Quantifying common and distinct information in single-cell multimodal data with Tilted Canonical Correlation Analysis.

Multimodal single-cell technologies profile multiple modalities for each cell simultaneously, enabling a more thorough characterization of cell populations. Existing dimension-reduction methods for multimodal data capture the "union of information," producing a lower-dimensional embedding that combines the information across modalities. While these tools are useful, we focus on a fundamentally different task of separating and quantifying the information among cells that is shared between the two modalities as well as unique to only one modality. Hence, we develop Tilted Canonical Correlation Analysis (Tilted-CCA), a method that decomposes a paired multimodal dataset into three lower-dimensional embeddings-one embedding captures the "intersection of information," representing the geometric relations among the cells that is common to both modalities, while the remaining two embeddings capture the "distinct information for a modality," representing the modality-specific geometric relations. We analyze single-cell multimodal datasets sequencing RNA along surface antibodies (i.e., CITE-seq) as well as RNA alongside chromatin accessibility (i.e., 10x) for blood cells and developing neurons via Tilted-CCA. These analyses show that Tilted-CCA enables meaningful visualization and quantification of the cross-modal information. Finally, Tilted-CCA's framework allows us to perform two specific downstream analyses. First, for single-cell datasets that simultaneously profile transcriptome and surface antibody markers, we show that Tilted-CCA helps design the target antibody panel to complement the transcriptome best. Second, for developmental single-cell datasets that simultaneously profile transcriptome and chromatin accessibility, we show that Tilted-CCA helps identify development-informative genes and distinguish between transient versus terminal cell types.

eSVD-DE: cohort-wide differential expression in single-cell RNA-seq data using exponential-family embeddings.

BACKGROUND: Single-cell RNA-sequencing (scRNA) datasets are becoming increasingly popular in clinical and cohort studies, but there is a lack of methods to investigate differentially expressed (DE) genes among such datasets with numerous individuals. While numerous methods exist to find DE genes for scRNA data from limited individuals, differential-expression testing for large cohorts of case and control individuals using scRNA data poses unique challenges due to substantial effects of human variation, i.e., individual-level confounding covariates that are difficult to account for in the presence of sparsely-observed genes. RESULTS: We develop the eSVD-DE, a matrix factorization that pools information across genes and removes confounding covariate effects, followed by a novel two-sample test in mean expression between case and control individuals. In general, differential testing after dimension reduction yields an inflation of Type-1 errors. However, we overcome this by testing for differences between the case and control individuals' posterior mean distributions via a hierarchical model. In previously published datasets of various biological systems, eSVD-DE has more accuracy and power compared to other DE methods typically repurposed for analyzing cohort-wide differential expression. CONCLUSIONS: eSVD-DE proposes a novel and powerful way to test for DE genes among cohorts after performing a dimension reduction. Accurate identification of differential expression on the individual level, instead of the cell level, is important for linking scRNA-seq studies to our understanding of the human population.

Post-selection inference for changepoint detection algorithms with application to copy number variation data.

Changepoint detection methods are used in many areas of science and engineering, for example, in the analysis of copy number variation data to detect abnormalities in copy numbers along the genome. Despite the broad array of available tools, methodology for quantifying our uncertainty in the strength (or the presence) of given changepoints post-selection are lacking. Post-selection inference offers a framework to fill this gap, but the most straightforward application of these methods results in low-powered hypothesis tests and leaves open several important questions about practical usability. In this work, we carefully tailor post-selection inference methods toward changepoint detection, focusing on copy number variation data. To accomplish this, we study commonly used changepoint algorithms: binary segmentation, as well as two of its most popular variants, wild and circular, and the fused lasso. We implement some of the latest developments in post-selection inference theory, mainly auxiliary randomization. This improves the power, which requires implementations of Markov chain Monte Carlo algorithms (importance sampling and hit-and-run sampling) to carry out our tests. We also provide recommendations for improving practical useability, detailed simulations, and example analyses on array comparative genomic hybridization as well as sequencing data.

eSVD-DE: Cohort-wide differential expression in single-cell RNA-seq data using exponential-family embeddings.

Background: Single-cell RNA-sequencing (scRNA) datasets are becoming increasingly popular in clinical and cohort studies, but there is a lack of methods to investigate differentially expressed (DE) genes among such datasets with numerous individuals. While numerous methods exist to find DE genes for scRNA data from limited individuals, differential-expression testing for large cohorts of case and control individuals using scRNA data poses unique challenges due to substantial effects of human variation, i.e., individual-level confounding covariates that are difficult to account for in the presence of sparsely-observed genes. Results: We develop the eSVD-DE, a matrix factorization that pools information across genes and removes confounding covariate effects, followed by a novel two-sample test in mean expression between case and control individuals. In general, differential testing after dimension reduction yields an inflation of Type-1 errors. However, we overcome this by testing for differences between the case and control individuals' posterior mean distributions via a hierarchical model. In previously published datasets of various biological systems, eSVD-DE has more accuracy and power compared to other DE methods typically repurposed for analyzing cohort-wide differential expression. Conclusions: eSVD-DE proposes a novel and powerful way to test for DE genes among cohorts after performing a dimension reduction. Accurate identification of differential expression on the individual level, instead of the cell level, is important for linking scRNA-seq studies to our understanding of the human population.

Bias-adjusted spectral clustering in multi-layer stochastic block models.

We consider the problem of estimating common community structures in multi-layer stochastic block models, where each single layer may not have sufficient signal strength to recover the full community structure. In order to efficiently aggregate signal across different layers, we argue that the sum-of-squared adjacency matrices contain sufficient signal even when individual layers are very sparse. Our method uses a bias-removal step that is necessary when the squared noise matrices may overwhelm the signal in the very sparse regime. The analysis of our method relies on several novel tail probability bounds for matrix linear combinations with matrix-valued coefficients and matrix-valued quadratic forms, which may be of independent interest. The performance of our method and the necessity of bias removal is demonstrated in synthetic data and in microarray analysis about gene co-expression networks.

