# Generalized Low-Rank Update: Model Parameter Bounds for Low-Rank Training Data Modifications

arXiv: https://arxiv.org/abs/2306.12670 · HTML: https://mlsanity.com/paper/2306.12670/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 22 Jun 2023.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [Incremental Gradient, Subgradient, and Proximal Methods for Convex Optimization: A Survey](https://mlsanity.com/paper/1507.01030/) (2015)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Simultaneous Safe Screening of Features and Samples in Doubly Sparse Modeling](https://mlsanity.com/paper/1602.02485/) (2016)
- [GAP Safe screening rules for sparse multi-task and multi-class models](https://mlsanity.com/paper/1506.03736/) (2015)
- [Screening Tests for Lasso Problems](https://mlsanity.com/paper/1405.4897/) (2014)
- [A Safe Screening Rule for Sparse Logistic Regression](https://mlsanity.com/paper/1307.4145/) (2013)
- [Safe Pattern Pruning: An Efficient Approach for Predictive Pattern Mining](https://mlsanity.com/paper/1602.04548/) (2016)
- [Safe Screening With Variational Inequalities and Its Application to LASSO](https://mlsanity.com/paper/1307.7577/) (2013)
- [Scaling SVM and Least Absolute Deviations via Exact Data Reduction](https://mlsanity.com/paper/1310.7048/) (2013)
- [Quick sensitivity analysis for incremental data modification and its application to leave-one-out CV in linear classification problems](https://mlsanity.com/paper/1504.02870/) (2015)
- [Regularization Path of Cross-Validation Error Lower Bounds](https://mlsanity.com/paper/1502.02344/) (2015)

## Built on by (most cited first, 3 of 3)

- [Distributionally Robust Coreset Selection under Covariate Shift](https://mlsanity.com/paper/2501.14253/) (2025)
- [Generalized Kernel Inducing Points by Duality Gap for Dataset Distillation](https://mlsanity.com/paper/2502.12607/) (2025)
- [Obliviate: Efficient Unlearning in Recommender Systems](https://mlsanity.com/paper/2607.22665/) (2026)

## Abstract (arXiv)

In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model selection, such as cross-validation (CV) and feature selection. Among the class of ML methods known as linear estimators, there exists an efficient model update framework called the low-rank update that can effectively handle changes in a small number of rows and columns within the data matrix. However, for ML methods beyond linear estimators, there is currently no comprehensive framework available to obtain knowledge about the updated solution within a specific computational complexity. In light of this, our study introduces a method called the Generalized Low-Rank Update (GLRU) which extends the low-rank update framework of linear estimators to ML methods formulated as a certain class of regularized empirical risk minimization, including commonly used methods such as SVM and logistic regression. The proposed GLRU method not only expands the range of its applicability but also provides information about the updated solutions with a computational complexity proportional to the amount of dataset changes. To demonstrate the effectiveness of the GLRU method, we conduct experiments showcasing its efficiency in performing cross-validation and feature selection compared to other baseline methods.