Multi-Component VAE with Gaussian Markov Random Field
This addresses the challenge of structural coherence in generative modeling for multi-component datasets like industrial assemblies or multi-modal imaging, offering a novel method that improves over existing simplified approaches.
The paper tackles the problem of generating multi-component datasets with intricate dependencies by introducing the GMRF MCVAE, which embeds Gaussian Markov Random Fields to model cross-component relationships, achieving state-of-the-art performance on a synthetic Copula dataset, competitive results on PolyMNIST, and significantly enhanced structural coherence on the BIKED dataset.
Multi-component datasets with intricate dependencies, like industrial assemblies or multi-modal imaging, challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders typically rely on simplified aggregation strategies, neglecting critical nuances and consequently compromising structural coherence across generated components. To explicitly address this gap, we introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder , a novel generative framework embedding Gaussian Markov Random Fields into both prior and posterior distributions. This design choice explicitly models cross-component relationships, enabling richer representation and faithful reproduction of complex interactions. Empirically, our GMRF MCVAE achieves state-of-the-art performance on a synthetic Copula dataset specifically constructed to evaluate intricate component relationships, demonstrates competitive results on the PolyMNIST benchmark, and significantly enhances structural coherence on the real-world BIKED dataset. Our results indicate that the GMRF MCVAE is especially suited for practical applications demanding robust and realistic modeling of multi-component coherence