# Automated Efficient Estimation using Monte Carlo Efficient Influence Functions

arXiv: https://arxiv.org/abs/2403.00158 · HTML: https://mlsanity.com/paper/2403.00158/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 75 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 30 of 36)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Knowledge Distillation as Semiparametric Inference](https://mlsanity.com/paper/2104.09732/) (2021)
- [Doubly Robust Self-Training](https://mlsanity.com/paper/2306.00265/) (2023)
- [ADEV: Sound Automatic Differentiation of Expected Values of Probabilistic Programs](https://mlsanity.com/paper/2212.06386/) (2022)
- [The Fundamental Limits of Structure-Agnostic Functional Estimation](https://mlsanity.com/paper/2305.04116/) (2023)
- [Higher Order Tangent Spaces and Influence Functions](https://mlsanity.com/paper/1502.00812/) (2015)
- [Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes](https://mlsanity.com/paper/2105.02088/) (2021)
- [Covariance Matrix Estimation under Total Positivity for Portfolio Selection](https://mlsanity.com/paper/1909.04222/) (2019)
- [Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation](https://mlsanity.com/paper/2106.11009/) (2021)
- [The Variational Predictive Natural Gradient](https://mlsanity.com/paper/1903.02984/) (2019)
- [Estimating covariance and precision matrices along subspaces](https://mlsanity.com/paper/1909.12218/) (2019)
- [Two-Stage TMLE to Reduce Bias and Improve Efficiency in Cluster Randomized Trials](https://mlsanity.com/paper/2106.15737/) (2021)
- [A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics](https://mlsanity.com/paper/2202.09096/) (2022)

## Built on by (most cited first, 4 of 4)

- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Debiasing Synthetic Data Generated by Deep Generative Models](https://mlsanity.com/paper/2411.04216/) (2024)
- [Causal identification with Y0](https://mlsanity.com/paper/2508.03167/) (2025)
- [Kernel Debiased Plug-in Estimation based on the Universal Least Favorable Submodel](https://mlsanity.com/paper/2603.08945/) (2026)

## Abstract (arXiv)

Many practical problems involve estimating low dimensional statistical quantities with high-dimensional models and datasets. Several approaches address these estimation tasks based on the theory of influence functions, such as debiased/double ML or targeted minimum loss estimation. This paper introduces textitMonte Carlo Efficient Influence Functions (MC-EIF), a fully automated technique for approximating efficient influence functions that integrates seamlessly with existing differentiable probabilistic programming systems. MC-EIF automates efficient statistical estimation for a broad class of models and target functionals that would previously require rigorous custom analysis. We prove that MC-EIF is consistent, and that estimators using MC-EIF achieve optimal √N convergence rates. We show empirically that estimators using MC-EIF are at parity with estimators using analytic EIFs. Finally, we demonstrate a novel capstone example using MC-EIF for optimal portfolio selection.