Why LASSO, Ridge Regression, and EN: Explanation Based on Soft Computing

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 {\it 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, ridge regression method, when we bound the sum of the squares, and a EN method in which these two approaches are combined. In this paper, we explain the empirical success of these methods by showing that these methods can be naturally derived from soft computing ideas