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How can we explain the predictions of a black-box model? In this paper, we use influence functions -- a classic technique from robust statistics -- to trace a model's prediction through the learning algorithm and back to its training data,…

Machine Learning · Statistics 2021-01-01 Pang Wei Koh , Percy Liang

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,…

Machine Learning · Computer Science 2019-11-22 Pang Wei Koh , Kai-Siang Ang , Hubert H. K. Teo , Percy Liang

Influence functions (IFs) elucidate how training data changes model behavior. However, the increasing size and non-convexity in large-scale models make IFs inaccurate. We suspect that the fragility comes from the first-order approximation…

Machine Learning · Computer Science 2024-05-07 Hyeonsu Lyu , Jonggyu Jang , Sehyun Ryu , Hyun Jong Yang

A critical aspect of analyzing and improving modern machine learning systems lies in understanding how individual training examples influence a model's predictive behavior. Estimating this influence enables critical applications, including…

Machine Learning · Computer Science 2025-10-15 Narine Kokhlikyan , Kamalika Chaudhuri , Saeed Mahloujifar

How can we explain the influence of training data on black-box models? Influence functions (IFs) offer a post-hoc solution by utilizing gradients and Hessians. However, computing the Hessian for an entire dataset is resource-intensive,…

Machine Learning · Computer Science 2025-11-03 Jungyeon Koh , Hyeonsu Lyu , Jonggyu Jang , Hyun Jong Yang

As machine learning is increasingly deployed in the real world, it is paramount that we develop the tools necessary to analyze the decision-making of the models we train and deploy to end-users. Recently, researchers have shown that…

Machine Learning · Computer Science 2022-05-05 Andrew Silva , Rohit Chopra , Matthew Gombolay

Natural policy gradient methods are popular reinforcement learning methods that improve the stability of policy gradient methods by utilizing second-order approximations to precondition the gradient with the inverse of the…

Machine Learning · Computer Science 2022-10-12 Brennan Gebotys , Alexander Wong , David A. Clausi

The goal of data attribution is to trace the model's predictions through the learning algorithm and back to its training data. thereby identifying the most influential training samples and understanding how the model's behavior leads to…

Machine Learning · Computer Science 2025-08-12 Hongbo Zhu , Angelo Cangelosi

Many language tasks (e.g., Named Entity Recognition, Part-of-Speech tagging, and Semantic Role Labeling) are naturally framed as sequence tagging problems. However, there has been comparatively little work on interpretability methods for…

Computation and Language · Computer Science 2022-10-26 Sarthak Jain , Varun Manjunatha , Byron C. Wallace , Ani Nenkova

Machine learning systems such as large scale recommendation systems or natural language processing systems are usually trained on billions of training points and are associated with hundreds of billions or trillions of parameters. Improving…

Machine Learning · Computer Science 2023-05-26 Michael Kounavis , Ousmane Dia , Ilqar Ramazanli

Data-trained predictive models see widespread use, but for the most part they are used as black boxes which output a prediction or score. It is therefore hard to acquire a deeper understanding of model behavior, and in particular how…

Large-scale black-box models have become ubiquitous across numerous applications. Understanding the influence of individual training data sources on predictions made by these models is crucial for improving their trustworthiness. Current…

Machine Learning · Computer Science 2024-06-21 Myeongseob Ko , Feiyang Kang , Weiyan Shi , Ming Jin , Zhou Yu , Ruoxi Jia

Model selection requires repeatedly evaluating models on a given dataset and measuring their relative performances. In modern applications of machine learning, the models being considered are increasingly more expensive to evaluate and the…

Machine Learning · Computer Science 2020-10-21 Anant Raj , Cameron Musco , Lester Mackey , Nicolo Fusi

Data plays a pivotal role in the groundbreaking advancements in artificial intelligence. The quantitative analysis of data significantly contributes to model training, enhancing both the efficiency and quality of data utilization. However,…

Machine Learning · Computer Science 2025-08-21 Haoru Tan , Sitong Wu , Xiuzhe Wu , Wang Wang , Bo Zhao , Zeke Xie , Gui-Song Xia , Xiaojuan Qi

Influence functions estimate effect of individual data points on predictions of the model on test data and were adapted to deep learning in Koh and Liang [2017]. They have been used for detecting data poisoning, detecting helpful and…

Machine Learning · Computer Science 2022-10-04 Nikunj Saunshi , Arushi Gupta , Mark Braverman , Sanjeev Arora

Influence functions approximate how removing a training example changes a quantity of interest, called the target function, such as a held-out loss. To estimate the influence of a group of examples, the standard practice is to sum the…

Machine Learning · Computer Science 2026-05-18 Jaeseung Heo , Kyeongheung Yun , Youngbin Choi , Sehyun Hwang , Jungseul Ok , Dongwoo Kim

Good models require good training data. For overparameterized deep models, the causal relationship between training data and model predictions is increasingly opaque and poorly understood. Influence analysis partially demystifies training's…

Machine Learning · Computer Science 2024-04-02 Zayd Hammoudeh , Daniel Lowd

Influence functions approximate the effect of training samples in test-time predictions and have a wide variety of applications in machine learning interpretability and uncertainty estimation. A commonly-used (first-order) influence…

Machine Learning · Computer Science 2021-02-12 Samyadeep Basu , Philip Pope , Soheil Feizi

A variety of fairness constraints have been proposed in the literature to mitigate group-level statistical bias. Their impacts have been largely evaluated for different groups of populations corresponding to a set of sensitive attributes,…

Machine Learning · Computer Science 2022-07-01 Jialu Wang , Xin Eric Wang , Yang Liu

We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…

Statistics Theory · Mathematics 2013-04-29 Edith Gabriel
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