Extended Linear Models with Gaussian Prior on the Parameters and Adaptive Expansion Vectors

We present an approximate Bayesian method for regression and classification with models linear in the parameters. Similar to the Relevance Vector Machine (RVM), each parameter is associated with an expansion vector. Unlike the RVM, the number of expansion vectors is specified beforehand. We assume an overall Gaussian prior on the parameters and find, with a gradient based process, the expansion vectors that (locally) maximize the evidence. This approach has lower computational demands than the RVM, and has the advantage that the vectors do not necessarily belong to the training set. Therefore, in principle, better vectors can be found. Furthermore, other hyperparameters can be learned in the same smooth joint optimization. Experimental results show that the freedom of the expansion vectors to be located away from the training data causes overfitting problems. These problems are alleviated by including a hyperprior that penalizes expansion vectors located far away from the input data.