Causal representation learning (CRL) aims to learn low-dimensional causal latent variables from high-dimensional observations. While identifiability has been extensively studied for CRL, estimation has been less explored. We use empirical Bayes (EB) to estimate causal representations from multiple domains whose differences reflect interventions in a shared causal model. Multi-domain CRL poses a simultaneous inference problem suited to EB. Here, we propose an EB $f$-modeling algorithm that improves the quality of learned causal variables by exploiting invariant structure within and across domains. Specifically, we consider linear measurement models with interventional priors induced by an acyclic latent causal model with known graph and intervention targets. We develop an EM-style algorithm based on causally structured score matching. In experiments on synthetic and semi-synthetic single-cell data, our proposed method achieves more accurate estimation than alternative methods and baselines.
Carolina Zheng, Claudia Shi, Keyon Vafa, Amir Feder, David M. Blei
Controlled generation refers to the problem of creating text that contains stylistic or semantic attributes of interest. Many approaches reduce this problem to training a predictor of the desired attribute. For example, researchers hoping to deploy a large language model to produce non-toxic content may use a toxicity classifier to filter generated text. In practice, the generated text to classify, which is determined by user prompts, may come from a wide range of distributions. In this paper, we show that the performance of controlled generation may be poor if the distributions of text in response to user prompts differ from the distribution the predictor was trained on. To address this problem, we cast controlled generation under distribution shift as an invariant learning problem: the most effective predictor should be invariant across multiple text environments. We then discuss a natural solution that arises from this characterization and propose heuristics for selecting natural environments. We study this characterization and the proposed method empirically using both synthetic and real data. Experiments demonstrate both the challenge of distribution shift in controlled generation and the potential of invariance methods in this setting.