弱矩条件下的误差估计

Error estimation under weak moment condition

研究了指数损失函数的学习问题。利用相关不等式及其性质,刻画了点态样本的过度泛化误差与预测误差之间的关系。不仅将矩条件弱化到阶1+α,而且得到一个关于指数损失函数的比较定理,为进一步研究经验风险最小算法的收敛率或更复杂的函数空的正则化学习提供必要的理论准备。

The learning problem of exponential cost function is studied in the paper.The relationship between excess generalization error and prediction error of pointwise samples is characterized by using related inequalities and their properties.It not only weakens the moment condition to the order of 1+α,but also obtains a comparison theorem about exponential cost function,which provides necessary theoretical preparation for further study of convergence rate of empirical risk minimization algorithm or regularization learning of more complex function spaces.