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Support higher-order influence computation #480

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eb8680 opened this issue Jan 5, 2024 · 0 comments
Open
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Support higher-order influence computation #480

eb8680 opened this issue Jan 5, 2024 · 0 comments
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@eb8680
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eb8680 commented Jan 5, 2024

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:
image

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.

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