Input decay: simple and effective soft variable selection

To deal with the overfitting problems that occur when there are not enough examples compared to the number of input variables in supervised learning, traditional approaches are weight decay and greedy variable selection. An alternative that has recently started to attract attention is to keep all the variables but to put more emphasis on the “most useful” ones. We introduce a new regularization method called input decay that exerts more relative penalty on the parameters associated with the inputs that contribute less to the learned function. This method, like weight decay and variable selection, still requires to perform a kind of model selection. Successful comparative experiments with this new method were performed both on a simulated regression task and a real-world financial prediction task