Advances in transcriptomic technologies have deepened our understanding of the cellular
gene expression programs of multicellular organisms and provided a theoretical basis for …

Dimension reduction and (spatial) clustering is usually performed sequentially; however, the
low-dimensional embeddings estimated in the dimension-reduction step may not be …

Heteroskedastic PCA: Algorithm, optimality, and applications Page 1 The Annals of Statistics
2022, Vol. 50, No. 1, 53–80 https://doi.org/10.1214/21-AOS2074 © Institute of Mathematical …

Distributed linear regression by averaging Page 1 The Annals of Statistics 2021, Vol. 49, No. 2,
918–943 https://doi.org/10.1214/20-AOS1984 © Institute of Mathematical Statistics, 2021 …

In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are
collected from different sources with heterogeneous trends while still sharing some …

Tensor decomposition is a well-known tool for multiway data analysis. This work proposes
using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor …

Spatial transcriptomics has transformed our understanding of gene expression by
preserving the spatial context within tissues. This review focuses on the application of spatial …

Estimating the rank of a corrupted data matrix is an important task in data analysis, most
notably for choosing the number of components in principal component analysis. Significant …

We study the problem of estimating a large, low-rank matrix corrupted by additive noise of
unknown covariance, assuming one has access to additional side information in the form of …

Dimensionality reduction via PCA and factor analysis is an important tool of data analysis. A
critical step is selecting the number of components. However, existing methods (such as the …