This paper introduces a novel generator called Perturbation-Assisted Sample
Synthesis (PASS), designed for drawing reliable conclusions from complex data,
especially when using advanced modeling techniques like deep neural networks.
PASS utilizes perturbation to generate synthetic data that closely mirrors the
distribution of raw data, encompassing numerical and unstructured data types
such as gene expression, images, and text. By estimating the data-generating
distribution and leveraging large pre-trained generative models, PASS enhances
estimation accuracy, providing an estimated distribution of any statistic
through Monte Carlo experiments. Building on PASS, we propose a generative
inference framework called Perturbation-Assisted Inference (PAI), which offers
a statistical guarantee of validity. In pivotal inference, PAI enables accurate
conclusions without knowing a pivotal's distribution as in simulations, even
with limited data. In non-pivotal situations, we train PASS using an
independent holdout sample, resulting in credible conclusions. To showcase
PAI's capability in tackling complex problems, we highlight its applications in
three domains: image synthesis inference, sentiment word inference, and
multimodal inference via stable diffusion