Research map / Probabilistic and scientific modeling / Variational and generative sampling
Gaussian Graphical Modelling Without Independence Assumptions for Uncentered Data
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes a noncentral Kronecker-sum-structured Gaussian model with a Kronecker-sum-structured mean, estimated by block coordinate descent wrapped around existing precision estimators (TeraLasso, GmGM), and proves the likelihood has a unique global optimum.
Problem
Multi-axis (Kronecker-sum) graphical models assume zero-mean data, which is untenable for single-sample tensor data; this causes large errors in estimated conditional dependency graphs when data have nonzero means.
Approach
Relax the zero-mean assumption to a Kronecker-sum-structured mean (sum of per-axis mean vectors), estimate it by closed-form coordinate-wise updates in a flip-flop scheme that wraps any precision estimator, and prove the resulting nonconvex MLE has a unique global optimum via a convex conic reformulation.
Key results
- On COIL-20, correct edges rose from 59/147 (40%) to 127/147 (86%) for GmGM and from 55/142 (39%) to 126/141 (89%) for TeraLasso after adding the mean-estimation wrapper.
- On E-MTAB-2805, GmGM assortativity moved from -0.47 without mean correction to 0.16 with correction, removing a spurious strong repulsion between same-cell-cycle-stage cells.
- Zero-mean methods performed near-worthless under a constant mean offset, while the noncentral variants maintained reasonable precision and recall on synthetic data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the mean-estimation wrapper | GmGM · COIL-20 duck frames | correct edges: 59/147 (40\%) -> 127/147 (86\%) | Helped |
| Add the mean-estimation wrapper | TeraLasso · COIL-20 duck frames | correct edges: 55/142 (39\%) -> 126/141 (89\%) | Helped |
| Add the mean-estimation wrapper | GmGM · COIL-20 duck frames | recall: 41\% -> 88\% | Helped |
| Add the mean-estimation wrapper | TeraLasso · COIL-20 duck frames | recall: 38\% -> 88\% | Helped |
| Add the mean-estimation wrapper | GmGM · E-MTAB-2805 cell-cycle dataset | assortativity: -0.47 -> 0.16 | Helped |
| Estimate the mean instead of assuming zero mean | Kronecker-sum precision estimation · Synthetic data with constant offset | precision and recall | Helped |
| Estimate the mean instead of assuming zero mean | Kronecker-sum precision estimation · Synthetic data with noncentral Kronecker-sum Gaussian data | precision and recall | Helped |
| Estimate the mean instead of assuming zero mean | Kronecker-sum precision estimation · Synthetic data with unstructured Gaussian random means | precision and recall | No clear effect |
| Estimate the mean instead of assuming zero mean | Kronecker-sum precision estimation · Synthetic data with unstructured Poisson random means | precision and recall | Mixed |
Surprising findings
- Standard zero-mean precision estimators infer a strong, incorrect repulsion between cells in the same cell-cycle stage (assortativity -0.47).
Limitations
- Estimator of the precision matrix is treated as a drop-in black box; the mean-correction is not integrated with its eigendecomposition efficiency in the reported experiments.
- TeraLasso results highly sensitive to regularization parameter, causing large variance; TeraLasso not run on E-MTAB-2805 due to slow runtime.
- Uniqueness proof for low-rank GmGM variant requires an extra assumption that the mean is orthogonal to the nullspace of the precision matrix.
Experimental setup
Datasets: COIL-20 E-MTAB-2805
Benchmarks: COIL-20 E-MTAB-2805
Metrics: precision recall assortativity edge correctness
Baselines: TeraLasso GmGM scBiGLasso
Builds on: TeraLasso GmGM Nonparanormal Skeptic Graphical Lasso
Closest papers by meaning
- Robust Estimation of Tree Structured Gaussian Graphical Models (ICML 2019 · similarity 0.86)
- Partially Linear Additive Gaussian Graphical Models (ICML 2019 · similarity 0.83)
- Fairness-Aware Estimation of Graphical Models (NeurIPS 2024 · similarity 0.82)
- Learning Gaussian DAG Models without Condition Number Bounds (ICML 2025 · similarity 0.82)
- Scalable Gaussian Processes with Latent Kronecker Structure (ICML 2025 · similarity 0.81)
- A Generic Family of Graphical Models: Diversity, Efficiency, and Heterogeneity (ICML 2025 · similarity 0.81)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.