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Dealing with datasets of very high dimension is a major challenge in machinelearning. In this paper, we consider the problem of feature selection inapplications where the memory is not large enough to contain all features. Inthis setting, we propose a novel tree-based feature selection approach thatbuilds a sequence of randomized trees on small subsamples of variables mixingboth variables already identified as relevant by previous models and variablesrandomly selected among the other variables. As our main contribution, weprovide an in-depth theoretical analysis of this method in infinite samplesetting. In particular, we study its soundness with respect to commondefinitions of feature relevance and its convergence speed under variousvariable dependance scenarios. We also provide some preliminary empiricalresults highlighting the potential of the approach.

Random Subspace with Trees for Feature Selection Under Memory Constraints