arXiv：cs.LG· Vikas Kanaujia, Riyansha Singh, Shashank Sharma, Vipul Arora·· 3 小时前
从样本估计未归一化分布符号表达式的新框架
Symbolic Density Estimators for Unnormalized Distributions
AI 导读
研究者提出一种结合深度生成模型与符号回归的框架，可从观测样本中估计未归一化分布的符号表达式。该框架引入领域先验知识（如相互作用范围与预定义基函数集合）和分解大分布等归纳偏置，所用生成模型包括基于似然的流模型与基于分数的模型。在多元玩具分布及计算物理中的 XY 模型和 φ⁴ 理论格点上验证了有效性，并直接从样本估计出 φ⁴ 理论重整化问题不同尺度下哈密顿量的紧凑符号近似。
正文
Abstract:Estimating the symbolic or analytical form of probability density functions (PDFs) from observed samples is a fundamental challenge in statistical and computational modelling. This process is critical for deriving interpretable and generalizable relationships characterizing the underlying phenomenon. Traditionally, this estimation depends strongly on domain expertise and prior field-specific knowledge, with experts selecting appropriate functional forms or parametric families based on empirical evidence and theoretical understanding. The coefficients of these forms are then typically determined through parameter estimation. In this paper, we develop a framework for estimating symbolic expressions of unnormalized distributions from observed samples using domain-specific prior knowledge, such as the range of interactions and a predefined set of primitive functions. We integrate deep generative models with symbolic regression (SR), incorporating inductive biases, such as factorizing large distributions, to keep the problem tractable. The deep generative models we examine include likelihood-based models, viz., flow models, and score-based models. Experiments show the effectiveness of the proposed framework for estimating density functions for multivariate toy distributions as well as lattices from computational physics, namely, XY model and $\phi^4$ theory. When applied to the renormalization problem in $\phi^4$ theory, the proposed framework estimates compact symbolic approximations of the hamiltonian function at different scales directly from samples, yielding expressions that may be challenging to derive using traditional perturbative or analytic approaches in nonperturbative settings.
| Comments: | 32 pages, 3 figures |
| Subjects: | Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat) |
| Cite as: | arXiv:2610.10807 [cs.LG] |
| (or arXiv:2610.10807v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10807 arXiv-issued DOI via DataCite (pending registration) |
|
| Journal reference: | Transactions on Machine Learning Research, issn={2835-8856},year={2026} |
Submission history
From: Vikas Kanaujia [view email]
[v1]
Wed, 7 Oct 2026 19:09:10 UTC (728 KB)
来源：arXiv：cs.LG · arxiv.org