The Variability of Model Specification

Abstract: It's regarded as an axiom that a good model is one that compromises between bias and variance. The bias is measured in training cost, while the variance of a (say, regression) model is measure by the cost associated with a validation set. If reducing bias is the goal, one will strive to fetch as complex a model as necessary, but complexity is invariably coupled with variance: greater complexity implies greater variance. In practice, driving training cost to near zero does not pose a fundamental problem; in fact, a sufficiently complex decision tree is perfectly capable of driving training cost to zero; however, the problem is often with controlling the model's variance. We investigate various regression model frameworks, including generalized linear models, Cox proportional hazard models, ARMA, and illustrate how misspecifying a model affects the variance.