  Modeling dependencies among features is fundamental for many machine learning
tasks. Although there are often multiple related instances that may be
leveraged to inform conditional dependencies, typical approaches only model
conditional dependencies over individual instances. In this work, we propose a
novel framework, partially observed exchangeable modeling (POEx) that takes in
a set of related partially observed instances and infers the conditional
distribution for the unobserved dimensions over multiple elements. Our approach
jointly models the intra-instance (among features in a point) and
inter-instance (among multiple points in a set) dependencies in data. POEx is a
general framework that encompasses many existing tasks such as point cloud
expansion and few-shot generation, as well as new tasks like few-shot
imputation. Despite its generality, extensive empirical evaluations show that
our model achieves state-of-the-art performance across a range of applications.
