Amortized Bayesian inference (ABI) offers fast, scalable approximations to posterior densities by training neural surrogates on data simulated from the statistical model. However, ABI methods are highly sensitive to model misspecification: when observed data fall outside the training distribution (generative scope of the statistical models), neural surrogates can behave unpredictably. This makes it a challenge in a model comparison setting, where multiple statistical models are considered, of which at least some are misspecified. Recent work on self-consistency (SC) provides a promising remedy to this issue, accessible even for empirical data (without ground-truth labels). In this work, we investigate how SC can improve amortized model comparison conceptualized in four different ways. Across two synthetic and two real-world case studies, we find that approaches for model comparison that estimate marginal likelihoods through approximate parameter posteriors consistently outperform methods that directly approximate model evidence or posterior model probabilities. SC training improves robustness when the likelihood is available, even under severe model misspecification. The benefits of SC for methods without access of analytic likelihoods are more limited and inconsistent. Our results suggest practical guidance for reliable amortized Bayesian model comparison: prefer parameter posterior-based methods and augment them with SC training on empirical datasets to mitigate extrapolation bias under model misspecification.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Authors propose a method of estimating a graphical model for continuous data that blends the following three, established ideas: 1) assume the data follows a multivariate Gaussian and estimate using the graphical lasso; 2) do not assume the data follows a multivariate Gaussian and instead use a Gaussian copula, the nonparanormal, to allow arbitrary single variable marginals; or 3) assume a specific tree-structured factorization and model arbitrary bivariate marginals along the tree structure. The proposed method introduces the blossom tree, which is a specific factorization of the model into a collection of densely connected blossom components that are connected by a specific set of tree edges. In particular, each blossom is connected (via a pedicel node) to at most one tree edge. The blossom components are modeled as sparse multivariate Gaussians (or using the non-paranormal copula) and the tree edges are modeled as arbitrary bivariate distributions with single variable marginals that are consistent with the marginal of any blossom pedicel to which they are attached.

Define the function f (t) null t log t which is convex. This section discusses the sparse GP model that is used in the classification of the synthetic moon dataset in Sec. A GP is fully specified by its prior mean (i.e., assumed to be Given the latent function values (i.e., also known as inducing variables) On the other hand, Figs. 9 and 10 visualize the approximate posterior beliefs Let us consider the experiment in Sec. Figure 1 shows results of averaged KL divergences (i.e., performance metric described in Sec. 4) achieved by EUBO, rKL, and However, the fourth row of Table 3 shows that both EUBO and rKL do not perform that well. EUBO may suffer from poor unlearning performance when λ is too small. One may wonder how our unlearning methods can handle multiple users' request arriving sequentially Figure 12: Graphs of averaged KL divergence vs.