Speaker
Description
High-throughput genomics and omics technologies generate data with intrinsic multi-way structure arising from multiple samples, molecular features, experimental conditions, and biological contexts. Standard matrix-based methods often obscure this structure through flattening or aggregation. Tensor-based representations provide a natural mathematical framework for preserving and exploiting the underlying multilinear organization of such data.
In this talk, we present tensor decomposition models for the analysis of high-dimensional omics datasets and demonstrate how these models yield low-rank representations that enable dimensionality reduction while maintaining interpretability through mode-specific latent factors. Applications include multi-sample gene expression analysis, multi-omics integration, and higher-order relational modeling of cell–cell interactions using multi-omics data.
We discuss key mathematical and computational challenges arising in these applications, including rank determination, identifiability and uniqueness, robustness to noise, scalability, and the incorporation of structural constraints motivated by domain knowledge. We conclude by outlining open problems at the interface of multilinear algebra, optimization, and statistical modeling, highlighting opportunities for theoretical advances driven by modern omics data.