This state of the art was recently critiqued by O'Bray et al.

While OT commonly seeks at computing the transport plan that minimizes the cost of moving between two distributions, it can naturally be extended to the multi-marginal setting (mOT) when considering several distributions.

Although the population (i.e, infinite-particle) limit dynamics of SVGD is well characterized, its behavior in the finite-particle regime is far less understood.

In many machine learning tasks, there are commonly sources of exogenous and endogenous distribution shift, necessitating that the algorithm be retrained repeatedly over time.

We refer the readers to ( Peters et al., 2017) for more detailed graphical terminology. We base our proof mostly on ( Kirsch, 2019). The first statement follows directly from the first theorem in ( Haviland, 1936). Without loss of generality, we reorder the variables according to reversed topological ordering, i.e. a Follows directly from Lemma 1. Lemma 4. Recall condition 2) in Causal de Finetti states that 8 i, 8 n 2 N: X The first equality holds by well-defindedness. The fourth equality follow from well-definedness.