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Statistical Analysis of Semi-Supervised Learning: The Limit of Infinite Unlabelled Data
Boaz Nadler · Nati Srebro · Xueyuan Zhou

Wed Dec 09 03:27 PM -- 03:28 PM (PST) @
We study the behavior of the popular Laplacian Regularization method for Semi-Supervised Learning at the regime of a fixed number of labeled points but a large number of unlabeled points. We show that in $\R^d$, $d \geq 2$, the method is actually not well-posed, and as the number of unlabeled points increases the solution degenerates to a noninformative function. We also contrast the method with the Laplacian Eigenvector method, and discuss the `smoothness assumptions associated with this alternate method.