Handling ill-conditioned omics data with deep probabilistic models

The advent of high-throughput technologies has produced an increase in the dimensionality of omics datasets, which limits the application of machine learning methods due to the great unbalance between the number of observations and features. In this scenario, dimensionality reduction is essential to extract the relevant information within these datasets and project it in a low-dimensional space, and probabilistic latent space models are becoming popular given their capability to capture the underlying structure of the data as well as the uncertainty in the information. This article aims to provide a general classification and dimensionality reduction method based on deep latent space models that tackles two of the main problems that arise in omics datasets: the presence of missing data and the limited number of observations against the number of features. We propose a semi-supervised Bayesian latent space model that infers a low-dimensional embedding driven by the target label: the Deep Bayesian Logistic Regression (DBLR) model. During inference, the model also learns a global vector of weights that allows to make predictions given the low-dimensional embedding of the observations. Since this kind of datasets is prone to overfitting, we introduce an additional probabilistic regularization method based on the semi-supervised nature of the model. We compared the performance of the DBLR against several state-of-the-art methods for dimensionality reduction, both in synthetic and real datasets with different data types. The proposed model provides more informative low-dimensional representations, outperforms the baseline methods in classification and can naturally handle missing entries. Highlights Inference of the latent space driven by the label value. The DBLR infers different low-dimensional latent distributions depending on the label value, forcing clustering in the latent space in an informative manner, thus capturing the underlying structure of the data. Classification. During inference, the model additionally learns a global vector of weights that allows to make predictions given the low-dimensional representation of the data. Handling missing data. As the DBLR is a probabilistic generative model, it can naturally handle partially missing observations during the training process, including not annotated observations as censored samples. In this article we cover the Missing at Random (MAR) case. Regularization method to handle small datasets. In order to handle small high-dimensional datasets, which usually entail overfitting problems, we introduced an additional regularization mechanism following a drop-out-like strategy that relies in the generative semi-supervised nature of the model. Handling different data types. We have defined and implemented different observation likelihood models that can be used to describe different data types. In particular, we show how to use the DBLR with binary and real-valued features.