The informationtheoretic value of unlabeled data in semisupervised learning
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:23282336, 2019.
Abstract
We quantify the separation between the numbers of labeled examples required to learn in two settings: Settings with and without the knowledge of the distribution of the unlabeled data. More specifically, we prove a separation by $\Theta(\log n)$ multiplicative factor for the class of projections over the Boolean hypercube of dimension $n$. We prove that there is no separation for the class of all functions on domain of any size. Learning with the knowledge of the distribution (a.k.a. fixeddistribution learning) can be viewed as an idealized scenario of semisupervised learning where the number of unlabeled data points is so great that the unlabeled distribution is known exactly. For this reason, we call the separation the value of unlabeled data.
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