Single-cell RNA sequencing (scRNA-seq), a powerful technique for investigating the transcriptome of individual cells, enables the discovery of heterogeneous cell populations, rare cell types, and transcriptional dynamics in separate cells. Yet, scRNA-seq data analysis is limited by the problem of measurement dropouts, i.e., genes displaying zero expression levels. We introduce ZiPo, a deep artificial neural network for rate estimation and library size prediction in scRNA-seq data that incorporates adjustable zero inflation in the distribution to capture dropouts. ZiPo builds upon established concepts, including using deep autoencoders and adopting the Poisson and negative binomial distributions, by taking advantage of novel strategies, including library size prediction and residual connections, to improve the overall performance. A significant innovation of ZiPo is the introduction of a scale-invariant loss term, making the weights sparse and, hence, the model biologically more interpretable. ZiPo quickly handles vast singular and mixed datasets, with the processing time directly proportional to the number of cells. In this paper, we demonstrate the power of ZiPo on three datasets and show its advantages over other current techniques.

In this paper, we consider an exponentially windowed sample covariance matrix (EWSCM) and propose an improved estimator for its eigenvalues. We use new advances in random matrix theory, which describe the limiting spectral distribution of the large dimensional doubly correlated Wishart matrices to find the support and distribution of the eigenvalues of the EWSCM. We then employ the complex integration and residue theorem to design an estimator for the eigenvalues, which satisfies the cluster separability condition, assuming that the eigenvalue multiplicities are known. We show that the proposed estimator is consistent in the asymptotic regime and has good performance in finite sample size situations. Simulation results show that the proposed estimator outperforms the traditional estimator, significantly.