Inferring large networks with matrix factorisation to capture non-linear dependencies among genes using sparse single-cell profiles

Abstract Inference of non-linear dependencies among a large number of features from their scores is an unresolved challenge. Especially when the feature-score matrix is very sparse, like single-cell transcriptome profiles, the problem of estimating dependencies among a large number of features to infer a network becomes an even more daunting task. Here, we propose a method of network inference in reduced dimension (NIRD) to handle sparsity and computational complexity while still inferring non-linear dependencies among genes (features) using large, sparse gene-expression matrices (feature scores). Our method is based on matrix factorisation of gene-expression matrix to facilitate internal imputation as well as network inference using tree ensemble-based non-linear regression. NIRD not only outperformed many other methods across multiple single-cell transcriptomic profiles but also provided consistent inferred networks even in the presence of batch effects. The consistency provided by NIRD helps compare inferred networks to identify genuine genes responsible for changes in regulation due to disease or stress. NIRD can also be used with RNA velocity for better inference of non-linear causality. Application of NIRD with RNA-velocity could improve the prediction of direct targets of transcription factors in human embryonic stem cells, which we validated using ChIP-seq and gene-knockout datasets. Competing Interest Statement The authors have declared no competing interest. Abbreviations - NIRD - Network inference in reduced dimension - OA - Osteoarthritis - PCA - Principal component analysis - SVD - singular value decomposition - NMF - non-negative matrix factorisation - BD - Bayesian decomposition - BMF - Binary matrix factorisation (BMF) - ICM - Iterated Conditional - SNMF - sparse non-negative matrix factorisation - PMF - probabilistic matrix factorisation - PMFCC - Penalised matrix factorisation for constrained clustering - SepNMF - separable non-negative matrix factorisation - KLD - AUC - area under curve - TF - transcription factors - PPI - protein-protein interaction - ChIP - chromatin immunoprecipitation - HTC - hypertrophic chondrocytes - preHTC - prehypertrophic chondrocytes