Tiger moms, Bach, and Reichenbach

Causal sufficiency and the Causal Frame Problem

This post is a draft excerpt from a book I'm writing on causal AI. Here, I'm explaining to the reader how to build a causal graph. I’ll share more information about the book later. For now, please enjoy.

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What is a relevant set of variables for my causal graph?

Before building the causal graph, you need to define the questions or broad set of questions you wish to answer with inference on the causal model. For example, perhaps you are interested in quantifying the causal relationship between X and Y (in formal terms, X's causal effect or average treatment effect on Y). Or perhaps you wish to build an expert system for clinical diagnosis that can infer which diseases (causes) might be causing an observed set of observed symptoms (effects). It is helpful in any investigation to start with the question or scope of questions you want to answer and then identifying the variables pertinent to those questions.

Causal inference theory provides us with a definition of a minimally sufficient set of variables. For example, suppose you are interested in asking questions about the causal relationships between variables X, Y, and Z. The variables X, Y, and Z wouldn't be sufficient by themselves. A set of variables is causally sufficient if that set doesn't exclude any causes for more than one of the set's variables. In other words, the set is not excluding any common causes.

Causal sufficiency tells us that if we want to reason causally about a set of variables, we must include not just those variables but all of their shared common causes in the causal graph.

Tiger moms, Bach, and Reichenbach

Reichenbach's common cause principle gives us intuition as to why we can't exclude common causes. The principle states that if two variables are dependent, then either one variable is the cause of the other, or they share a common cause. 

Imagine you are at a dinner party, and guests are talking about a study that suggests exposure to classical music while in the womb leads to higher standardized test scores. One member of the group rightly says, "Well, you know, correlation does not imply causation." Reichenbach's uncertainty principle empowers you to give this nuanced rebuttal.

"That is true. But when we observe that two things are correlated, one either causes the other, or they share a common cause. For example, the notion that getting good test scores in school would cause you to listen to classical music in the womb violates several laws of physics. But it is plausible that there is a certain type of parent who might drive her children to do well on standardized tests (e.g., pay for coaching) and enjoys Baroque music, often whilst pregnant. So we simply need to ask ourselves if the study did a good job controlling for whether or not someone is both a Tiger mom and a Baroque music fan."

Causal Sufficiency and the Causal Frame Problem

Causal sufficiency lets us build a causal graph specific to a problem domain and a set of questions we want to ask, rather than create one giant causal graph representing all of existence. Relatedly, in philosophy of science, there is an epistemological puzzle called the causal frame problem. The problem asks how the human mind can disregard seemingly irrelevant causal information when faced with a decision problem.  

An approach to this problem is to attempt to reverse-engineer this human ability into an algorithm. Such an algorithm would selectively query a database of causal relationships and compose a causal model bespoke to a specific scenario. For example, given our graph-based definition of causal sufficiency, an obvious algorithm would simply draw a causally sufficient set of variables.  

However, robust empirical studies show that humans often neglect members of the causally sufficient set of variables concerning a given problem. One issue is that some variables, such as common causes, that would improve inferences are latent, meaning the human can't observe them. Humans might be inclined to ignore things we can't observe even if we know they exist. But the evidence shows humans also ignore some of those useful variables even if we can observe them. This phenomenon, called alternative neglect, suggests that human causal reasoning is fundamentally flawed and that we shouldn't strive to mimic it with our algorithms.

An alternative view is that inference on a causally sufficient set of variables might be intractable for complex problems. This is because the mind needs to make decisions within finite constraints on time and cognitive load. So we may bias our decisions by ignoring some variables in the causally sufficient set if the added efficiency is worth the cost of the bias. This idea follows a line of research in cognitive science concerned with bounded rationality. It also has implications for building causal reasoning algorithms. We care about the time and computation resources consumed by inference, especially for agents who need to make instantaneous decisions, such as with self-driving cars.

Go Deeper

• Icard, T. and Goodman, N.D., 2015, July. A Resource-Rational Approach to the Causal Frame Problem. In CogSci.

• Nobandegani, A.S. and Psaromiligkos, I.N., 2017. The causal frame problem: An algorithmic perspective. arXiv preprint arXiv:1701.08100.