在少于d个环境、粗粒度干预下,仍可识别潜在因子的变动节点。
Identifying General Mechanism Shifts in Linear Causal Representations
- 放宽条件:允许少于d个环境、粗粒度干预。
- 只需识别变动节点集合,无需完整因果结构。
- 算法可直接用于样本数据,验证有效。
我们研究线性因果表征学习场景,其中观测到d个未知潜在因子的线性混合,这些因子遵循线性结构性因果模型。已有研究证明,在至少d个环境中对单个潜在节点进行完美干预时,可恢复潜在因子及其因果结构(至排列与尺度变换)。但实际中,干预可能不完美,且环境数量远少于潜在因子数。本文考虑此类更现实设定:环境数小于d,且干预仅能粗略改变潜在因子间的因果图。我们不再要求恢复完整因果结构,而仅需识别出在至少一个环境中发生变动的节点。在极弱的标准假设下,我们给出了令人惊讶的可识别性结果:确实可准确识别出变动节点集合。该证明是构造性的,明确给出了节点为变动节点的充要条件,并说明可通过观测数据验证。算法自然适用于样本数据场景,即每个环境中提供样本数据集。我们在合成数据和一个心理测量数据集上验证了方法的有效性。代码见https://github.com/TianyuCodings/iLCS。
原文摘要 · Abstract (English)
We consider the linear causal representation learning setting where we observe a linear mixing of $d$ unknown latent factors, which follow a linear structural causal model. Recent work has shown that it is possible to recover the latent factors as well as the underlying structural causal model over them, up to permutation and scaling, provided that we have at least $d$ environments, each of which corresponds to perfect interventions on a single latent node (factor). After this powerful result, a key open problem faced by the community has been to relax these conditions: allow for coarser than perfect single-node interventions, and allow for fewer than $d$ of them, since the number of latent factors $d$ could be very large. In this work, we consider precisely such a setting, where we allow a smaller than $d$ number of environments, and also allow for very coarse interventions that can very coarsely \textit{change the entire causal graph over the latent factors}. On the flip side, we relax what we wish to extract to simply the \textit{list of nodes that have shifted between one or more environments}. We provide a surprising identifiability result that it is indeed possible, under some very mild standard assumptions, to identify the set of shifted nodes. Our identifiability proof moreover is a constructive one: we explicitly provide necessary and sufficient conditions for a node to be a shifted node, and show that we can check these conditions given observed data. Our algorithm lends itself very naturally to the sample setting where instead of just interventional distributions, we are provided datasets of samples from each of these distributions. We corroborate our results on both synthetic experiments as well as an interesting psychometric dataset. The code can be found at https://github.com/TianyuCodings/iLCS.
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