MOTIVATION: Gene regulatory networks define regulatory relationships between transcription factors and target genes within a biological system, and reconstructing them is essential for understanding cellular growth and function. Methods for inferring and reconstructing networks from genomics data have evolved rapidly over the last decade in response to advances in sequencing technology and machine learning. The scale of data collection has increased dramatically; the largest genome-wide gene expression datasets have grown from thousands of measurements to millions of single cells, and new technologies are on the horizon to increase to tens of millions of cells and above. RESULTS: In this work, we present the Inferelator 3.0, which has been significantly updated to integrate data from distinct cell types to learn context-specific regulatory networks and aggregate them into a shared regulatory network, while retaining the functionality of the previous versions. The Inferelator is able to integrate the largest single-cell datasets and learn cell-type-specific gene regulatory networks. Compared to other network inference methods, the Inferelator learns new and informative Saccharomyces cerevisiae networks from single-cell gene expression data, measured by recovery of a known gold standard. We demonstrate its scaling capabilities by learning networks for multiple distinct neuronal and glial cell types in the developing Mus musculus brain at E18 from a large (1.3 million) single-cell gene expression dataset with paired single-cell chromatin accessibility data. AVAILABILITY AND IMPLEMENTATION: The inferelator software is available on GitHub (https://github.com/flatironinstitute/inferelator) under the MIT license and has been released as python packages with associated documentation (https://inferelator.readthedocs.io/). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

This paper describes a method for answering all relational calculus queries under the assumption that the domain of data values is sufficiently large. The method extends recent theoretical results that use extended relation representations to answer domain dependent queries, without the use of auxilliary variables or invented constants or an explicit enumeration of the active domain. The method is shown to be logically correct and to have polynomial data complexity. By identifying relational algebra operations with relational calculus queries this approach extends relational algebra to a full boolean algebra, where intersection, union, and difference are defined between any two relations, whether or not they are union compatible. An example illustrates that this approach can be useful in distributed query optimization.

A new definition of complex objects is introduced which provides a denotation for incomplete tuples as well as partially described sets. Set values are “sandwiched” between “complete” and “consistent” descriptions (respectively represented in the Smyth and Hoare powerdomains), allowing the maximal values to be arbitrary subsets of maximal elements in the domain of the space of descriptions. We then restrict our attention to complex objects which are in some sense “natural,” i.e., those which represent “views” of entity-relationship databases, and define rules over these objects. The rules can be used not only as an integrity check on the information in the database, but can be used constructively to infer consistent instances of conclusions and to refine complete instances of the hypothesis. The system is shown to extend the power of datalog (without negation) and the relational algebra (with set difference), and to have an efficient implementation.

A new definition of complex objects is introduced which provides a denotation for incomplete tuples as well as partially described sets. Set values are “sandwiched” between “complete” and “consistent” descriptions (representing the Smyth and Hoare powerdomains respectively), allowing the maximal values to be arbitrary subsets of maximal elements in the domain of the set. We also examine the use of rules in defining queries over such objects.