平衡因果博弈：分离、识别与循环潜在状态的可识别性
Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent States
浏览论文内容
中文总结 AI 辅助
研究平衡因果博弈中，通过结合博弈与多种模型及规则，探讨在不同条件下因果关系的分离、识别等问题，包括线性和非线性传感情况，明确平衡数据能支持的因果结论及需针对性实验的情况。
中文摘要 AI 辅助
电网、市场和相互作用的群体通过未知传感器进入由反馈驱动的平衡状态。我们的平衡因果博弈（ECG）将博弈与其循环因果模型、隐藏输入、传感器映射以及干预和平衡选择规则相结合；干预编辑声明的对象并重新计算平衡。在特定条件下，ECG分离在我们的示例中是合理但不完整的。后门/半路径识别观测查询。对于未触及的旋转对称高斯块，二阶矩仅确定源框架旋转，在此旋转下不同变量的效应通常会改变。未知传感产生单独的模糊性。在无自效应的被动稳定线性模型中，未知布线和满秩未知传感使得对于\(d\geq2\)时\(B\)完全无法识别。在LiNG下，非高斯性消除源旋转；机制干预将传感与相互作用分离。在未知支持、不变传感、对齐响应和适定单目标干预下，可识别\((H,B)\)直至声明等价。对于\(d\)个目标，当唯一未靶向节点直接为所有其他节点的父节点时，\(d - 1\)个就足够，否则需要\(d\)个。排除采集探针；已知布线没有通用计数。对于非线性传感，各向同性高斯源块在标记环境中允许块内和块间存在隐藏扭曲，同时保持所需的径向定律。相反，在规定的正性、信息性单块变化、秩和不可约性条件下，在规定的替代类中，直至块置换和块坐标变化，可识别最精细的独立源块表示，但无法识别下游机制或传感器/相互作用的划分。总之，这些结果表明平衡数据支持哪些因果结论以及哪些需要有针对性的实验。
英文摘要
Power grids, markets, and interacting populations, settle into feedback driven equilibria observed through unknown sensors. Our Equilibrium Causal Game (ECG) joins a game to its cyclic causal model, hidden inputs, sensor map, and rules for interventions and equilibrium selection; interventions edit declared objects and recompute equilibrium. Under stated conditions, ECG-separation is sound but incomplete in our examples. Back-door/half-trek routes identify observed queries. Yet for an untouched rotationally symmetric Gaussian block, second moments determine only a source-frame rotation, across which distinct-variable effects generically change. Unknown sensing creates a separate ambiguity. In passive stable linear models without self-effects, unknown wiring and full-rank unknown sensing leave $B$ completely unidentified for $d\ge2$. Under LiNG, non-Gaussianity removes the source rotation; mechanism interventions separate sensing from interactions. With unknown support, invariant sensing, aligned responses, and well-posed single-target interventions identify $(H,B)$ up to declared equivalence. Of $d$ targets, $d-1$ suffice exactly when the sole untargeted node directly parents all others; otherwise $d$ are needed. Acquisition probes are excluded; known wiring gives no universal count. With nonlinear sensing, isotropic Gaussian source blocks admit hidden twists within and across blocks in labelled environments preserving required radial laws. Conversely, under stated positivity, informative one-block changes, rank, and irreducibility conditions, the finest independent source-block representation is identified within the stated alternative class up to block permutation and blockwise coordinate changes, but not downstream mechanisms or the sensor/interaction split. Together, these results show which causal conclusions equilibrium data support and which require targeted experiments.
发表机构
- Department of Mechanical & Industrial Engineering, Montana State University（机械与工业工程系，蒙大拿州立大学）
- Gianforte School of Computing, Montana State University（计算机学院，蒙大拿州立大学）
机构由 AI 辅助整理，请以论文原文为准。
