Implicit generative models based on deep neural networks have revolutionized many scientific fields, from weather research to language generation. They successfully model complex random objects arising in real-world problems.

In this work, we propose a sample-efficient training mechanism for these models. Our approach leverages regularized inference with shrinkage priors and generalized Bayes.

In the large $p$ (parameter dimension) and small $n$ (sample size) setting, sparsity-inducing priors have been successfully used for linear regression when $p \gg n$. However, their application to implicit generative models remains challenging due to the intractability of the likelihood function.

To address this, we adapt a scoring rule posterior based on a strictly proper scoring rule, following the generalized Bayes framework. We then propose a block SGMCMC within Gibbs sampling mechanism.

This enables efficient exploration of high-dimensional parameter spaces by identifying a sparse representation of neural implicit generative models. We demonstrate the performance of our proposed method through experiments on $p \gg n$ linear regression and an application of neural generative models.