Section: New Results

Low-rank Interaction Contingency Tables

ontingency tables are collected in many scientific and engineering tasks including image processing, single-cell RNA sequencing and ecological studies. Low-rank methods have proved useful to analyze them, by facilitating visualization and interpretation. However, common methods do not take advantage of extra information which is often available, such as row and column covariates. We propose a method to denoise and visualize high-dimensional count data which directly incorporates the covariates at hand. Estimation is done by minimizing a Poisson log-likelihood and enforcing a low-rank structure on the interaction matrix with a nuclear norm penalty. We also derive theoretical upper and lower bounds on the Frobenius estimation risk. A complete methodology is proposed, including an algorithm based on the alternating direction method of multipliers, and automatic selection of the regularization parameter. The simulation study reveals that our estimator compares favorably to competitors. Then, analyzing environmental science data, we show the interpretability of the model using a biplot visualization. The method is available as an R package.