Generative processes in biology and other fields often produce data that can be regarded as resulting from a composition of basic features. Here we present an unsupervised method based on autoencoders for inferring these basic features of data. The main novelty in our approach is that the training is based on the optimization of the 'local entropy' rather than the standard loss, resulting in a more robust inference, and enhancing the performance on this type of data considerably. Algorithmically, this is realized by training an interacting system of replicated autoencoders. We apply this method to synthetic and protein sequence data, and show that it is able to infer a hidden representation that correlates well with the underlying generative process, without requiring any prior knowledge. AUTHOR SUMMARYExtracting compositional features from noisy data and identifying the corresponding generative models is a fundamental challenge across sciences. The composition of elementary features can have highly non-linear effects which makes them very hard to identify from experimental data. In biology, for instance, one challenge is to identify the key steps or components of molecular and cellular processes. Representative examples are the modeling of protein sequences as the composition of patterns influenced by phylogeny or the identification of gene clusters in which the presence of specific genes depends on the evolutionary history of the cell. Here we present an unsupervised machine learning technique for the analysis of compositional data which is based on entropic neural autoencoders. Our approach aims at finding deep autoencoders that are highly invariant with respect to perturbations in the inputs and in the parameters. The procedure is efficient to implement and we have validated it both on synthetic and protein sequence data, where it can be shown that the latent variables of the autoencoders are non trivially correlated with the true underlying generative processes. Our results suggests that the local entropy approach represents a general valuable tool for the extraction of compositional features in hard unsupervised learning problems.

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