Backpropogation & Effect Adjustments

Before we start the back-propogation process, we have already successfully completed these two :

1. FCI based Causal Discovery based on the Causal Graph
2. Ridge Regression based Direct & Nested Direct effect estimation (A detailed view of this approach can be seen here )

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Effect Adjustments - Getting to Indirect & Total Effects from Direct Effects

To explain how the adjustment of contributions happens, let us take a simple example and go through the various stages

Stage 1 - We start with a DAG, backed by domain knowledge. Let us assume that the DAG looks like this :

Stage 2 - Apply Causal Discovery on this and we get to know the strength of these relationships

[Refer this page to know about the algorithm ]

Step 3 - Get the direct effect and contribution from the ML based process based on ridge regression

Step 4 - Run separate ridge regression approaches to explain the change in mediator variables as a function of its drivers

This gives us the nested direct contribution of "Drivers" to "Mediators"

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The True Contribution with Back-propagation

True contribution is the sum of Direct & Indirect Contributions, also know as the Total Effect.

• For Drivers, Total Effect = Direct Effect + Indirect Effects
• For Mediator variables, Total Effect = Direct Effect - (Sum of Indirect Effects through them)

This way we penalise the mediator and distribute the Effect (which is the incremental contribution) to the true causal drivers

Example

Next let us understand the core ML algorithm that powers this inference. It is detailed here