Daniel C comments on Resampling Conserves Redundancy (Approximately)

[Daniel C]

Would this still give us guarantees on the conditional distribution $P\left(X|\Lambda \right)$?

E.g. Mediation: $D_{KL}\left(P\right(X_1,X_2,\Lambda )\parallel P(X_1|\Lambda \left)P\right(X_2|\Lambda \left)P\right(\Lambda \left)\right)$$=D_{KL}\left(P\right(X_1,X_2|\Lambda \left)P\right(\Lambda )\parallel P(X_1|\Lambda \left)P\right(X_2|\Lambda \left)P\right(\Lambda \left)\right)$$=D_{KL}\left(P\right(X_1,X_2|\Lambda )\parallel P(X_1|\Lambda \left)P\right(X_2|\Lambda \left)\right)$

is really about the expected error conditional on individual values of $\Lambda$, & it seems like there are distributions with high mediation error but low error when the latent is marginalized inside $D_{KL}$, which could be load-bearing when the agents cast out predictions on observables after updating on $\Lambda$