Naiqi Li

The Hierarchical Dirichlet Process (HDP) provides a flexible Bayesian nonparametric framework for modeling grouped data with a shared yet unbounded collection of mixture components. While existing applications of the HDP predominantly focus on the Dirichlet-multinomial conjugate structure, the framework itself is considerably more general and, in principle, accommodates a broad class of conjugate prior-likelihood pairs. In particular, exponential family distributions offer a unified and analytically tractable modeling paradigm that encompasses many commonly used distributions. In this paper, we investigate analytic results for two important members of the exponential family within the HDP framework: the Poisson distribution and the normal distribution. We derive explicit closed-form expressions for the corresponding Gamma-Poisson and Normal-Gamma-Normal conjugate pairs under the hierarchical Dirichlet process construction. Detailed derivations and proofs are provided to clarify the underlying mathematical structure and to demonstrate how conjugacy can be systematically exploited in hierarchical nonparametric models. Our work extends the applicability of the HDP beyond the Dirichlet-multinomial setting and furnishes practical analytic results for researchers employing hierarchical Bayesian nonparametrics.

We introduce ProcGen3D, a new approach for 3D content creation by generating procedural graph abstractions of 3D objects, which can then be decoded into rich, complex 3D assets. Inspired by the prevalent use of procedural generators in production 3D applications, we propose a sequentialized, graph-based procedural graph representation for 3D assets. We use this to learn to approximate the landscape of a procedural generator for image-based 3D reconstruction. We employ edge-based tokenization to encode the procedural graphs, and train a transformer prior to predict the next token conditioned on an input RGB image. Crucially, to enable better alignment of our generated outputs to an input image, we incorporate Monte Carlo Tree Search (MCTS) guided sampling into our generation process, steering output procedural graphs towards more image-faithful reconstructions. Our approach is applicable across a variety of objects that can be synthesized with procedural generators. Extensive experiments on cacti, trees, and bridges show that our neural procedural graph generation outperforms both state-of-the-art generative 3D methods and domain-specific modeling techniques. Furthermore, this enables improved generalization on real-world input images, despite training only on synthetic data.