We introduce an iterative normalization and clustering method for single-cell gene expression data. The emerging technology of single-cell RNA-seq gives access to gene expression measurements for thousands of cells, allowing discovery and characterization of cell types. However, the data is confounded by technical variation emanating from experimental errors and cell type-specific biases. Current approaches perform a global normalization prior to analyzing biological signals, which does not resolve missing data or variation dependent on latent cell types. Our model is formulated as a hierarchical Bayesian mixture model with cell-specific scalings that aid the iterative normalization and clustering of cells, teasing apart technical variation from biological signals. We demonstrate that this approach is superior to global normalization followed by clustering. We show identifiability and weak convergence guarantees of our method and present a scalable Gibbs inference algorithm. This method improves cluster inference in both synthetic and real single-cell data compared with previous methods, and allows easy interpretation and recovery of the underlying structure and cell types.

This paper presents a new computational technique for the identification of HIV haplotypes. HIV tends to generate many potentially drug-resistant mutants within the HIV-infected patient and being able to identify these different mutants is important for efficient drug administration. With the view of identifying the mutants, we aim at analyzing short deep sequencing data called reads. From a statistical perspective, the analysis of such data can be regarded as a nonstandard clustering problem due to missing pairwise similarity measures between non-overlapping reads. To overcome this problem we propagate a Dirichlet Process Mixture Model by sequentially updating the prior information from successive local analyses. The model is verified using both simulated and real sequencing data.