Scalable and generalized non-negative tensor decompositions for multilayer networks, hypergraphs, and beyond

Many familiar modeling approaches for measuring meaningful latent structure from multidimensional data — such as admixture modeling for population genetics, stochastic blockmodeling for networks, topic modeling for text corpora, latent class analysis for psychometrics, or collaborative filtering for recommender systems — can be generalized and unified under the framework of non-negative tensor factorization. Such models posit a "parts-based" representation of the observed data that often yields a natural domain-specific interpretation.

In this talk, I will discuss some of our recent work that seeks to substantially expand the scope, scale, and applicability of non-negative tensor factorization. The first part of the talk is motivated by "dyadic event data" in political science, i.e., micro-records of the form "country i took action a to country j at time t", that can be viewed as a dynamic multilayer network and represented as a four-way count tensor. While recent work advocates for non-negative Tucker decomposition as a natural model for such data, the practical application of Tucker-based models to this setting is hampered by a combinatorial explosion in the dimensionality of the "core tensor". To address this, we constrain the core tensor to be sparse and develop inference schemes that exploit this sparsity to enable large-core Tucker to be applied to large observed tensors with billions of cells.

I will then show how the same basic idea — constraining the core to avoid exponential blowup — extends from sparse cores to low-rank cores, enabling us to develop models for hypergraphs and higher-order networks. The resulting models are among the first in the literature for hypergraphs that can scalably discover a broad spectrum of "mesoscale structure", ranging from assortative to disassortative patterns. Finally, time permitting, I will sketch how these ideas are further generalized by non-negative einsum factorization, which lets researchers specify and fit a very wide range of highly customized non-negative tensor decomposition models.

This talk is based on the following three papers led by John Hood, a PhD candidate in Statistics at UChicago:

1. John Hood and Aaron J. Schein (2024). "The AL$\ell_0$CORE tensor decomposition for sparse count data." AISTATS 2024.
2. John Hood, Caterina De Bacco and Aaron Schein (2026). "Broad spectrum structure discovery in large-scale higher-order networks." Nature Communications.
3. John Hood and Aaron Schein (2026). "Near-universal multiplicative updates for nonnegative einsum factorization." To appear at ICML 2026.