发表机构
Embry-Riddle Aeronautical University（安柏瑞德航空大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何控制高斯点云的复杂度，提出用截断的折断棒狄利克雷过程先验等方法，使组件数量适应数据，更新为闭式步骤。实验表明有效复杂度能适应场景，DP先验贡献在复杂度选择，在多方面表现优于固定K的VBGS。
AI 中文摘要
3D高斯点云将场景表示为各向异性高斯的有限混合，其组件数量K由启发式密度控制或用户上限设置。变分贝叶斯高斯点云（VBGS）将点云拟合重塑为共轭变分推理，但K保持固定。我们用截断的折断棒狄利克雷过程先验代替混合权重上的有限对称狄利克雷，以及作为理论支持的替代方案的稀疏过拟合有限狄利克雷，使占用组件的数量适应数据，同时每次更新仍然是一个闭式坐标上升步骤；自然梯度随机变体使每步成本与点数无关。我们给出了精确的单调性保证、严格的截断误差界，纠正了常用的反保守大α近似，并诚实地说明了拟合组件数量估计的内容。从经验上看：（i）有效复杂度K适应场景复杂度，并在具有适当浓度的良好分离的合成数据上，在±1范围内恢复真实的K；（ii）去混淆比较表明，DP先验的贡献是复杂度选择，而不是每个组件的效率——在匹配预算下，收敛的DP拟合比单通道固定K的VBGS高出2.7dB，但与同样收敛的固定K基线相当，并且在3D场景上，DP-Splat用少5.9-7.6倍的组件匹配或超过VBGS的留出颜色预测；（iii）后验预测颜色方差在模型匹配的合成数据上校准良好；（iv）精确后验渐近性建议的排序在平均场坐标上升下反转：DP先验抵抗过度分裂，而稀疏有限混合饱和其截断，这是在N中跨越三个数量级记录的变分实践和后验渐近性之间的差距。
英文摘要
3D Gaussian Splatting represents scenes as finite mixtures of anisotropic Gaussians whose number of components $K$ is set by heuristic density control or user caps. Variational Bayes Gaussian Splatting (VBGS) recast splat fitting as conjugate variational inference, but $K$ remains fixed. We replace the finite symmetric Dirichlet over mixture weights with a truncated stick-breaking Dirichlet-process prior (or a sparse overfitted finite Dirichlet), so that the number of occupied components adapts to the data while every update remains a closed-form coordinate-ascent step; a natural-gradient stochastic variant scales to large point sets. We give an ELBO monotonicity-and-convergence guarantee, a rigorous truncation-error bound that corrects a large-$α$ approximation in common use which undershoots the exact Ishwaran-James bound, and an honest account of what the fitted number of components estimates. Empirically: (i) the effective complexity $\hat{K}$ adapts to data complexity and recovers the true $K$ within $\pm 1$; (ii) a deconfounded comparison shows the DP prior's contribution is complexity selection, not per-component efficiency: converged DP fits beat single-pass fixed-$K$ VBGS by +2.7 dB yet tie an equally converged fixed-$K$ baseline, and on all eight NeRF-synthetic scenes DP-Splat holds held-out point-space color prediction within 0.33 dB of VBGS with 3.9-7.9x fewer occupied components, while under full rasterization on held-out views it renders 3.4-9.0 dB below the unpruned baseline; (iii) the posterior-predictive color variance is well calibrated, and a seeded matched-capacity ablation attributes that calibration to the conjugate color model rather than to the weight prior; (iv) the ordering suggested by exact-posterior asymptotics reverses under mean-field coordinate ascent: the DP prior resists over-splitting while the sparse finite mixture saturates its truncation.
Comments32 pages, 12 figures, 8 tables. Published in Transactions on Machine Learning Research (2026); reviews and decision: https://openreview.net/forum?id=75Hx0RDPMr. Code and experiment records: https://github.com/archiedong/dp-splat
Journal refTransactions on Machine Learning Research, 2026
