Stability Of Causal Identification From The Perspective Of Condition Numbers
summary
The work studies numerical and model robustness of causal identification by treating the symbolic output of the ID algorithm as a function of the observed distribution and measuring its condition number. It proves upper bounds when each C-component is small, shows a linear-program/duality expression for the condition number, and exhibits equivalent identification formulas with dramatically different stability (one constant vs another growing like sqrt(n)). Results let one quantify loss of precision and sensitivity to weak hidden-edge perturbations.
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chapters (16)
- 0:00Intro
- 0:40Causal identification: Experimental intervention
- 2:06Semi-Markovian models
- 2:45Interventions without experiments
- 4:11Causal identification: The problem
- 6:12Causal identification: Robustness
- 8:06Condition number: a classical measure of stability
- 11:03Condition number: model stability
- 11:25Approximate causal identification through stability
- 14:06A quiz
- 15:13Results: Instance-specific condition number bounds
- 17:19Results: Tools for instance-specific condition number bounds
- 19:31Results: some intrigue
- 24:38Recap and future directions
- 26:27A linear program for the condition number
- 27:41The condition number calculus
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