Statistical estimation theory using perturbed optimization

The talk discusses estimation problem for complex high-dimensional models like Deep Neuronal Networks (DNN). The approach reduces the original problem to perturbed optimization. Under some mild conditions, we establish finite sample expansions for the loss of estimation and for the excess risk. This enables us to obtain sharp nonasymptotic risk bounds in terms of the so called efficient dimension of the problem. The results are specified to the case of nonlinear regression and DNN training.