Single-cell trajectories can unveil how gene regulation governs cell fate decisions. However, learning the structure of complex trajectories with two or more branches remains a challenging computational problem. We present Monocle 2, which uses reversed graph embedding to describe multiple fate decisions in a fully unsupervised manner. Applied to two studies of blood development, Monocle 2 revealed that mutations in key lineage transcription factors diverts cells to alternative fates.

Singlecell transcriptome sequencing now routinely samples thousands of cells, potentially providing enough data to reconstruct causal gene regulatory networks from observational data. Here, we present Scribe, a toolkit for detecting and visualizing causal regulatory interactions between genes and explore the potential for singlecell experiments to power network reconstruction. Scribe employs Restricted Directed Information to determine causality by estimating the strength of information transferred from a potential regulator to its downstream target. We apply Scribe and other leading approaches for causal network reconstruction to several types of singlecell measurements and show that there is a dramatic drop in performance for "pseudotime" ordered singlecell data compared to true time series data. We demonstrate that performing causal inference requires temporal coupling between measurements. We show that methods such as "RNA velocity" restore some degree of coupling through an analysis of chromaffin cell fate commitment. These analyses therefore highlight an important shortcoming in experimental and computational methods for analyzing gene regulation at singlecell resolution and point the way towards overcoming it..

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Many scientific datasets are of high dimension, and the analysis usually requires retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are mathematically formulated by curves, which is quite restrictive for real applications. A few methods can overcome the above problem, but they either require complicated human-made rules for a specific task with lack of adaption flexibility to different tasks, or cannot obtain explicit structures of data. To address these issues, we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding. As showcases, models that can learn a spanning tree or a weighted undirected ℓ1 graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure from data, simultaneously. The new algorithm is simple with guaranteed convergence. We then extend the proposed framework to deal with large-scale data. Experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly.

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