Cannings and Samworth introduce a very general method for high dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors

High-dimensional statistics refers to statistical inference when the number of unknown parameters p is much larger than the sample size n. This includes regression and supervised classification models, when the number of covariates is of much larger order than n, and unsupervised settings, such as clustering, with more variables than observations. Image processing, information retrieval in text documents, food authentication studies are only a few examples of the applications in which such problems arise. In those contexts, standard statistical methods cannot be applied, as the involved matrices are in general not full rank and cannot be inverted. A solution to this problem, which has attracted large attention in the statistical literature, involves imposing a sparse structure on the estimated vector parameters through the introduction of an L1 penalty on their norm. Lasso (Tibshirani 1996) based approaches to regression, classification and dimension reduction methods have been populating the statistical literature since Tibshirani’s seminal paper. See Buhlmann, van de Geer (2011) and Hastie, Tibshirani, Wainwright (2015) for detailed references.