Confounding variation, such as batch effects, are a pervasive issue in single-cell RNA sequencing experiments. While methods exist for aligning cells across batches, it is yet unclear how to correct for other types of confounding variation which may be observed at the subject level, such as age and sex, and at the cell level, such as library size and other measures of cell quality. On the specific problem of batch alignment, many questions still persist despite recent advances: Existing methods can effectively align batches in low-dimensional representations of cells, yet their effectiveness in aligning the original gene expression matrices is unclear. Nor is it clear how batch correction can be performed alongside data denoising, the former treating technical biases due to experimental stratification while the latter treating technical variation due inherently to the random sampling that occurs during library construction and sequencing. Here, we propose SAVERCAT, a method for dimension reduction and denoising of single-cell gene expression data that can flexibly adjust for arbitrary observed covariates. We benchmark SAVERCAT against existing single-cell batch correction methods and show that while it matches the best of the field in low-dimensional cell alignment, it significantly improves upon existing methods on the task of batch correction in the high-dimensional expression matrix. We also demonstrate the ability of SAVERCAT to effectively integrate batch correction and denoising through a data down-sampling experiment. Finally, we apply SAVERCAT to a single cell study of Alzheimer's disease where batch is confounded with the contrast of interest, and demonstrate how adjusting for covariates other than batch allows for more interpretable analysis.

14Detection of genetically distinct subclones and profiling the transcriptomic differences between them is 15 important for studying the evolutionary dynamics of tumors, as well as for accurate prognosis and 16 effective treatment of cancer in the clinic. For the profiling of intra-tumor transcriptional heterogeneity, 17 single cell RNA-sequencing (scRNA-seq) is now ubiquitously adopted in ongoing and planned cancer 18 studies. Detection of somatic DNA mutations and inference of clonal membership from scRNA-seq, 19 however, is currently unreliable. We propose DENDRO, an analysis method for scRNA-seq data that 20 detects genetically distinct subclones, assigns each single cell to a subclone, and reconstructs the 21 phylogenetic tree describing the tumor's evolutionary history. DENDRO utilizes information from single 22