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We present PAC-Bayesian bounds for the generalisation error of theK-nearest-neighbour classifier (K-NN). This is achieved by casting the K-NNclassifier into a kernel space framework in the limit of vanishing kernelbandwidth. We establish a relation between prior measures over the coefficientsin the kernel expansion and the induced measure on the weight vectors in kernelspace. Defining a sparse prior over the coefficients allows the application ofa PAC-Bayesian folk theorem that leads to a generalisation bound that is afunction of the number of redundant training examples: those that can be leftout without changing the solution. The presented bound requires to quantify aprior belief in the sparseness of the solution and is evaluated after learningwhen the actual redundancy level is known. Even for small sample size (m ~ 100)the bound gives non-trivial results when both the expected sparseness and theactual redundancy are high.

A PAC-Bayesian Analysis of Distance-Based Classifiers: Why Nearest-Neighbour works!