AXIL: Exact Instance Attribution for Gradient Boosting

[2301.01864] AXIL: Exact Instance Attribution for Gradient Boosting Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2301.01864 (cs) [Submitted on 5 Jan 2023 ( v1 ), last revised 10 Apr 2026 (this version, v2)] Title: AXIL: Exact Instance Attribution for Gradient Boosting Authors: Paul Geertsema , Helen Lu View a PDF of the paper titled AXIL: Exact Instance Attribution for Gradient Boosting, by Paul Geertsema and Helen Lu View PDF HTML (experimental) Abstract: We derive an exact, prediction-specific instance-attribution method for fitted gradient boosting machines (GBMs) trained with squared-error loss, with the learned tree structure held fixed. Each prediction can be written as a weighted sum of training targets, with coefficients determined only by the fitted tree structure and learning rate. These coefficients are exact instance attributions, or AXIL weights. Our main algorithmic contribution is a matrix-free backward operator that computes one AXIL attribution vector in O(TN) time, or S vectors in O(TNS), without materialising the full N x N matrix. This extends to out-of-sample predictions and makes exact instance attribution practical for large datasets. AXIL yields exact fixed-structure sensitivity by construction in target-perturbation tests, where competing GBM-specific attribution methods (BoostIn, TREX, and LeafInfluence) generally fail. In retraining-based faithfulness tests on 20 regression datasets, AXIL achieves the highest faithfulness score on 14 datasets and statistically ties for the best on 4 others, while also running substantially faster than the competing methods. We also show that the AXIL weight matrix is the globally constant special case of a target-response Jacobian that provides first-order instance attribution for any differentiable learner via implicit differentiation, placing the exact decomposition inside a broader framework. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2301.01864 [cs.LG] (or arXiv:2301.01864v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2301.01864 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Paul Geertsema [ view email ] [v1] Thu, 5 Jan 2023 01:03:17 UTC (167 KB) [v2] Fri, 10 Apr 2026 12:13:40 UTC (609 KB) Full-text links: Access Paper: View a PDF of the paper titled AXIL: Exact Instance Attribution for Gradient Boosting, by Paul Geertsema and Helen Lu View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2023-01 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• dattri-LLM: A Unified and Efficient Library for Training Data Attribution at LLM Scale#1143368
• Spectrally Deconfounded Gradient Boosting#361461
• Don't Drop Dropout: Optimizing Layer Sparsity for Efficient LLM Training and Inference#660858
• Explainable Token-level Noise Filtering for LLM Fine-tuning Datasets#986202
• Probabilistic scoring lists for interpretable machine learning#164141