Shape Parameter Estimation

Performance of machine learning approaches depends strongly on the choice of misfit penalty, and correct choice of penalty parameters, such as the threshold of the Huber function. These parameters are typically chosen using expert knowledge, cross-validation, or black-box optimization, which are time consuming for large-scale applications. We present a principled, data-driven approach to simultaneously learn the model pa- rameters and the misfit penalty parameters. We discuss theoretical properties of these joint inference problems, and develop algorithms for their solution. We show synthetic examples of automatic parameter tuning for piecewise linear-quadratic (PLQ) penalties, and use the approach to develop a self-tuning robust PCA formulation for background separation.