Learning to Estimate Without Bias

The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in models. In this paper, we take first step towards extending result to non-linear settings via deep learning with bias constraints. classical approach designing MVUEs through maximum likelihood (MLE) which often involves real-time computationally challenging optimizations. On other hand, methods allow for estimators fixed computational complexity. Learning based perform optimally on average respect their training set but may suffer from significant parameters. To avoid this, propose add simple constraint loss function, resulting an refer as Bias Constrained Estimator (BCE). We prove yields asymptotic behave similarly MLEs and asymptotically attain Cramer Rao bound. demonstrate advantages of our context signal noise ratio well covariance estimation. A second motivation BCE applications where multiple estimates same unknown are averaged improved performance. Examples include distributed sensor networks data augmentation test-time. such applications, show leads consistent estimators.