Interventional quantity

As explained in Causal Inference for Data Science

An interventional quantity is a probability or statistical quantity evaluated under a specified intervention rather than under natural assignment.

An interventional quantity estimates a probability or distribution under a specified change, asking what would happen if an action were imposed rather than merely observed. section 4.0

Conditional probabilities forecast outcomes from historical assignments; interventional quantities address different scenarios, such as giving the same treatment to everyone. They are especially useful when future assignments may differ from the past. section 4.0

Discounts, loyalty, and purchases

Suppose loyalty affects both discount assignment and purchases. For a fixed loyalty level, the intervened and observed distributions coincide: P(Purchase | do(discount), loyalty) = P(Purchase | discount, loyalty). A predictive model therefore matches the interventional quantity only when it includes all possible confounders. section 4.1.4

Figure 4.2 Loyal customers receive discounts, which at the same time affect purchases.

Use the causal diagram to trace how loyalty influences both discounts and purchases, creating the confounding that adjustment must address. section 4.1.4

Applying the adjustment formula

Use the adjustment-formula diagram to connect interventional quantities with conditional probabilities estimated by supervised learning. section 4.0

How Causal Inference for Data Science covers it

How deep it goes

Defines intervention-based probabilities and gives do-notation, stopping at confounder adjustment rather than developing identification theory.

Examples

Uses a discount-and-loyalty purchasing scenario, a kidney-stones treatment contrast, and causal diagrams for confounding and adjustment.

What it assumes

Assumes familiarity with conditional probabilities, interventions, confounders, and the adjustment formula.

What you can do after

Apply supervised learning to estimate conditional probabilities for the adjustment formula when many confounders must be handled.

How it connects

Connects conditional probability, supervised learning, causal inference, confounding, and the adjustment formula.

liveBookmanning.com

Read Causal Inference for Data Science on liveBook Get the book at manning.com

Related concepts

• language modelequivalent to · A language model is a computational model that represents patterns in linguistic tokens to estimate sequence probabilities and predict or generate language from context.
• interventional expectationincludes · An interventional expectation is the expected value of a quantity under an externally imposed intervention on one or more variables.

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