Synthetic Data, Information, and Prior Knowledge: Why Synthetic Data Augmentation to Boost Sample Doesn't Work for Statistical Inference

The use of synthetic data to deidentify data and to improve predictive models is well-attested to. The augmentation of datasets using synthetically generated data is an alluring proposition: in the best case, it generates realistic data textitin silico at a fraction of the cost of authentic data which may be found textitin vivo or textitin vitro. This poses novel epistemic challenges. We contend that synthetic data augmentation is best understood as a novel way of accounting for prior knowledge. In this manuscript, we propose a definition of synthetic distributions and analyze how synthetic data augmentation interplays with standard accounts of maximum likelihood and Bayesian estimation. We observe that the marginal Fisher information contributed by synthetic data processes is subject to fundamental bounds, and enumerate obstacles to the use of synthetic data augmentation to aid in inferential tasks. We then articulate a Bayesian formulation of the way that synthetic data augmentation can be coherently understood, but argue that naive approaches to the specification of the prior are epistemically unjustifiable. This suggests that enhanced scrutiny must be placed on identifying justifiable priors to warrant the use and inclusion of data drawn from specific synthetic distributions. While our analysis shows the challenges and limitations of using synthetic data augmentation to improve upon traditional statistical model reasoning, it does suggest that augmentation is the principal approach analysts using outcome reasoning (i.e. using train/test splits to justify the analysis) can constrain an otherwise high-dimensional model space, providing an alternative to trying to encode the constraints into the potentially complex architecture of the algorithm.