# Statistical and Computational Guarantees for Influence Diagnostics

arXiv: https://arxiv.org/abs/2212.04014 · HTML: https://mlsanity.com/paper/2212.04014/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 57 references that are in the map.
- First posted on arXiv 8 Dec 2022.

## Builds on (most cited first, 18 of 18)

- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [Zero-Shot Relation Extraction via Reading Comprehension](https://mlsanity.com/paper/1706.04115/) (2017)
- [Katyusha: The First Direct Acceleration of Stochastic Gradient Methods](https://mlsanity.com/paper/1603.05953/) (2016)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Variance Reduced Stochastic Gradient Descent with Neighbors](https://mlsanity.com/paper/1506.03662/) (2015)
- [Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice](https://mlsanity.com/paper/1712.05654/) (2017)
- [Finite-sample analysis of M-estimators using self-concordance](https://mlsanity.com/paper/1810.06838/) (2018)
- [An Automatic Finite-Sample Robustness Metric: When Can Dropping a Little Data Make a Big Difference?](https://mlsanity.com/paper/2011.14999/) (2020)
- [A Markov Chain Theory Approach to Characterizing the Minimax Optimality of Stochastic Gradient Descent (for Least Squares)](https://mlsanity.com/paper/1710.09430/) (2017)
- [Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation](https://mlsanity.com/paper/2201.00508/) (2022)
- [Small steps and giant leaps: Minimal Newton solvers for Deep Learning](https://mlsanity.com/paper/1805.08095/) (2018)
- [The Influence Function of Graphical Lasso Estimators](https://mlsanity.com/paper/2209.07374/) (2022)

## Built on by (most cited first, 1 of 1)

- [Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics](https://mlsanity.com/paper/2607.09250/) (2026)

## Abstract (arXiv)

Influence diagnostics such as influence functions and approximate maximum influence perturbations are popular in machine learning and in AI domain applications. Influence diagnostics are powerful statistical tools to identify influential datapoints or subsets of datapoints. We establish finite-sample statistical bounds, as well as computational complexity bounds, for influence functions and approximate maximum influence perturbations using efficient inverse-Hessian-vector product implementations. We illustrate our results with generalized linear models and large attention based models on synthetic and real data.