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 )

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"

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