This same algorithm can then be used to reconstruct the true DAGGfrom the true ordering . Once the ordering is known, existing nonlinear variable selection methods [4, 11, 16, 25, 28, 46] suffice to learn the parent setspa(j)and hence the graphG. In our experiments, we use exactly this procedure to learnGfrom the order, based on the data. There are two cases: (i)Bj =, and (ii)Bj 6= . If instead we haveσ23 = var(z3) = 1/3, the condition would be violated.

Instead, we impose a condition on the residual variances that is closely related to previous work on linear models with equal variances.

This "inconsistency" of the encoder lowers the quality of the learned representations,

The spectacular success ofdeep generativemodels calls forquantitativetools to measure their statistical performance. Divergence frontiers have recently been proposed as an evaluation framework for generative models, due to their ability to measure the quality-diversity trade-off inherent to deep generative modeling. We establish non-asymptotic bounds on the sample complexity of divergence frontiers.

The use of machine learning models in high-stake applications (e.g., healthcare, lending, college admission) has raised growing concerns due to potential biases