Eliciting Structure in Genomics Data

Trajectory inference methods analyze thousands of cells from single-cell sequencing technologies and computationally infer their developmental trajectories. Though many tools have been developed for trajectory inference, most of them lack a coherent statistical model and reliable uncertainty quantification. In this talk, I will introduce our latest computational tool VITAE, which combines a latent hierarchical mixture model with variational autoencoders to infer trajectories from posterior approximations. VITAE is computationally scalable and can adjust for confounding covariates to integrate multiple datasets. We show that VITAE outperforms other state-of-the-art trajectory inference methods on both real and synthetic data under various trajectory topologies. We also apply VITAE to jointly analyze two single-cell RNA sequencing datasets on the mouse neocortex. Our results suggest that VITAE can successfully uncover a shared developmental trajectory of the projection neurons and reliably order cells from both datasets along the inferred trajectory.

In this talk I will present Low Distortion Local Eigenmaps (LDLE), a “bottom-up” manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding. The local views are constructed using subsets of the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis. The choice of these eigenvectors may vary across the regions. In contrast to existing techniques, LDLE is more geometric and can embed manifolds without boundary as well as non-orientable manifolds into their intrinsic dimension.

Joint work with Dhruv Kohli and Alex Cloninger.

The cell cycle is a highly conserved, continuous process which controls faithful replication and division of cells. Single-cell technologies have enabled increasingly precise measurements of the cell cycle both as a biological process of interest and as a possible confounding factor. Despite its importance and conservation, there is no universally applicable approach to infer position in the cell cycle with high-resolution from single-cell RNA-seq data. here, we present tricycle, a method with associated software, to address this challenge by leveraging key features of the biology of the cell cycle, the mathematical properties of principal component analysis of periodic functions, and the applicability of transfer learning. Tricycle works by first constructing a reference latent space using a fixed reference dataset as well as a projection operator which allows us to project any new dataset into the fixed reference space. We show that tricycle can predict any cell’s position in the cell cycle regardless of the cell type, species of origin, and even sequencing assay. The accuracy of tricycle compares favorably to gold-standard experimental assays which generally require specialized measurements in specifically designed in vitro systems. Unlike gold-standard assays, tricycle is easily applicable to any single-cell RNA-seq dataset. We will highlight features of the problem and tricycle which we believe are specifically important for achieving high generalizability.

The estimation of phylogenetic trees for individual genes or multi-locus datasets is a basic part of considerable biological research, and is approached through methods that are based on stochastic models of sequence and gene evolution. Statistical properties of methods, including statistical consistency and sample complexity, are important, and theoretical advances in these aspects have resulted in new methods with outstanding theoretical properties. Yet, empirical performance has been of mixed quality. In this talk, I will discuss algorithm design issues that arise, and present new results that shed light on those strategies that maintain theoretical advantages while providing excellent empirical performance on large simulated datasets. I will also present some open questions of interest to mathematicians that would be important to further method development.  

Extracting interpretable, lower dimensional representation from data is not a new problem. Over the years, numerous algorithms and models have been developed across a range of disciplines such as statistics, computer science and operation research. In computational biology, under the auspice of single cell technology development, one challenging task is to select a small set of informative markers to identify and differentiate specific cellular information (e.g cell type, cell state or cell location) as precisely as possible. In this talk, I will discuss scGene-Fit, a method for selecting gene transcript markers that jointly optimize cell label recovery using a simple label-aware compressive classification approach. Beyond presenting its features and limitations, I will also discuss on-going work aimed at improving them. Finally, I will review recent literature on the topic and related interpretable machine learning approaches that need further understanding and exploration, but which hold promise in the genomic context.