Data-driven models routinely face ambiguous datasets, whether from sensor or target noise, insufficient information, or noise in the inputs. Best-fit machine learning methods often handle such ambiguity by modelling uncertainty, but the guarantees they offer are typically probabilistic. A new preprint on arXiv instead asks what can be guaranteed in the worst case, independent of distributional assumptions.
The paper, titled "Deterministic Bounds on Accuracy and Stability of Metric-Space Regression and Classification," introduces bounds that hold for both regression and classification when data live in a metric space. The key idea is to quantify how much accuracy and stability can degrade under adversarial or unknown noise, giving a deterministic alternative to uncertainty-based approaches.
These results are likely to be of interest for safety-critical applications where worst-case behaviour matters more than average-case performance. As with any preprint, the findings have not yet undergone peer review, and the abstract leaves the exact form of the bounds to the full paper.