How to Marginalize in Causal Structure Learning?

Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners approach this problem by inferring a posterior distribution over the possible directed acyclic graphs underlying the BN. The inference process often requires marginalizing over probability distributions, which is typically done using dynamic programming methods that restrict the set of possible parents for each node. Instead, we present a novel method that utilizes tractable probabilistic circuits to circumvent this restriction. This method utilizes a new learning routine that trains these circuits on both the original distribution and marginal queries. The architecture of probabilistic circuits then inherently allows for fast and exact marginalization on the learned distribution. We then show empirically that utilizing our method to answer marginals allows Bayesian structure learners to improve their performance compared to current methods.

Segment Any Mesh: Zero-shot Mesh Part Segmentation via Lifting Segment Anything 2 to 3D

We propose Segment Any Mesh (SAMesh), a novel zero-shot method for mesh part segmentation that overcomes the limitations of shape analysis-based, learning-based, and current zero-shot approaches. SAMesh operates in two phases: multimodal rendering and 2D-to-3D lifting. In the first phase, multiview renders of the mesh are individually processed through Segment Anything 2 (SAM2) to generate 2D masks. These masks are then lifted into a mesh part segmentation by associating masks that refer to the same mesh part across the multiview renders. We find that applying SAM2 to multimodal feature renders of normals and shape diameter scalars achieves better results than using only untextured renders of meshes. By building our method on top of SAM2, we seamlessly inherit any future improvements made to 2D segmentation. We compare our method with a robust, well-evaluated shape analysis method, Shape Diameter Function (ShapeDiam), and show our method is comparable to or exceeds its performance. Since current benchmarks contain limited object diversity, we also curate and release a dataset of generated meshes and use it to demonstrate our method's improved generalization over ShapeDiam via human evaluation. We release the code and dataset at https://github.com/gtangg12/samesh