Co-Validation: Using Model Disagreement on Unlabeled Data to Validate Classification Algorithms

Part of Advances in Neural Information Processing Systems 17 (NIPS 2004)

Bibtex Metadata Paper


Omid Madani, David Pennock, Gary Flake


In the context of binary classification, we define disagreement as a mea- sure of how often two independently-trained models differ in their clas- sification of unlabeled data. We explore the use of disagreement for error estimation and model selection. We call the procedure co-validation, since the two models effectively (in)validate one another by comparing results on unlabeled data, which we assume is relatively cheap and plen- tiful compared to labeled data. We show that per-instance disagreement is an unbiased estimate of the variance of error for that instance. We also show that disagreement provides a lower bound on the prediction (gen- eralization) error, and a tight upper bound on the "variance of prediction error", or the variance of the average error across instances, where vari- ance is measured across training sets. We present experimental results on several data sets exploring co-validation for error estimation and model selection. The procedure is especially effective in active learning set- tings, where training sets are not drawn at random and cross validation overestimates error.