We establish new generalisation bounds for multiclass classification by abstracting to a more general setting of discretised error types. Extending the PAC-Bayes theory, we are hence able to provide fine-grained bounds on performance for multiclass classification, as well as applications to other learning problems including discretisation of regression losses. Tractable training objectives are derived from the bounds. The bounds are uniform over all weightings of the discretised error types and thus can be used to bound weightings not foreseen at training, including the full confusion matrix in the multiclass classification case.
翻译:我们通过抽取到更笼统的离散错误类型设置,为多级分类建立了新的通用界限。 扩展了PAC- Bayes理论,因此,我们可以提供细微的界限,说明多级分类的性能,以及适用于包括回归损失分解在内的其他学习问题。 易变培训目标来自这些界限。 与离散错误类型所有加权一致,因此可用于约束培训中未预见到的加权,包括多级分类案件中的完全混乱矩阵。