Warped Matrix Factorisation for Multi-view Data Integration.

Matrix factorisation is a widely used tool with applications in collaborative filtering, image analysis and in genomics. Several extensions of the classical model have been proposed, such as modelling of multiple related “data views” or accounting for side information on the latent factors. However, as the complexity of these models increases even subtle mismatches of the distributional assumptions on the input data can severely affect model performance. Here, we propose a simple yet effective solution to address this problem by modelling the observed data in a transformed or warped space. We derive a joint model of a multi-view matrix factorisation model that infers view-specific data transformations and provide a computationally efficient variational approximation for parameter inference. We first validate the model on synthetic data before applying it to a matrix completion problem in genomics. We show that our model improves the imputation of missing values in gene-disease association analysis and allows for discovering enhanced consensus structures across multiple data views The data and software related to this paper are available at https://github.com/PMBio/WarpedMF.