Order-preserving factor discovery from misaligned data

We present a factor analysis method that accounts for possible temporal misalignment of the factor loadings across the population of samples. Our main hypothesis is that the data contains a subset of variables with similar but delayed profiles obeying a consistent precedence ordering relationship. Our model is motivated by the difficulty of gene expression analysis across subjects who have common patterns of immune response but show different onset times after a uniform innoculation time of a viral pathogen. The proposed method is based on a linear model with additional degrees of freedom that account for each subject's inherent delays. We present an algorithm to fit this model in a totally unsupervised manner and demonstrate its effectiveness on extracting gene expression factors affecting host response using a flu-virus human challenge study dataset.