Correlation imputation in single cell RNA-seq using auxiliary information and ensemble learning
Single cell RNA sequencing is a powerful technique that measures the gene expression of individua... more Single cell RNA sequencing is a powerful technique that measures the gene expression of individual cells in a high throughput fashion. However, due to sequencing inefficiency, the data is unreliable due to dropout events, or technical artifacts where genes erroneously appear to have zero expression. Many data imputation methods have been proposed to alleviate this issue. Yet, effective imputation can be difficult and biased because the data is sparse and high-dimensional, resulting in major distortions in downstream analyses. In this paper, we propose a completely novel approach that imputes the gene-by-gene correlations rather than the data itself. We call this method SCENA: Single cell RNA-seq Correlation completion by ENsemble learning and Auxiliary information. The SCENA gene-by-gene correlation matrix estimate is obtained by model stacking of multiple imputed correlation matrices based on known auxiliary information about gene connections. In an extensive simulation study based...
We investigate the problem of conditional dependence graph estimation when several pairs of nodes... more We investigate the problem of conditional dependence graph estimation when several pairs of nodes have no joint observation. For these pairs even the simplest metric of covariability, the sample covariance, is unavailable. This problem arises, for instance, in calcium imaging recordings where the activities of a large population of neurons are typically observed by recording from smaller subsets of cells at once, and several pairs of cells are never recorded simultaneously. With no additional assumption, the unavailability of parts of the covariance matrix translates into the unidentifiability of the precision matrix that, in the Gaussian graphical model setting, specifies the graph. Recovering a conditional dependence graph in such settings is fundamentally an extremely hard challenge, because it requires to infer conditional dependences between network nodes with no empirical evidence of their covariability. We call this challenge the "graph quilting problem". We demonstrate that, under mild conditions, it is possible to correctly identify not only the edges connecting the observed pairs of nodes, but also a superset of those connecting the variables that are never observed jointly. We propose an ℓ1 regularized graph estimator based on a partially observed sample covariance matrix and establish its rates of convergence in high-dimensions. We finally present a simulation study and the analysis of calcium imaging data of ten thousand neurons in mouse visual cortex.
The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of... more The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of shapes without causing a possibly large loss of information. Dictionary learning and sparse coding allow us to reduce the high dimensional space of shapes into a manageable low dimensional continuous vector space. Statistical inference can be done in the reduced space via probability distribution estimation and manifold estimation.
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Papers by Giuseppe Vinci