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Deep generative models can be trained to represent the joint distribution of data, such as measurements of single nucleotide polymorphisms (SNPs) from several individuals. Subsequently, synthetic observations are obtained by drawing from this distribution. This has been shown to be useful for several tasks, such as removal of noise, imputation, for better understanding underlying patterns, or even exchanging data under privacy constraints. Yet, it is still unclear how well these approaches work with limited sample size. We investigate such settings specifically for binary data, e.g. as relevant when considering SNP measurements, and evaluate three frequently employed generative modeling approaches, variational autoencoders (VAEs), deep Boltzmann machines (DBMs) and generative adversarial networks (GANs). This includes conditional approaches, such as when considering gene expression conditional on SNPs. Recovery of pair-wise odds ratios (ORs) is considered as a primary performance criterion. For simulated as well as real SNP data, we observe that DBMs generally can recover structure for up to 300 variables, with a tendency of over-estimating ORs when not carefully tuned. VAEs generally get the direction and relative strength of pairwise relations right, yet with considerable under-estimation of ORs. GANs provide stable results only with larger sample sizes and strong pair-wise relations in the data. Taken together, DBMs and VAEs (in contrast to GANs) appear to be well suited for binary omics data, even at rather small sample sizes. This opens the way for many potential applications where synthetic observations from omics data might be useful.

Synthetic observations from deep generative models and binary omics data with limited sample size