Deterministic Bounds on Accuracy and Stability of Metric-Space Regression and Classification

Data-driven approaches often face ambiguity in datasets due to sensor or target noise, insufficient information, and noise in the input data. While best-fit machine learning methods can accommodate such noise through uncertainty estimates, they are prone to overfitting and it is challenging to quantify ambiguity of the relation between inputs and targets. We introduce a geometric framework that quantifies this ambiguity through the average kernel size, computed with data-dependent, i.e. model-independent, feasible sets derived from worst-case input and target noise. The framework provides computable, deterministic, non-asymptotic bounds on the best achievable empirical error and accuracy ...

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