# Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent

arXiv: https://arxiv.org/abs/1802.01737 · HTML: https://mlsanity.com/paper/1802.01737/

## Key facts

- Cited by 68 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2018.

## Built on by (most cited first, 30 of 68)

- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [GCR: Gradient Coreset Based Replay Buffer Selection For Continual Learning](https://mlsanity.com/paper/2111.11210/) (2021)
- [RETRIEVE: Coreset Selection for Efficient and Robust Semi-Supervised Learning](https://mlsanity.com/paper/2106.07760/) (2021)
- [Soft-Label Anonymous Gastric X-ray Image Distillation](https://mlsanity.com/paper/2104.02857/) (2021)
- [In Search of Lost Online Test-time Adaptation: A Survey](https://mlsanity.com/paper/2310.20199/) (2023)
- [Overview of Deep Learning-based CSI Feedback in Massive MIMO Systems](https://mlsanity.com/paper/2206.14383/) (2022)
- [Compressed Gastric Image Generation Based on Soft-Label Dataset Distillation for Medical Data Sharing](https://mlsanity.com/paper/2209.14635/) (2022)
- [Data curation via joint example selection further accelerates multimodal learning](https://mlsanity.com/paper/2406.17711/) (2024)
- [Grain: Improving Data Efficiency of Graph Neural Networks via Diversified Influence Maximization](https://mlsanity.com/paper/2108.00219/) (2021)
- [Bad Students Make Great Teachers: Active Learning Accelerates Large-Scale Visual Understanding](https://mlsanity.com/paper/2312.05328/) (2023)
- [AUTOMATA: Gradient Based Data Subset Selection for Compute-Efficient Hyper-parameter Tuning](https://mlsanity.com/paper/2203.08212/) (2022)
- [NLU on Data Diets: Dynamic Data Subset Selection for NLP Classification Tasks](https://mlsanity.com/paper/2306.03208/) (2023)
- [Unlocking the Potential of Federated Learning: The Symphony of Dataset Distillation via Deep Generative Latents](https://mlsanity.com/paper/2312.01537/) (2023)
- [Training Data Subset Selection for Regression with Controlled Generalization Error](https://mlsanity.com/paper/2106.12491/) (2021)
- [Surrogate Likelihoods for Variational Annealed Importance Sampling](https://mlsanity.com/paper/2112.12194/) (2021)
- [Provable Data Subset Selection For Efficient Neural Network Training](https://mlsanity.com/paper/2303.05151/) (2023)
- [Bayesian inference via sparse Hamiltonian flows](https://mlsanity.com/paper/2203.05723/) (2022)
- [ℓ_∞-Robustness and Beyond: Unleashing Efficient Adversarial Training](https://mlsanity.com/paper/2112.00378/) (2021)
- [On Divergence Measures for Bayesian Pseudocoresets](https://mlsanity.com/paper/2210.06205/) (2022)
- [Zero-Shot Coreset Selection via Iterative Subspace Sampling](https://mlsanity.com/paper/2411.15349/) (2024)
- [Bayesian Active Learning by Disagreements: A Geometric Perspective](https://mlsanity.com/paper/2105.02543/) (2021)
- [Fast Bayesian Coresets via Subsampling and Quasi-Newton Refinement](https://mlsanity.com/paper/2203.09675/) (2022)
- [Adversarial Coreset Selection for Efficient Robust Training](https://mlsanity.com/paper/2209.05785/) (2022)
- [ELIP: Enhanced Visual-Language Foundation Models for Image Retrieval](https://mlsanity.com/paper/2502.15682/) (2025)
- [Data Summarization via Bilevel Optimization](https://mlsanity.com/paper/2109.12534/) (2021)
- [Iterative Teaching by Data Hallucination](https://mlsanity.com/paper/2210.17467/) (2022)
- [Fair Wasserstein Coresets](https://mlsanity.com/paper/2311.05436/) (2023)
- [A Novel Sequential Coreset Method for Gradient Descent Algorithms](https://mlsanity.com/paper/2112.02504/) (2021)
- [Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2206.01162/) (2022)

## Abstract (arXiv)

Coherent uncertainty quantification is a key strength of Bayesian methods. But modern algorithms for approximate Bayesian posterior inference often sacrifice accurate posterior uncertainty estimation in the pursuit of scalability. This work shows that previous Bayesian coreset construction algorithms---which build a small, weighted subset of the data that approximates the full dataset---are no exception. We demonstrate that these algorithms scale the coreset log-likelihood suboptimally, resulting in underestimated posterior uncertainty. To address this shortcoming, we develop greedy iterative geodesic ascent (GIGA), a novel algorithm for Bayesian coreset construction that scales the coreset log-likelihood optimally. GIGA provides geometric decay in posterior approximation error as a function of coreset size, and maintains the fast running time of its predecessors. The paper concludes with validation of GIGA on both synthetic and real datasets, demonstrating that it reduces posterior approximation error by orders of magnitude compared with previous coreset constructions.