Our focus in this paper is to solve causal inference problems using only observational data and (potentially partial) knowledge on the causal graph of the underlying structural causal model (SCM).

An important result is that for linear functionsf it is possible to recovers from observationsx up to certain symmetries, i.e., the model isidentifiable [8].

We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional functions ("mixtures") of the variables. Prior work relies on weak supervision, in the form of counterfactual pre-and post-intervention views or temporal structure; places restrictive assumptions, such as linearity, on the mixing function or latent causal model; or requires partial knowledge of the generative process, such as the causal graph or intervention targets. We instead consider the general setting in which both the causal model and the mixing function are nonparametric. The learning signal takes the form of multiple datasets, or environments, arising from unknown interventions in the underlying causal model. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data.

Artificial intelligence (AI) systems hold great promise for advancing various scientific disciplines, and are increasingly used in real-world applications. Despite their remarkable progress, further capabilities are expected in order to achieve more general types of intelligence. A critical distinction in this context is between factual knowledge, which can be evaluated against true or false answers (e.g., "what is the capital of England?"), and probabilistic knowledge, reflecting probabilistic properties of the real world (e.g., "what is the sex of a computer science graduate in the US?"). In this paper, our goal is to build a benchmark for understanding the capabilities of LLMs in terms of knowledge of probability distributions describing the real world. Given that LLMs are trained on vast amounts of text, it may be plausible that they internalize aspects of these distributions. Indeed, LLMs are touted as powerful universal approximators of real-world distributions. At the same time, classical results in statistics, known as curse of dimensionality, highlight fundamental challenges in learning distributions in high dimensions, challenging the notion of universal distributional learning. In this work, we develop the first benchmark to directly test this hypothesis, evaluating whether LLMs have access to empirical distributions describing real-world populations across domains such as economics, health, education, and social behavior. Our results demonstrate that LLMs perform poorly overall, and do not seem to internalize real-world statistics naturally. When interpreted in the context of Pearl's Causal Hierarchy (PCH), our benchmark demonstrates that language models do not contain knowledge on observational distributions (Layer 1 of PCH), and thus the Causal Hierarchy Theorem implies that interventional (Layer 2) and counterfactual (Layer 3) knowledge of these models is also limited.