On partially blind learning complexity

We call a learning environment partially blind when there is an admixture o f supervised and unsupervised (or blind) learning. Such situations typically arise in practice when supervised training data labelled by a teacher are scarce or expensive and are supplemented by inexpensive unlabelled (or blind) data available in relative profusion. Vapnik-eervonenkis theory can be deployed in such settings to quantify the relative worth o f supervision (and the lack thereof) in learning. We illustrate the nature o f the tradeo s possible in a simple setting o f hyperplane decision functions and make explicit the role o f dimensionality and side-information in these tradeo s in the context o f d-variate Gaussian mixtures.