Destin2: Integrative and cross-modality analysis of single-cell chromatin accessibility data.

We propose Destin2, a novel statistical and computational method for cross-modality dimension reduction, clustering, and trajectory reconstruction for single-cell ATAC-seq data. The framework integrates cellular-level epigenomic profiles from peak accessibility, motif deviation score, and pseudo-gene activity and learns a shared manifold using the multimodal input, followed by clustering and/or trajectory inference. We apply Destin2 to real scATAC-seq datasets with both discretized cell types and transient cell states and carry out benchmarking studies against existing methods based on unimodal analyses. Using cell-type labels transferred with high confidence from unmatched single-cell RNA sequencing data, we adopt four performance assessment metrics and demonstrate how Destin2 corroborates and improves upon existing methods. Using single-cell RNA and ATAC multiomic data, we further exemplify how Destin2's cross-modality integrative analyses preserve true cell-cell similarities using the matched cell pairs as ground truths. Destin2 is compiled as a freely available R package available at https://github.com/yuchaojiang/Destin2.

Integration of spatial and single-cell data across modalities with weak linkage.

single-cell sequencing methods have enabled the profiling of multiple types of molecular readouts at cellular resolution, and recent developments in spatial barcoding, in situ hybridization, and in situ sequencing allow such molecular readouts to retain their spatial context. Since no technology can provide complete characterization across all layers of biological modalities within the same cell, there is pervasive need for computational cross-modal integration (also called diagonal integration) of single-cell and spatial omics data. For current methods, the feasibility of cross-modal integration relies on the existence of highly correlated, a priori "linked" features. When such linked features are few or uninformative, a scenario that we call "weak linkage", existing methods fail. We developed MaxFuse, a cross-modal data integration method that, through iterative co-embedding, data smoothing, and cell matching, leverages all information in each modality to obtain high-quality integration. MaxFuse is modality-agnostic and, through comprehensive benchmarks on single-cell and spatial ground-truth multiome datasets, demonstrates high robustness and accuracy in the weak linkage scenario. A prototypical example of weak linkage is the integration of spatial proteomic data with single-cell sequencing data. On two example analyses of this type, we demonstrate how MaxFuse enables the spatial consolidation of proteomic, transcriptomic and epigenomic information at single-cell resolution on the same tissue section.

Integration of spatial and single-cell data across modalities with weakly linked features.

Although single-cell and spatial sequencing methods enable simultaneous measurement of more than one biological modality, no technology can capture all modalities within the same cell. For current data integration methods, the feasibility of cross-modal integration relies on the existence of highly correlated, a priori 'linked' features. We describe matching X-modality via fuzzy smoothed embedding (MaxFuse), a cross-modal data integration method that, through iterative coembedding, data smoothing and cell matching, uses all information in each modality to obtain high-quality integration even when features are weakly linked. MaxFuse is modality-agnostic and demonstrates high robustness and accuracy in the weak linkage scenario, achieving 20~70% relative improvement over existing methods under key evaluation metrics on benchmarking datasets. A prototypical example of weak linkage is the integration of spatial proteomic data with single-cell sequencing data. On two example analyses of this type, MaxFuse enabled the spatial consolidation of proteomic, transcriptomic and epigenomic information at single-cell resolution on the same tissue section.

Covariance-based sample selection for heterogeneous data: Applications to gene expression and autism risk gene detection.

Risk for autism can be influenced by genetic mutations in hundreds of genes. Based on findings showing that genes with highly correlated gene expressions are functionally interrelated, "guilt by association" methods such as DAWN have been developed to identify these autism risk genes. Previous research analyze the BrainSpan dataset, which contains gene expression of brain tissues from varying regions and developmental periods. Since the spatiotemporal properties of brain tissue is known to affect the gene expression's covariance, previous research have focused only on a specific subset of samples to avoid the issue of heterogeneity. This analysis leads to a potential loss of power when detecting risk genes. In this article, we develop a new method called COBS (COvariance-Based sample Selection) to find a larger and more homogeneous subset of samples that share the same population covariance matrix for the downstream DAWN analysis. To demonstrate COBS's effectiveness, we use genetic risk scores from two sequential data freezes obtained in 2014 and 2020. We show COBS improves DAWN's ability to predict risk genes detected in the newer data freeze when using the risk scores of the older data freeze as input.

Exponential-Family Embedding With Application to Cell Developmental Trajectories for Single-Cell RNA-Seq Data.

Scientists often embed cells into a lower-dimensional space when studying single-cell RNA-seq data for improved downstream analyses such as developmental trajectory analyses, but the statistical properties of such nonlinear embedding methods are often not well understood. In this article, we develop the exponential-family SVD (eSVD), a nonlinear embedding method for both cells and genes jointly with respect to a random dot product model using exponential-family distributions. Our estimator uses alternating minimization, which enables us to have a computationally efficient method, prove the identifiability conditions and consistency of our method, and provide statistically principled procedures to tune our method. All these qualities help advance the single-cell embedding literature, and we provide extensive simulations to demonstrate that the eSVD is competitive compared to other embedding methods. We apply the eSVD via Gaussian distributions where the standard deviations are proportional to the means to analyze a single-cell dataset of oligodendrocytes in mouse brains. Using the eSVD estimated embedding, we then investigate the cell developmental trajectories of the oligodendrocytes. While previous results are not able to distinguish the trajectories among the mature oligodendrocyte cell types, our diagnostics and results demonstrate there are two major developmental trajectories that diverge at mature oligodendrocytes. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplementary materials.