Simplifying debiased inference via automatic differentiation and probabilistic programming

Area of Science:

• Statistics
• Computer Science
• Machine Learning

Background:

• Constructing efficient estimators typically requires complex mathematical derivations, such as calculating the efficient influence function.
• This complexity limits the accessibility of advanced statistical estimation techniques to a broader audience.

Purpose of the Study:

• To introduce Dimple, an algorithm designed to simplify the construction of efficient estimators.
• To make efficient estimation more accessible by automating the derivation of necessary components.

Main Methods:

• Dimple takes computer code defining a parameter of interest and outputs an efficient estimator.
• It utilizes automatic differentiation applied to the statistical functional, avoiding manual derivation of the efficient influence function.
• The approach requires expressing the functional as a composition of primitives meeting a novel differentiability condition.

Main Results:

• Dimple successfully generates efficient estimators without requiring users to compute the efficient influence function.
• The algorithm identifies necessary nuisance parameters through the functional composition.
• A Python implementation demonstrates that Dimple enables efficient estimation with minimal code.

Conclusions:

• Dimple significantly simplifies the process of constructing efficient estimators.
• The algorithm broadens the accessibility of advanced statistical estimation techniques.
• Reusable software primitives enhance efficiency and applicability across diverse estimation problems.