# Tutorial: Deriving The Efficient Influence Curve for Large Models

arXiv: https://arxiv.org/abs/1903.01706 · HTML: https://mlsanity.com/paper/1903.01706/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2019.

## Built on by (most cited first, 6 of 6)

- [Predicting Cellular Responses with Variational Causal Inference and Refined Relational Information](https://mlsanity.com/paper/2210.00116/) (2022)
- [Counterfactual Generative Modeling with Variational Causal Inference](https://mlsanity.com/paper/2410.12730/) (2024)
- [A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics](https://mlsanity.com/paper/2202.09096/) (2022)
- [Variational Causal Inference](https://mlsanity.com/paper/2209.05935/) (2022)
- [Doubly Robust Estimation of Direct and Indirect Quantile Treatment Effects with Machine Learning](https://mlsanity.com/paper/2307.01049/) (2023)
- [Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems](https://mlsanity.com/paper/2602.24131/) (2026)

## Abstract (arXiv)

This paper aims to provide a tutorial for upper level undergraduate and graduate students in statistics, biostatistics and epidemiology on deriving influence functions for non-parametric and semi-parametric models. The author will build on previously known efficiency theory and provide a useful identity and formulaic technique only relying on the basics of integration which, are self-contained in this tutorial and can be used in most any setting one might encounter in practice. The paper provides many examples of such derivations for well-known influence functions as well as for new parameters of interest. The influence function remains a central object for constructing efficient estimators for large models, such as the one-step estimator and the targeted maximum likelihood estimator. We will not touch upon these estimators at all but readers familiar with these estimators might find this tutorial of particular use.