Non-asymptotic estimates of the minimal risk in statistical learning
In this paper we prove some concentration inequalities for two types of error probabilities in the Empirical Risk Principle (ERP) in statistical learning, which provide a lower bound and an upper bound for the minimal risk (in terms of the minimal empirical risk) with non-asymptotic high confidence. The usual boundedness condition of the empirical risk function is relaxed to the Gaussian or exponential integrability condition. The confidence of the lower bound of the minimal risk is shown to be independent of the number of training parameters and the dimension of the input vectors, allowing one to detect the deficiency of a learning machine efficiently; and the confidence of the upper bou...
| Authors | Liming Wu, Sen Yang |
|---|---|
| Primary category | cs.LG |
| Published | 22 June 2026 |
| Last updated at source | 22 June 2026 |
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