Characterizations of an Empirical Influence Function for Detecting Influential Cases in Regression

By R. Dennis Cook, Sanford Weisberg. 1980

Subfields: Statistics and Probability, Causal Inference & Discovery

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

In Causal Inference & Discovery

Citations in the corpus

Understanding the Origins of Bias in Word Embeddings (2018, background): “For a more thorough treatment of the subject see [12, 5].”
Coresets via Bilevel Optimization for Continual Learning and Streaming (2020, background): “The empirical influence function, known from robust statistics [13], denotes the effect of a single sample on the estimator.”
Machine Unlearning (2019, background): “While research has attempted to trace a particular test-time prediction through the model’s architecture and back to its training data [28], [29], these techniques rely on influence functions, which involve expensive computations of secondorder derivatives of the model’s training algorithm.”
Incorporating Interpretability into Latent Factor Models via Fast Influence Analysis (2018, methodology): “Influence functions stemmed from robust statistics [12] and were recently adopted to understand black-box predictions [22].”
Explainable artificial intelligence (XAI) in deep learning-based medical image analysis (2021, methodology): “Since it is expensive to assess this by perturbation, they provided an efficient approximation using influence functions (Cook and Weisberg (1980)).”
xGEMs: Generating Examplars to Explain Black-Box Models (2018, background): “For example, Koh and Liang [25] use inﬂuence functions, motivated by robust statistics Cook and Weisberg [7] to determine importance of each training sample for model predictions.”
Multi-Stage Influence Function (2020, background): “To find the most influential training data responsible for a model’s prediction, the influence function was first introduced by [5].”
Less is More: Culling the Training Set to Improve Robustness of Deep Neural Networks (2018, methodology): “Influence functions is a technique from robust statistics to measure the estimator on the value of one of the points in the sample [5, 18].”
Cluster-robust inference: A guide to empirical practice (2022, background): “Another measure is the partial leverage of each cluster for the coefficient(s) of interest, which generalizes the observationlevel notion of partial leverage of Cook and Weisberg (1980). If x́j denotes the vector of residuals from regressing xj on all the other regressors, and x́gj is the subvector ”
Model Agnostic Supervised Local Explanations (2018, background): “The most general form of an example-based explanation is influence functions [6].”
Influence Functions in Deep Learning Are Fragile (2020, methodology): “In machine learning, influence functions [1, 2] can be used to estimate the change in model parameters when the empirical weight distribution of the training samples is perturbed by an infinitesimal amount.”
The Impact of Outliers on Cronbach’s Coefficient Alpha Estimate of Reliability: Ordinal/Rating Scale Item Responses (2010, background): “…been shown that outliers may distort the parameter estimation, such as mean, correlation, and regression parameters, and even a single outlier can severely bias the descriptive and inferential statistics (Blair & Higgins, 1980; Cook & Weisberg, 1980; Huber, 1981; Lind & Zumbo, 1993; Stevens, 1984).”
Interpreting Black Box Predictions using Fisher Kernels (2018, methodology): “Influence functions [5] have recently been proposed as a tool for interpreting model predictions [17].”
Post-hoc Interpretability for Neural NLP: A Survey (2021, methodology): “Influence functions is a classical technique from robust statistics [32]. we feel everything for these characters 0.02 -”
On Memorization in Probabilistic Deep Generative Models (2021, background): “The problem of memorization is also related to the concept of influence functions in statistics [38, 39].”
Interpretable Off-Policy Evaluation in Reinforcement Learning by Highlighting Influential Transitions (2020, methodology): “Finally, the notion of inﬂuence that we use throughout this work has a long history in statistics as a technique for evaluating the robustness of estimators (Cook & Weisberg, 1980).”
On Optimal Generalizability in Parametric Learning (2017, background): “This work is also related to the concept of influence functions [13], which has recently received renewed interest [14].”