Learning Causal Models from Conditional Moment Restrictions by Importance Weighting
International Conference on Learning Representations (ICLR), 2022. Spotlight (top 4%, 176/3391).
[OpenReview][arXiv][Slides][Poster]
- conditional moment restrictions
- instrumental variables
- density ratio
- nonparametric estimation
In one sentence. Conditional moment restrictions are converted into unconditional ones by importance weighting with a conditional density ratio estimator, which makes flexible models — including neural networks — usable for nonparametric instrumental variable problems.
Why conditional restrictions are hard
Many causal models are defined by a moment condition that must hold conditional on an instrument or a covariate, rather than on average. Unconditional moment restrictions can be handled by standard GMM-style machinery; conditional ones cannot, because a single conditional restriction is really a continuum of restrictions. In high dimensions this becomes a serious obstacle, and the usual workarounds — sieves, kernel weighting, adversarial formulations — each carry their own tuning burden.
The transformation
The paper transforms conditional moment restrictions into unconditional ones by importance weighting, using an estimator of the conditional density ratio as the weight. Once the problem is unconditional, the nonparametric function defined by the restriction can be estimated by ordinary risk minimization, and the model class is unconstrained: neural networks and other flexible learners can be plugged in directly.
Guarantees
The estimation error is analyzed to give theoretical support for the transformation, and experiments confirm that the approach behaves as the analysis predicts. The framework is general, applying to a wide range of methods rather than to one estimator.