Estimation Under Model Misspecification With Fake Features

We consider estimation under model misspecification where there is a mismatch between the underlying system, which generates data, and used during estimation. propose framework enables joint treatment of types having fake features as well incorrect covariance assumptions on unknowns noise. present decomposition output error into components that relate to different subsets parameters corresponding underlying, missing features. Here, are included in but not system. Under this framework, we characterize performance reveal trade-offs number samples, features, possibly noise level assumption. In contrast existing work focusing or central component our framework. Our results show can significantly improve performance, even though they correlated with particular, be decreased by including more model, point overparametrized, i.e., contains than observations.