Causal mathematics

As explained in Causal AI

Causal mathematics is the formal probabilistic or expectation-based representation of a causal question.

Causal mathematics translates an intervention, explanation, or counterfactual question into a probability or expectation that can be estimated from data. It separates causal reasoning from ordinary prediction: first define the causal question, then formalize its target, then perform statistical inference. section 1.5.3

A practical workflow is:

• Pose the causal question: specify the intervention, outcome, conditions, or decision of interest. section 1.5.3
• Write the causal math: represent the question with causal notation, probabilities, or expectations. section 1.5.3
• Perform statistical inference: choose an analysis that estimates the formalized causal quantity. section 1.5.3

Conditional effects in causal MNIST

To estimate how writer type affects images of digit 4 at a specified stroke thickness, compare expected images under interventions setting writer type to “high school” and “bureaucrat.” Their pixel-by-pixel difference represents the conditional average treatment effect. section 1.5.3

Figure 1.8 Visualization of an example CATE of writer type on an image. It is the pixel-by-pixel difference of the expected image under one intervention (W=_{"high school"}) minus the expected image under another intervention (W=_"bureaucrat"), with both expectations conditional on being images of the digit 4 with a certain level of thickness.

Visualizes a conditional average treatment effect as the pixel-by-pixel difference between two intervention-specific expected images. section 1.5.3

How Causal AI covers it

How deep it goes

Formalizes causal questions through notation, probabilities, and expectations, then connects them to statistical estimation.

Examples

Uses causal MNIST questions about writer type, digit images, stroke thickness, and stroke curviness.

What you can do after

Evaluate/understand causal questions by defining targets, writing probability or expectation expressions, and selecting statistical analyses.

How it connects

Connects causal discovery, causal effects, causal decision-making, intervention prediction, counterfactual reasoning, and statistical inference.

liveBookmanning.com

Read Causal AI on liveBook Get the book at manning.com

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.