On Pearl’s Hierarchy and the Foundations of Causal Inference

Cause-and-effect relationships play a central role in how we perceive and make sense of the world around us, how we act upon it, and ultimately, how we under­ stand ourselves. Almost two decades ago, computer scientist Judea Pearl made a breakthrough in understanding causality by discovering and systematically study­ ing the “Ladder of Causation,” a framework that highlights the distinct roles of seeing, doing, and imagining. In honor of this landmark discovery, we name this the Pearl Causal Hierarchy (PCH). In this chapter, we develop a novel and comprehensive treatment of the PCH through two complementary lenses: one logical-probabilistic and another inferential-graphical. Following Pearl’s own pre­ sentation of the hierarchy, we begin by showing how the PCH organically emerges from a well-specified collection of causal mechanisms (a structural causal model, or SCM). We then turn to the logical lens. Our first result, the Causal Hierarchy Theorem (CHT), demonstrates that the three layers of the hierarchy almost always separate in a measure-theoretic sense. Roughly speaking, the CHT says that data at one layer virtually always underdetermines information at higher layers. As in most practical settings the scientist does not have access to the precise form of the underlying causal mechanisms—only to data generated by them with respect to some of the PCH’s layers—this motivates us to study inferences within the PCH through the graphical lens. Specifically, we explore a set of methods known as causal inference that enable inferences bridging the PCH’s layers given a partial 510 Chapter 27 On Pearl’s Hierarchy and the Foundations of Causal Inference specification of the SCM. For instance, one may want to infer what would happen had an intervention been performed in the environment (second-layer statement) when only passive observations (first-layer data) are available. We introduce a fam­ ily of graphical models that allows the scientist to represent such a partial speci­ fication of the SCM in a cognitively meaningful and parsimonious way. Finally, we investigate an inferential system known as do-calculus, showing how it can be suf­ ficient, and in many cases necessary, to allow inferences across the PCH’s layers. We believe that connecting with the essential dimensions of human experience as delineated by the PCH is a critical step toward creating the next generation of arti­ ficial intelligence (AI) systems that will be safe, robust, human-compatible, and aligned with the social good. 27.