# Optimal Sample Selection Through Uncertainty Estimation and Its Application in Deep Learning

arXiv: https://arxiv.org/abs/2309.02476 · HTML: https://mlsanity.com/paper/2309.02476/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 61 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Learning Loss for Active Learning](https://mlsanity.com/paper/1905.03677/) (2019)
- [Variational Adversarial Active Learning](https://mlsanity.com/paper/1904.00370/) (2019)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Task-Aware Variational Adversarial Active Learning](https://mlsanity.com/paper/2002.04709/) (2020)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [Stochastic Linear Bandits Robust to Adversarial Attacks](https://mlsanity.com/paper/2007.03285/) (2020)
- [Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2205.06811/) (2022)
- [Model Agnostic Sample Reweighting for Out-of-Distribution Learning](https://mlsanity.com/paper/2301.09819/) (2023)
- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Training Gaussian Mixture Models at Scale via Coresets](https://mlsanity.com/paper/1703.08110/) (2017)
- [Corruption-Robust Algorithms with Uncertainty Weighting for Nonlinear Contextual Bandits and Markov Decision Processes](https://mlsanity.com/paper/2212.05949/) (2022)
- [Optimal Subsampling for Large Sample Logistic Regression](https://mlsanity.com/paper/1702.01166/) (2017)
- [Probabilistic Bilevel Coreset Selection](https://mlsanity.com/paper/2301.09880/) (2023)
- [Optimal subsampling for quantile regression in big data](https://mlsanity.com/paper/2001.10168/) (2020)
- [More Efficient Estimation for Logistic Regression with Optimal Subsample](https://mlsanity.com/paper/1802.02698/) (2018)
- [Local Uncertainty Sampling for Large-Scale Multi-Class Logistic Regression](https://mlsanity.com/paper/1604.08098/) (2016)
- [Leveraging Importance Weights in Subset Selection](https://mlsanity.com/paper/2301.12052/) (2023)

## Built on by (most cited first, 4 of 4)

- [Refined Coreset Selection: Towards Minimal Coreset Size under Model Performance Constraints](https://mlsanity.com/paper/2311.08675/) (2023)
- [Model Performance-Guided Evaluation Data Selection for Effective Prompt Optimization](https://mlsanity.com/paper/2505.10736/) (2025)
- [Daunce: Data Attribution through Uncertainty Estimation](https://mlsanity.com/paper/2505.23223/) (2025)
- [Are Candidate Models Really Needed for Active Learning?](https://mlsanity.com/paper/2605.14689/) (2026)

## Abstract (arXiv)

Modern deep learning heavily relies on large labeled datasets, which often comse with high costs in terms of both manual labeling and computational resources. To mitigate these challenges, researchers have explored the use of informative subset selection techniques, including coreset selection and active learning. Specifically, coreset selection involves sampling data with both input (bx) and output (by), active learning focuses solely on the input data (bx). In this study, we present a theoretically optimal solution for addressing both coreset selection and active learning within the context of linear softmax regression. Our proposed method, COPS (unCertainty based OPtimal Sub-sampling), is designed to minimize the expected loss of a model trained on subsampled data. Unlike existing approaches that rely on explicit calculations of the inverse covariance matrix, which are not easily applicable to deep learning scenarios, COPS leverages the model's logits to estimate the sampling ratio. This sampling ratio is closely associated with model uncertainty and can be effectively applied to deep learning tasks. Furthermore, we address the challenge of model sensitivity to misspecification by incorporating a down-weighting approach for low-density samples, drawing inspiration from previous works. To assess the effectiveness of our proposed method, we conducted extensive empirical experiments using deep neural networks on benchmark datasets. The results consistently showcase the superior performance of COPS compared to baseline methods, reaffirming its efficacy.