Making Multi-Axis Models Robust to Multiplicative Noise: How, and Why?

Bailey Andrew; David R. Westhead; Luisa Cutillo

stat.MEMar 27, 2026

Making Multi-Axis Models Robust to Multiplicative Noise: How, and Why?

Authors: Bailey Andrew, David R. Westhead, Luisa Cutillo

Organizations: School of Computer Science, University of Leeds, Woodhouse, Leeds, UK; LS2 9JT · School of Molecular and Cellular Biology, University of Leeds · School of Mathematics, University of Leeds

Abstract

In this paper we develop a graph-learning algorithm, MED-MAGMA, to fit multi-axis (Kronecker-sum-structured) models corrupted by multiplicative noise. This type of noise is natural in many application domains, such as that of single-cell RNA sequencing, in which it naturally captures technical biases of RNA sequencing platforms. Our work is evaluated against prior work on each and every public dataset in the Single Cell Expression Atlas under a certain size, demonstrating that our methodology learns networks with better local and global structure. MED-MAGMA is made available as a Python package (MED-MAGMA).

Figures & tables

Figure 1: Estimated tail dependence across 1000 randomly selected pairs of genes (left) and cells (right) from the E-MTAB-7249 scRNA-seq dataset discussed in Section 4.3 , compared to random data generated from a Gaussian copula.

Figure 2: (Both) Results across 20 synthetic Kronecker-sum-structured Gaussian

100\times 150

datasets corrupted by varying levels of multiplicative noise. Median result is highlighted. As noise strength varies, we plot the area under PR curves (left), assortativity (center), and AMI (right).

Figure 3: (Both) The datasets are ordered by increasing performance along the x-axis. GmGM/nonpara refers to GmGM equipped with the nonparanormal skeptic. The median performance is highlighted. (Left) Assortativities below 0 represent a statistical tendency for cells of different categories to connect, which indicates the network does capture information about the dataset, but it is harder to interpret.

Figure 4: (All) A UMAP plot of E-MTAB-7249 cells based on gene expression. (Left) Cell type. (Middle, Right) The percentage of gene expression from genes in modules m0 and m3, respectively.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: (Both) Results across 20 synthetic Kronecker-sum-structured Gaussian

200\times 200

datasets corrupted by varying levels of multiplicative noise. Median result is highlighted. As noise strength varies, we plot the area under PR curves (left), assortativity (center), and AMI (right).

Figure 6: (Both) Area under PR curves across 20 synthetic

200\times 201

Kronecker-sum-structured Gaussian datasets corrupted by varying levels of multiplicative noise and sparsity. Median result is highlighted. (Left) As percentage of nonzero entries vary (noise strength 0.2) (Right) Area under PR curves as noise strength varies (density 0.5).

Dataset	Categorical Variable	Categories	Cells	Genes
E-MTAB-4850 [ 11 ]	Sample Characteristic[cell line]	2	60	63
E-GEOD-75367 [ 20 ]	Sample Characteristic[facs marker]	4	72	70
E-MTAB-6142 [ 23 ]	Sample Characteristic[cell cycle phase]	3	96	91
E-GEOD-36552 [ 42 ]	Sample Characteristic[cell type]	6	115	127
E-CURD-10 [ 24 ]	Sample Characteristic[growth condition]	3	118	104
E-GEOD-99795 [ 18 ]	Factor Value[compound]	2	144	128

Appendix

Table 1: All datasets analyzed during Section 4.2 . The ‘genes’ column counts genes after preprocessing.

Graph Structure Learning

Graph structure learning infers or adapts network connections from data for statistical discovery and downstream prediction.

See all 139 papers

When Does Gene Regulatory Network Inference Break? A Controlled Diagnostic Study of Causal and Correlational Methods on Single-Cell Data
May 6, 2026Miguel Fernandez-de-Retana, Ruben Sanchez-Corcuera, Unai Zulaika +2Causal Discovery Gene Regulatory Network Inference
Faculty of Engineering University of Deusto Bilbao, Spain
Graph Additive Models disentangling feature, topology, and interactions
Oct 14, 2026Clara Alvarez-Rodriguez, Steve Azzolin, Vincenzo Marco De Luca +3Graph Neural Networks GNN Explainability
The Arctic University of Norway
Prior-Guided Multi-Omic Transformers for Single-Cell Gene Regulatory Network Inference
May 30, 2026Tianyang Xu, Tianci Liu, Niraj Rayamajhi +4Transformer Gene Regulatory Network Inference
Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA · Department of Horticulture and Landscape Architecture, Purdue University, West Lafayette, IN, USA · School of Biological Sciences, Illinois State University, Normal, IL, USA

May 6, 2026J/K move · Enter open · S save

When Does Gene Regulatory Network Inference Break? A Controlled Diagnostic Study of Causal and Correlational Methods on Single-Cell Data

Miguel Fernandez-de-Retana, Ruben Sanchez-Corcuera, Unai Zulaika, Aritz Bilbao-Jayo+1

Faculty of Engineering University of Deusto Bilbao, Spain

Causal Discovery Gene Regulatory Network Inference Spurious Correlation Robustness Genomics Single-Cell RNA Sequencing

Open paper AskPDF arXiv

Despite theoretical advantages, causal methods for Gene Regulatory Network (GRN) inference from single-cell RNA-seq data consistently fail to match or outperform correlation-based baselines in many realistic benchmarks, a persistent puzzle which casts doubt on the value of causality for this task. We argue that existing benchmarks are insufficiently controlled to answer this question because they evaluate on real or semi-real data where multiple pathologies co-occur, confounding failure modes, and obscuring the specific conditions under which different inference methods excel or fail. To address this gap, we introduce a controlled diagnostic framework that isolates seven biologically motivated pathologies (dropout, latent confounders, cell-type mixing, feedback loops, network density, sample size, and pseudotime drift) and measure how six representative methods spanning three inference paradigms degrade as each pathology intensifies. Across 6,120 controlled experiments, we find that causal methods genuinely dominate in clean and structurally favorable regimes, but specific pathologies (notably dropout and latent confounders) selectively neutralize their advantages. We further introduce an error-type decomposition that reveals methods with similar aggregate accuracy commit qualitatively different errors. To probe whether single-pathology effects persist when multiple stressors co-occur, we perform an interaction sweep over the three most impactful pathologies and find that their joint effects are sub-additive, while also exposing density-conditional cross-overs invisible to single-dial analysis. Our findings offer a nuanced understanding of when and why different methods succeed or fail for GRN inference, providing actionable insights for method development and practical guidance for practitioners.

Abstract

Graph Structure Learning

Explore similar work

When Does Gene Regulatory Network Inference Break? A Controlled Diagnostic Study of Causal and Correlational Methods on Single-Cell Data

Graph Additive Models disentangling feature, topology, and interactions

Prior-Guided Multi-Omic Transformers for Single-Cell Gene Regulatory Network Inference