Семинар HDI Lab: Inference in Error-in-Operator model.

We consider the problem of recovering the source signal \( x \) from the noise observation \( Y \) given by the equation \( Y = A x + \epsilon \) in the situation when the operator \( A \) is not precisely known. Instead, a pilot estimate \( \hat{A} \} is available. 

The study is motivated by Hoffmann & Reiss [2008] and Trabs [2018] and by recent results on high dimensional regression with random design; see e.g. [Tsigler and Bartlett, 2020] and [Cheng and Montanari, 2022] among many others.

New approach is suggested which allows to obtain finite sample nearly sharp accuracy guarantees and incorporate the smoothness of the signal \( x \) and the operator \( A \) in a rather general form.