Many causal systems such as biological processes in cells can only be
observed indirectly via measurements, such as gene expression. Causal
representation learning -- the task of correctly mapping low-level observations
to latent causal variables -- could advance scientific understanding by
enabling inference of latent variables such as pathway activation. In this
paper, we develop methods for inferring latent variables from multiple related
datasets (environments) and tasks. As a running example, we consider the task
of predicting a phenotype from gene expression, where we often collect data
from multiple cell types or organisms that are related in known ways. The key
insight is that the mapping from latent variables driven by gene expression to
the phenotype of interest changes sparsely across closely related environments.
To model sparse changes, we introduce Tree-Based Regularization (TBR), an
objective that minimizes both prediction error and regularizes closely related
environments to learn similar predictors. We prove that under assumptions about
the degree of sparse changes, TBR identifies the true latent variables up to
some simple transformations. We evaluate the theory empirically with both
simulations and ground-truth gene expression data. We find that TBR recovers
the latent causal variables better than related methods across these settings,
even under settings that violate some assumptions of the theory.

通过从多个相关数据集和任务中推断潜在变量，我们开发了一种从基因表达预测表型等任务中学习潜在因果变量的方法，其中关键观点是基于基因表达引起的潜在变量与感兴趣表型之间的映射在密切相关的环境下变化稀疏。我们引入了树状正则化来建模稀疏变化，通过最小化预测误差并对密切相关的环境进行正则化以学习相似的预测器，理论证明了在稀疏变化程度的某些简单转换下，树状正则化能够识别出真正的潜在变量。我们在模拟实验和真实的基因表达数据上进行了理论验证，发现在这些设置下，相比相关方法，树状正则化更好地恢复了潜在因果变量，即使在违背某些理论假设的情况下也是如此。