arXiv：cs.LG· Nishanth Shetty, Saisuchith Mahajan, Chandra Sekhar Seelamantula·· 4 小时前AI 评分35
凸域上的广义分数匹配
Generalised Score Matching on Convex Domains
AI 导读
研究者将凸域上的广义分数匹配推导为最小概率流的邻域极限，邻域几何决定权重，且所有 C² 正定权重均可由此生成，涵盖经典分数匹配及非负数据变体。针对指数族，作者将凸性、一致性与渐近正态性结果扩展到任意此类权重，并证明估计量在特定边界条件下收敛到真实参数。在多面体截断高斯与单纯形 Dirichlet 分布上，所提估计量在 50 组真值配置中至少 42 组取得最低中位误差。
正文
Abstract:Score matching avoids computing the normalising constant that maximum-likelihood estimation requires. On constrained domains, its generalised variants weight the Fisher divergence so that boundary terms vanish. We derive generalised score matching on open convex subsets of $\mathbb{R}^{d}$ as the small-neighbourhood limit of minimum probability flow, in which the geometry of the neighbourhoods determines the weight. Every $C^{2}$ positive definite weight arises in this way, including those of classical score matching on $\mathbb{R}^{d}$ and of its variants for non-negative data on $\mathbb{R}_{+}^{d}$. For exponential families, we extend the standard convexity, consistency and asymptotic normality results to every such weight and show that the estimator converges to the true parameter under certain boundary conditions. For a truncated Gaussian on a polytope and a Dirichlet distribution on the simplex, proposed estimators attain the lowest median error of all methods compared, in at least 42 of 50 ground-truth configurations.
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2609.11521 [cs.LG] |
| (or arXiv:2609.11521v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.11521 arXiv-issued DOI via DataCite |
Submission history
From: Nishanth Shetty [view email]
[v1]
Thu, 10 Sep 2026 13:23:41 UTC (5,445 KB)
[v2]
Wed, 7 Oct 2026 17:35:05 UTC (209 KB)
来源：arXiv：cs.LG · arxiv.org