从静态数据中无参数恢复连续时间因果扩散机制
Non-parametric recovery of causal diffusion mechanisms from steady-state observations
- 基于稳态观测数据，通过核估计无参数推断因果扩散漂移函数
- 在弱非爆炸条件下可完全识别因果机制，且估计器具有一致性
- 适用于基因表达等不可重复测量场景，与生成模型有深层联系
我们研究稀疏多变量随机系统在连续时间下的因果演化过程，提出仅从横截面数据中恢复其瞬时转移机制的方法。该范式源于基因表达分析等应用，因实验破坏性导致仅能记录细胞生命周期内一次数据。假设系统服从已达到稳态的时齐扩散过程，因果机制由漂移函数完全描述，且因果图结构已知且无环。在此设定下，证明了在弱非爆炸条件下，漂移函数可无参数识别；并推导出针对该困难逆问题的核估计器，证明其一致性。此外，提出超参数调优的交叉验证方案，通过模拟展示估计器行为，并讨论其与不可逆生成扩散模型及低频采样数据的关联。
原文摘要 · Abstract (English)
We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data. This observational paradigm is motivated by applications such as gene expression analysis, where destructive experimental techniques may only allow recording data once over a cell's lifetime. Precisely, we assume the system follows a time-homogeneous diffusion process that has reached an equilibrium distribution at observation time. Further, we assume the causal mechanism is fully described by the diffusion drift, is acyclic, and its causal structure graph is known. In this setting, we prove that the full causal mechanism, i.e., the drift function, can be non-parametrically identified under a weak non-explosion criterion. We derive a non-parametric kernel estimator for this challenging inverse problem and prove its consistency. Moreover, we propose a cross-validation scheme for hyperparameter tuning, illustrate the behavior of our estimator in simulations, and we discuss connections with irreversible generative diffusion models and low-frequency sampled data.
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