Research map / Probabilistic and scientific modeling / Variational and generative sampling
Learning Local Neighborhoods of Non-Gaussian Graphical Models
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Proposes L-SING, which learns a conditional transport map (UMNN-parameterized, sparsity-regularized) for each node in parallel and builds a generalized precision matrix to recover local Markov structure of non-Gaussian distributions.
Problem
Recovering the conditional independence (Markov) structure of high-dimensional, possibly non-Gaussian distributions from samples; existing methods either assume parametric (Gaussian) or copula forms, or estimate the full joint map, which scales poorly.
Approach
Learn a monotone transport map component per node that represents its conditional given all other variables, with a group-sparsity penalty on input dependence; derive a generalized precision matrix from these maps (entries E|∂j∂k log π|) and threshold it to get edges. Shows linear maps reduce to Lasso neighborhood selection and Gaussian-copula/nonparanormal settings are special cases.
Key results
- On the 40-dimensional butterfly distribution with threshold 0.1, L-SING achieves F1 ≈ 0.941 and FPR ≈ 6.58e-3.
- On the butterfly distribution, GLASSO and nonparanormal recover only diagonal entries and miss the Xi–Yi dependencies that L-SING recovers.
- On the 156-gene ovarian cancer dataset, L-SING runs in 42.3 s for map estimation versus 13.1 s for GLASSO, and ranks CTSE highest by mean centrality while EPCAM ranks 14th.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use L-SING instead of GLASSO | Graph structure recovery on the butterfly distribution · Butterfly distribution | conditional-dependency graph recovery | Helped |
| Use L-SING instead of the nonparanormal method | Graph structure recovery on the butterfly distribution · Butterfly distribution | conditional-dependency graph recovery | Helped |
| Increase the threshold τ (ablation) | L-SING edge detection · Gaussian distribution | false positive rate | Helped |
| Increase the threshold τ (ablation) | L-SING edge detection · Gaussian distribution | sensitivity | Mixed |
| Increase the number of training samples M (ablation) | L-SING · Gaussian distribution | false positive rate | Helped |
| Increase the threshold τ (ablation) | L-SING edge detection · Ovarian Cancer dataset | graph sparsity | Helped |
| Use L-SING instead of GLASSO | Gene-network identification · Ovarian Cancer dataset | CTSE identification | Helped |
Surprising findings
- GLASSO and the nonparanormal method recover none of the true non-Gaussian dependencies on the butterfly distribution, only self-edges.
- On the ovarian cancer data, L-SING ranks EPCAM 14th of 156 genes, unlike GLASSO-based analysis which highlighted it second.
Limitations
- Edge recovery depends on a threshold tau that must be chosen by hand or prior knowledge.
- Theory requires twice-differentiable, strictly positive densities; extension to mixed continuous and discrete variables is future work.
- No ground-truth graph for the ovarian cancer dataset, so biological evaluation relies on centrality ranks and literature.
Experimental setup
Datasets: synthetic Gaussian (d=10) synthetic butterfly distribution (d=10, 40) Ovarian Cancer gene expression (TCGA, 578 patients, 156 genes)
Benchmarks: synthetic Gaussian graph (d=10) butterfly distribution (d=10, 40) Ovarian Cancer TCGA gene network
Metrics: false positive rate F1 score edge count/sparsity centrality rank Frobenius norm difference
Baselines: GLASSO nonparanormal (npn) neighborhood selection with Lasso SING
Builds on: SING neighborhood selection with Lasso graphical lasso nonparanormal UMNN
Closest papers by meaning
- Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting (NeurIPS 2017 · similarity 0.92)
- The Multiple Quantile Graphical Model (NeurIPS 2016 · similarity 0.88)
- Conditional Matrix Flows for Gaussian Graphical Models (NeurIPS 2023 · similarity 0.87)
- T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs (NeurIPS 2021 · similarity 0.87)
- A Fast and Scalable Joint Estimator for Integrating Additional Knowledge in Learning Multiple Related Sparse Gaussian Graphical Models (ICML 2018 · similarity 0.87)
- Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models (NeurIPS 2026 · similarity 0.86)
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