Stein-Rule Shrinkage for Stochastic Gradient Estimation in High Dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| author | Arashi, M. Amintoosi, M. |
| author_facet | Arashi, M. Amintoosi, M. |
| contents | Stochastic gradient methods are central to large-scale learning, but they treat mini-batch gradients as unbiased estimators, which classical decision theory shows are inadmissible in high dimensions. We formulate gradient computation as a high-dimensional estimation problem and introduce a framework based on Stein-rule shrinkage. We construct a gradient estimator that adaptively contracts noisy mini-batch gradients toward a stable estimator derived from historical momentum. The shrinkage intensity is determined in a data-driven manner using an online estimate of gradient noise variance, leveraging statistics from adaptive optimizers. Under a Gaussian noise model, we show our estimator uniformly dominates the standard stochastic gradient under squared error loss and is minimax-optimal. We incorporate this into the Adam optimizer, yielding SR-Adam, a practical algorithm with negligible computational cost. Empirical evaluations on CIFAR10 and CIFAR100 across multiple levels of input noise show consistent improvements over Adam in the large-batch regime. Ablation studies indicate that gains arise primarily from selectively applying shrinkage to high-dimensional convolutional layers, while indiscriminate shrinkage across all parameters degrades performance. These results illustrate that classical shrinkage principles provide a principled approach to improving stochastic gradient estimation in deep learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01777 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stein-Rule Shrinkage for Stochastic Gradient Estimation in High Dimensions Arashi, M. Amintoosi, M. Machine Learning Artificial Intelligence Statistics Theory Stochastic gradient methods are central to large-scale learning, but they treat mini-batch gradients as unbiased estimators, which classical decision theory shows are inadmissible in high dimensions. We formulate gradient computation as a high-dimensional estimation problem and introduce a framework based on Stein-rule shrinkage. We construct a gradient estimator that adaptively contracts noisy mini-batch gradients toward a stable estimator derived from historical momentum. The shrinkage intensity is determined in a data-driven manner using an online estimate of gradient noise variance, leveraging statistics from adaptive optimizers. Under a Gaussian noise model, we show our estimator uniformly dominates the standard stochastic gradient under squared error loss and is minimax-optimal. We incorporate this into the Adam optimizer, yielding SR-Adam, a practical algorithm with negligible computational cost. Empirical evaluations on CIFAR10 and CIFAR100 across multiple levels of input noise show consistent improvements over Adam in the large-batch regime. Ablation studies indicate that gains arise primarily from selectively applying shrinkage to high-dimensional convolutional layers, while indiscriminate shrinkage across all parameters degrades performance. These results illustrate that classical shrinkage principles provide a principled approach to improving stochastic gradient estimation in deep learning. |
| title | Stein-Rule Shrinkage for Stochastic Gradient Estimation in High Dimensions |
| topic | Machine Learning Artificial Intelligence Statistics Theory |
| url | https://arxiv.org/abs/2602.01777 |