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Synthetic datasets are often presented as a silver-bullet solution to theproblem of privacy-preserving data publishing. However, for many applications,synthetic data has been shown to have limited utility when used to trainpredictive models. One promising potential application of these data is in theexploratory phase of the machine learning workflow, which involvesunderstanding, engineering and selecting features. This phase often involvesconsiderable time, and depends on the availability of data. There would besubstantial value in synthetic data that permitted these steps to be carriedout while, for example, data access was being negotiated, or with fewerinformation governance restrictions. This paper presents an empirical analysisof the agreement between the feature importance obtained from raw and fromsynthetic data, on a range of artificially generated and real-world datasets(where feature importance represents how useful each feature is when predictinga the outcome). We employ two differentially-private methods to producesynthetic data, and apply various utility measures to quantify the agreement infeature importance as this varies with the level of privacy. Our resultsindicate that synthetic data can sometimes preserve several representations ofthe ranking of feature importance in simple settings but their performance isnot consistent and depends upon a number of factors. Particular caution shouldbe exercised in more nuanced real-world settings, where synthetic data can leadto differences in ranked feature importance that could alter key modellingdecisions. This work has important implications for developing syntheticversions of highly sensitive data sets in fields such as finance andhealthcare.

Faking feature importance: A cautionary tale on the use of differentially-private synthetic data