Bias Variance Decomposition

Definition

The bias-variance decomposition is a useful theoretical tool to understand the performance characteristics of a learning algorithm. The following discussion is restricted to the use of squared loss as the performance measure, although similar analyses have been undertaken for other loss functions. The case receiving most attention is the zero-one loss (i.e., classification problems), in which case the decomposition is nonunique and a topic of active research. See Domingos (1992) for details.

The decomposition allows us to see that the mean squared error of a model (generated by a particular learning algorithm) is in fact made up of two components. The bias component tells us how accurate the model is, on average across different possible training sets. The variance component tells us how sensitive the learning algorithm is to small changes in the training set (Fig. 1).

Bias Variance Decomposition, Fig. 1

The bias-variance decomposition is like trying to hit the bullseye on a...