We introduce Mira, a sample-based score for assessing the accuracy of a candidate conditional distribution using only joint samples from the true data-generating process. Relying on the principle that distributions coincide if they assign equal probability mass to all regions, we derive an analytic expression for the Mira statistic, whose average defines the Mira score. This formulation further allows us to compute theoretical reference values and uncertainty estimates when the candidate distribution matches the true one. This framework enables model comparison by quantifying the alignment between the conditional distribution of a candidate model and the true data generating process. Consequently, Mira enables Bayesian model comparison through direct posterior validation, bypassing the challenging evidence computation. We demonstrate its effectiveness across several toy problems and Bayesian inference tasks.

Vision-language models, such as CLIP, have shown promising Out-of-Distribution (OoD) generalization under various types of distribution shifts. Recent studies attempted to investigate the leading cause of this capability. In this work, we follow the same path, but focus on a specific type of OoD data - images with novel compositions of attribute-object pairs - and study whether such models can successfully classify those images into composition classes. We carefully designed an authentic image test dataset called ImageNet-AO, consisting of attributes for objects that are unlikely encountered in the CLIP training sets. We found that CLIPs trained with large datasets such as OpenAI CLIP, LAION-400M, and LAION-2B show orders-of-magnitude improvement in effective compositional OoD generalization compared to both supervised models and CLIPs trained with smaller datasets, such as CC-12M and YFCC-15M. Our results provide evidence that the scale and diversity of training data and language supervision play a key role in unlocking the compositional generalization abilities of vision-language models.