What is Causal Feature Learning?

Causal Feature Learning (CFL) is a novel algorithm designed to construct macrovariables that preserve the causal relationships between variables. These macrovariables are intended to reduce the complexity of finding causal relationships in data by identifying a small number of relevant macrostates that can be used to test causal hypotheses.

What are macrovariables?

Macrovariables are a useful way to summarize the relevant features of detailed, low-level data. For example, instead of attempting to keep track of the kinetic energy of every particle in a room, we can instead monitor just the temperature of the room. In this case, ‘temperature’ is a macrovariable which summarizes ‘kinetic energy of each particle in the room’, a micro-state. Temperature is a useful macrovariable because all the particle configurations which have the same temperature are functionally identical for many purposes. This is an example of how macrovariables can abstract away unnecessary details while preserving important distinctions. The relevant features to preserve depend on the task for which the macrovariable is being used.

How does CFL work?

CFL is designed to take two micro-level data sets as input: a ‘causal’ data set (X) and an ‘effect’ data set (Y). CFL then assigns each data point in X and Y to a macrovariable state: the causal data is partitioned into a set of macro-causes (e.g. the temperature of the room) and effect data into a set of macro-effects (e.g. whether or not the air conditioner turns on).

As discussed above, when constructing a macrovariable, a choice must be made about what information to preserve and what details to abstract away. In the case of CFL, we attempt to preserve the causal relationships between microvariables in the cause and effect data sets. In other words, every microvariable configuration assigned to a given cause macro-state should produce the same effect on Y as any other member of that same macro-state. Similarly, each microvariable configuration in Y that is assigned to the same effect macro-state should be expected to respond similarly to any cause data.

CFL works in two steps to create these macrovariables: first, CFL estimates a conditional probability distribution P(Y|X); second, it clusters the cause and effect data based on that distribution. The cluster labels that CFL outputs correspond to the macrovariable state of each data point.

In addition to these labels, the underlying rules to predict the macrovariable state of any new data point are implicitly stored in the parameters of the trained CFL pipeline. New data can be passed through the trained pipeline and given macrovariable assignments as well.