# Representer Point Selection for Explaining Regularized High-dimensional Models

arXiv: https://arxiv.org/abs/2305.20002 · HTML: https://mlsanity.com/paper/2305.20002/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 64 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 29 of 29)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Explainable Recommendation: A Survey and New Perspectives](https://mlsanity.com/paper/1804.11192/) (2018)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [FastIF: Scalable Influence Functions for Efficient Model Interpretation and Debugging](https://mlsanity.com/paper/2012.15781/) (2020)
- [Multi-Interest Network with Dynamic Routing for Recommendation at Tmall](https://mlsanity.com/paper/1904.08030/) (2019)
- [SimpleX: A Simple and Strong Baseline for Collaborative Filtering](https://mlsanity.com/paper/2109.12613/) (2021)
- [Influence Function based Data Poisoning Attacks to Top-N Recommender Systems](https://mlsanity.com/paper/2002.08025/) (2020)
- [Interpreting Black Box Predictions using Fisher Kernels](https://mlsanity.com/paper/1810.10118/) (2018)
- [A representer theorem for deep neural networks](https://mlsanity.com/paper/1802.09210/) (2018)
- [HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks](https://mlsanity.com/paper/2102.02515/) (2021)
- [Simplify and Robustify Negative Sampling for Implicit Collaborative Filtering](https://mlsanity.com/paper/2009.03376/) (2020)
- [Identifying a Training-Set Attack's Target Using Renormalized Influence Estimation](https://mlsanity.com/paper/2201.10055/) (2022)
- [A representer theorem for deep kernel learning](https://mlsanity.com/paper/1709.10441/) (2017)
- [Nuclear Norm based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes](https://mlsanity.com/paper/1405.1207/) (2014)
- ["Influence Sketching": Finding Influential Samples In Large-Scale Regressions](https://mlsanity.com/paper/1611.05923/) (2016)
- [Adapting and Evaluating Influence-Estimation Methods for Gradient-Boosted Decision Trees](https://mlsanity.com/paper/2205.00359/) (2022)
- [Explaining Latent Factor Models for Recommendation with Influence Functions](https://mlsanity.com/paper/1811.08120/) (2018)
- [TracInAD: Measuring Influence for Anomaly Detection](https://mlsanity.com/paper/2205.01362/) (2022)

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

- [Interpretable Self-Supervised Learning via Representer Landmarks and Nystr"om Approximation](https://mlsanity.com/paper/2509.24467/) (2025)

## Abstract (arXiv)

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ℓ1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.