Scientists Propose Method for More Efficient Resource Use in Machine Learning
An international group of researchers, including mathematicians from the AI and Digital Science Institute at the HSE Faculty of Computer Science, has provided a theoretical justification for a simple and computationally efficient method of estimating uncertainty in Stochastic Gradient Descent (SGD). The paper has been published on the scientific preprint server arXiv.org and presented at AISTATS 2026.
Stochastic algorithms, including SGD, are widely used in optimisation and machine learning tasks. Because these algorithms incorporate randomness, such as randomly selected mini-batches of data, an important feature of their solutions is the confidence interval—the range within which the true solution is likely to lie. Traditional approaches to constructing such intervals rely on complex statistical estimations, particularly explicit estimates of the solution’s marginal covariance matrix. These methods can be computationally expensive and may still produce inaccurate uncertainty estimates.
A covariance matrix is a table that shows how several random variables, such as features or parameters, are related to one another and how they vary around their mean values.
An international team, including researchers from the AI and Digital Science Institute at the HSE Faculty of Computer Science, analysed an empirically popular approach to estimating confidence intervals for averaged SGD that does not require repeated model training or complex calculations. The authors demonstrated that this method accurately reproduces the distribution of the averaged SGD solution and does not require an explicit estimate of the marginal covariance matrix.
Marina Sheshukova
'Similar methods have already been used in practice and have often demonstrated better results than alternative approaches. We wanted to understand the reasons behind this empirical advantage and were able to provide a rigorous mathematical interpretation,' explained Marina Sheshukova, Junior Research Fellow of the International Laboratory of Stochastic Algorithms and High-Dimensional Inference at the HSE AI and Digital Science Institute.
This mathematical justification makes it possible to reassess simple empirical methods for estimating uncertainty in machine learning. Developers will be able to obtain reliable uncertainty estimates faster and with fewer computational resources. This is particularly important in fields where it is essential to know not only the prediction itself but also the level of confidence associated with it, such as medicine, finance, and autonomous systems.
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