Conditions for UMNN-based cGNFs to achieve accurate estimation

Determine the architectural configurations, training hyper-parameter settings, and sample size requirements under which unconstrained monotonic neural networks (UMNNs) used within causal-graphical normalizing flows (cGNFs) achieve sufficient accuracy to estimate causal effects with no more than trivial error.

Background

UMNNs are universal density approximators that, in principle, can recover complex distributions without parametric restrictions. The authors emphasize that the practical conditions under which UMNN-based cGNFs reach high accuracy remain unclear, motivating a need to identify design and data requirements—such as network architectures, hyper-parameters, and sample sizes—that ensure reliable estimation of causal effects.