TLDR: This research paper introduces “Counterfactual Models” (also called canonical representations) as an alternative framework to traditional Structural Causal Models (SCMs) for counterfactual reasoning. It highlights that SCMs implicitly encode unfalsifiable counterfactual assumptions, making them difficult to interpret and modify. The new framework separates counterfactual assumptions from observational and interventional knowledge, allowing analysts to transparently choose and implement various counterfactual conceptions (e.g., deterministic, stochastic, comonotonic) without altering the model’s observational or interventional properties. This approach simplifies the process of exploring different “what if” scenarios at the individual level, emphasizing that counterfactual beliefs are a choice, not something to be estimated from data.
Understanding cause and effect is a fundamental goal in many fields, from medicine to economics. However, not all causal questions are the same. Judea Pearl, a pioneer in causal inference, introduced a “causality ladder” with three distinct levels: observational, interventional, and counterfactual.
The first rung, observational, deals with predictions based on what we see. For example, “What is the recovery rate among people taking aspirin?” This level focuses on associations between variables.
The second rung, interventional, addresses predictions from actions or “doing.” This is about what would happen if we actively intervene in a system, like in a randomized controlled trial. An example question is, “What percentage of patients would recover if we gave them aspirin?”
The third and most complex rung is counterfactual reasoning, which involves imagining contrary-to-fact events. This level asks questions like, “Had Alice taken aspirin (assuming she did not), would she have recovered?” Counterfactuals deal with “singular causes” – what would have happened to a specific individual under different circumstances – and are crucial for concepts like individual fairness, even though they cannot be directly observed or empirically verified.
Traditionally, Structural Causal Models (SCMs) have been the go-to framework for formalizing causal beliefs across all three levels. SCMs describe how variables are generated from underlying, independent “noise” variables through a set of structural equations. While SCMs can capture observational and interventional relationships, the paper argues that they present significant challenges when it comes to the counterfactual level.
One major issue is that SCMs can be difficult to translate into intuitive counterfactual knowledge. It’s often unclear how altering the structural equations specifically changes counterfactual assumptions without unintentionally affecting the observational and interventional aspects of the model. Furthermore, many different SCMs can produce the same observational and interventional outcomes, yet lead to vastly different counterfactual conclusions. This means that the choice of an SCM implicitly encodes a specific, often unstated, counterfactual belief.
To address these challenges, Lucas De Lara introduces “Counterfactual Models,” also referred to as “canonical representations of structural causal models.” These new models offer an alternative, yet mathematically equivalent, way to represent counterfactuals. The core idea is to separate the layers of causation more clearly. Instead of relying on abstract structural equations and noise variables, counterfactual models directly specify “one-step-ahead counterfactual distributions.” These distributions describe how a variable would respond to interventions on its direct causes, across multiple hypothetical scenarios or “parallel worlds.”
A key innovation within this framework is the concept of “normalizations.” Normalizations allow analysts to define the intrinsic cross-dependencies of counterfactual joint probability distributions independently of the observed marginal distributions. This is achieved by first specifying the dependencies in a standardized, latent space (e.g., a Gaussian distribution with zero mean and unit variance) and then transforming these dependencies into the actual observation space. This approach makes the choice of a counterfactual conception explicit and transparent.
For instance, one can choose a “comonotonic” normalization, which implies that counterfactually paired outcomes maintain the same rank in their respective distributions (e.g., taller women are associated with taller men in a counterfactual scenario). Or, one could explore “stochastic” normalizations, where counterfactual outcomes are not deterministically linked. The crucial point is that these choices are made by the analyst, as counterfactuals cannot be falsified by data. The framework makes it easy to experiment with different counterfactual beliefs without re-estimating the entire causal model.
The practical benefits are significant. By disentangling the counterfactual assumptions from the observational and interventional constraints, the framework allows for more flexible and efficient exploration of different counterfactual scenarios. Once the observational and interventional aspects (captured by the causal graphical model) are learned, testing various counterfactual conceptions becomes computationally inexpensive, as it only involves choosing a normalization and sampling from it.
The paper illustrates its approach with theoretical and numerical examples, including a toy dose-response model and a real-world dataset on the effect of 401(k) pension plan eligibility on asset holdings. These examples demonstrate how different counterfactual conceptions can lead to distinct conclusions about individual causal effects, highlighting the importance of explicitly stating these assumptions.
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- Enhancing Multi-Agent Learning Through Causal Knowledge Transfer in Dynamic Settings
In conclusion, this research enriches our understanding and modeling of counterfactuals in causality. It provides a clearer and more convenient framework than traditional SCMs for formalizing, discussing, and implementing counterfactual beliefs. The authors advocate for greater transparency in the causality literature, urging researchers to clearly specify whether their studies concern general or singular causation and to justify their chosen counterfactual conceptions. For more details, you can read the full research paper here.
