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Parametric inference with universal function approximators

Andreas Joseph

No 784, Bank of England working papers from Bank of England

Abstract: 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 from machine learning models.

Keywords: Machine learning; statistical inference; Shapley values; numerical simulations; macroeconomics; time series (search for similar items in EconPapers)
JEL-codes: C45 C52 C71 E47 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2019-03-08, Revised 2020-07-22
New Economics Papers: this item is included in nep-big, nep-cmp, nep-ecm, nep-ets and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Working Paper: Parametric inference with universal function approximators (2020) Downloads
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