Identifiability for continuous conditional priors

Characterize the types of identifiability that hold for the covariate-dependent iMoE model when the true conditional prior is continuous.

Background

Identifiability determines whether distinct conditional prior measures can induce the same observable distribution. The paper notes that when the true prior is discrete, identifiability is guaranteed by classical results for normally used distributions, such as several standard mixture settings.

The unresolved case is a continuous true prior in the covariate-dependent framework. The authors do not specify which forms of identifiability—such as global, local, or identification under particular covariate designs—can be established, and explicitly state that the relevant types remain unknown.

References

On the other hand, the problem of identifiability remains. When the true prior is discrete, the identifiability is guaranteed from classical discussion in for normally used several distributions. However, if the prior is continuous, it is unknown what types of identifiability hold.

— Covariate-dependent Nonparametric $g$-modeling for regression via infinite Mixture-of-Expertizing class  (2610.08321 - Okazaki et al., 6 Oct 2026) in Section Discussion