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Our implementation of chirho.robust.ops.influence_fn estimates the first-order efficient influence function, but there are some settings where computing higher-order influence functions may enable additional bias correction (e.g. https://arxiv.org/abs/0805.3040 or https://arxiv.org/abs/2305.04116 ).
As with ordinary derivatives, the discussion in "Higher Order Tangent Spaces and Influence Functions" suggests it should be possible to compute higher-order influence functions and correction terms by applying a first-order influence estimator to itself recursively:
This recursion should not be difficult to implement using our existing machinery, although nesting our naive Monte Carlo gradient estimators may not be computationally feasible beyond order 4 or so.
Our implementation of
chirho.robust.ops.influence_fn
estimates the first-order efficient influence function, but there are some settings where computing higher-order influence functions may enable additional bias correction (e.g. https://arxiv.org/abs/0805.3040 or https://arxiv.org/abs/2305.04116 ).As with ordinary derivatives, the discussion in "Higher Order Tangent Spaces and Influence Functions" suggests it should be possible to compute higher-order influence functions and correction terms by applying a first-order influence estimator to itself recursively:
This recursion should not be difficult to implement using our existing machinery, although nesting our naive Monte Carlo gradient estimators may not be computationally feasible beyond order 4 or so.
Tasks:
influence_fn
to better support self-composition Make influence_fn a higher-order Functional #492The text was updated successfully, but these errors were encountered: