On the Accuracy of Influence Functions for Measuring Group Effects

By Pang Wei Koh, Kai-Siang Ang, Hubert Teo, Percy Liang. 2019

247 citations recorded by the source corpus.

Influence functions estimate the effect of removing a training point on a model without the need to retrain. They are based on a first-order Taylor approximation that is guaranteed to be accurate for sufficiently small changes to the model, and so are commonly used to study the effect of individual points in large datasets. However, we often want to study the effects of large groups of training points, e.g., to diagnose batch effects or apportion credit between different data sources. Removing such large groups can result in significant changes to the model. Are influence functions still accurate in this setting? In this paper, we find that across many different types of groups and for a range of real-world datasets, the predicted effect (using influence functions) of a group correlates surprisingly well with its actual effect, even if the absolute and relative errors are large. Our theoretical analysis shows that such strong correlation arises only under certain settings and need not hold in general, indicating that real-world datasets have particular properties that allow the influence approximation to be accurate.

Subfields: Computer Networks and Communications, General Social Sciences, Management Science and Operations Research

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Citations in the corpus

Causal Interpretability for Machine Learning - Problems, Methods and Evaluation (2020, background): “The same authors [51] also investigate the effect of removing large groups of training points in large datasets on the”
Counterfactual Memorization in Neural Language Models (2021, methodology): “Previous papers adopted it to analyze neural network predictions [Koh and Liang, 2017, Koh et al., 2019].”
Machine Unlearning of Features and Labels (2021, methodology): “Our approach is inspired by the concept of influence functions, a technique from robust statistics [39], that allows for estimating the influence of data on learning models [43, 44].”
Interpretable deep learning: interpretation, interpretability, trustworthiness, and beyond (2021, methodology): “Influence Functions and Variants Influence Functions [91], Group Influences [90], HYDRA [38]”
DataComp: In search of the next generation of multimodal datasets (2023, methodology): “[75] Pang Wei Koh, Kai-Siang Ang, Hubert Teo, and Percy S Liang.”
Large Language Model Unlearning (2023, background): “When it happens, LLM practitioners need a way of removing the old user data from the trained LLMs.”
Multi-Stage Influence Function (2020, background): “There is a series of work on influence functions, including investigating the influence of a group of data on the prediction [12], using influence functions to detect bias in word embeddings [2], and using it in preventing data poisoning attacks [24].”
Influence Functions in Deep Learning Are Fragile (2020, methodology): “The main idea used by [3, 4, 11] is to approximate θ {z} by the first-order Taylor series expansion around the optimal model parameters represented by θ∗, which leads to: θ {z} ≈ θ ∗ − H−1 θ∗ ∇θ`(hθ∗(z)), (3)”
TRAK: Attributing Model Behavior at Scale (2023, unknown): “In particular, the one-step Newton approximation (Pregibon, 1981; Wojnowicz et al., 2016; Rad & Maleki, 2018; Koh et al., 2019), which we present as a data attribution method τNS below, is a standard tool for analyzing and understanding logistic regression models in terms of their training data.”
Fast Yet Effective Machine Unlearning (2021, background): “Estimating the effect of a data sample or a class of data samples on the deep model parameters is a challenging problem [17, 27, 28].”
Interpretable Counterfactual Explanations Guided by Prototypes (2019, background): “Alterna-tively, we can also assess the impact of individual training data instances on a speciﬁc prediction by using in-ﬂuence functions (Koh and Liang 2017; Koh et al. 2019; Khanna et al. 2019).”
Datamodels: Predicting Predictions from Training Data (2022, background): “Such data counterfactuals can be helpful tools for finding brittle predictions (as in the previous section), estimating group influence (as done by (Koh et al., 2019) for linear models), and more broadly for understanding how training examples combine (through the lens of the model class) to…”