effects in simulated and
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data. The proposed framework is unique in the sense that it is identical to the conventional case of statistical inference on a linear model if the model is linear in parameters. This makes it a well-motivated extension to more general models and strengthens the case for the use of machine learning to inform decisions
randomised experiments. We introduce an explicit treatment function based on higher-order Shapley-Taylor indices. This can be used to identify potentially complex treatment channels and help the generalisation of findings from experimental settings. More generally, the presented approach allows for a standardised use and communication of results form machine learning models