Meta-probabilistic Modeling

TL;DR

Meta-probabilistic modeling (MPM) tackles the challenge of selecting well-specified probabilistic graphical models by learning a shared global generative structure across multiple related datasets while allowing dataset-specific local parameters. It introduces a bi-level optimization framework fed by a variational surrogate objective inspired by VAEs, enabling tractable inference even with neural parameterizations and providing closed-form updates for key local variables. Through two case studies—object-centric image modeling and sequential text modeling—MPM demonstrates the ability to recover meaningful latent structure, adapt to diverse data, and reveal connections to existing approaches such as slot attention. The approach unifies interpretable probabilistic structure with strong representational power, offering a principled path to cross-dataset learning of generative processes and latent attributes with practical impact for modeling heterogeneous data collections.

Abstract

While probabilistic graphical models can discover latent structure in data, their effectiveness hinges on choosing well-specified models. Identifying such models is challenging in practice, often requiring iterative checking and revision through trial and error. To this end, we propose meta-probabilistic modeling (MPM), a meta-learning algorithm that learns generative model structure directly from multiple related datasets. MPM uses a hierarchical architecture where global model specifications are shared across datasets while local parameters remain dataset-specific. For learning and inference, we propose a tractable VAE-inspired surrogate objective, and optimize it through bi-level optimization: local variables are updated analytically via coordinate ascent, while global parameters are trained with gradient-based methods. We evaluate MPM on object-centric image modeling and sequential text modeling, demonstrating that it adapts generative models to data while recovering meaningful latent representations.

Figures (7)

• Figure 1: MPM learns dataset-specific and global structure using multiple datasets, whereas most prior work focuses only on dataset structure only.
• Figure 2: Graphical representation for a latent variable MPM, which learns structure across datasets by using global parameters $\eta, \theta$ to model dataset parameters $\lambda$ and observations $x$, respectively.
• Figure 3: Toy example illustrating MPM for clustering with Gaussian Mixture Models. MPM leverages multiple datasets to learn the shared spiral-shaped transformation $A$, resulting in cluster assignments (\ref{['fig:toy_mpm']}, right panel) that more closely match the ground truth (\ref{['fig:toy_true']}, right panel) compared to a standard GMM (\ref{['fig:toy_gmm']}).
• Figure 4: Object and image visualizations produced by our mixture-based and additive decoder MPM models, slot attention, and the GMM baseline (from top to bottom). Border colors correspond to the alpha mask colors shown in the third column.
• Figure 5: Visualizations of global clusters learned by our MPM model using the mixture-based (\ref{['fig:global_clusters_mix']}) and additive (\ref{['fig:global_clusters_add']}) decoders. For each global cluster, we display the five objects with the highest responsibility scores, with border colors indicating the corresponding cluster assignment.

Theorems & Definitions (1)

• Proposition 1