Publication Date



Technical Report: UTEP-CS-19-72


In many practical situations, observations and measurement results are consistent with many different models -- i.e., the corresponding problem is ill-posed. In such situations, a reasonable idea is to take into account that the values of the corresponding parameters should not be too large; this idea is known as regularization. Several different regularization techniques have been proposed; empirically the most successful are LASSO method, when we bound the sum of absolute values of the parameters, and EN and CLOT methods in which this sum is combined with the sum of the squares. In this paper, we explain the empirical success of these methods by showing that they are the only ones which are invariant with respect to natural transformations -- like scaling which corresponds to selecting a different measuring unit.