Research map / Probabilistic and scientific modeling / Variational and generative sampling
Transfer Learning for Latent Variable Network Models
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.
Studies transfer learning for latent variable network models, estimating a target edge-probability matrix from a small induced target subgraph plus a fully observed source network, using a graph-distance rankings assumption, with a minimax-optimal algorithm for SBMs.
Problem
Estimating the full edge probability matrix of a target network when edges are observed only on a vanishingly small induced subgraph (o(1) fraction of nodes), while a fully observed source network is available.
Approach
Shows vanishing error is possible when latent variables are shared, using a graph distance (based on squared common-neighbor profiles) and a rankings assumption that relates source and target neighborhoods; for SBMs a simple cluster-then-block-average estimator attains the minimax rate.
Key results
- On simulated Noisy-MMSB transfer, the graph-distance algorithm achieved MSE 0.7473 vs 1.3761 for the spectral baseline (x1e-2, n=200, n_Q=50).
- On the latent distance model (R^10), the graph-distance algorithm achieved 0.5744 vs 1.1773 for the spectral baseline and 0.7715 for the p=0.1 oracle.
- The paper proves a minimax lower bound of order k_Q^2/n_Q^2 for SBM transfer and shows the cluster-based algorithm attains it in the weak consistency regime.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ranking-based transfer instead of SBM transfer | Noisy-MMSB transfer · Noisy-MMSB source → Noisy-MMSB target | mean-squared error (×1e2): 1.3761\pm 1.1586 -> 0.7473$\pm$ 0.0648 | Helped |
| Use ranking-based transfer instead of Oracle USVT (p=0.1) | Noisy-MMSB transfer · Noisy-MMSB source → Noisy-MMSB target | mean-squared error (×1e2): 0.9556 $\pm$ 0.0633 -> 0.7473$\pm$ 0.0648 | Helped |
| Use ranking-based transfer instead of SBM transfer | Smooth graphon transfer · 0.1-Smooth Graphon → 0.5-Smooth Graphon | mean-squared error (×1e2): 4.5033 \pm 1.5613 -> 1.7656 $\pm$ 0.7494 | Helped |
| Use ranking-based transfer instead of Oracle USVT (p=0.1) | Smooth graphon transfer · 0.1-Smooth Graphon → 0.5-Smooth Graphon | mean-squared error (×1e2): 0.5016 $\pm$ 0.0562 -> 1.7656 $\pm$ 0.7494 | Hurt |
| Use ranking-based transfer instead of SBM transfer | Latent distance transfer · R^10 Latent(2.5) → R^10 Latent(1.0) | mean-squared error (×1e2): 1.1773 \pm 1.0481 -> 0.5744 $\pm$ 0.1086 | Helped |
| Use ranking-based transfer instead of Oracle USVT (p=0.1) | Latent distance transfer · R^10 Latent(2.5) → R^10 Latent(1.0) | mean-squared error (×1e2): 0.7715 $\pm$ 0.0456 -> 0.5744 $\pm$ 0.1086 | Helped |
Surprising findings
- On the smooth graphon setting the USVT oracle with p=0.1 outperformed the proposed graph-distance transfer algorithm, which is the best only for some settings.
- Graph-distance transfer performs worse than the spectral baseline on the 0.1-smooth graphon target setup with error variance.
Limitations
- Theory requires dense-ish networks with edge density around 1/sqrt(n); extension to sparser O(log n / n) regimes left open.
- Error bound scales exponentially in 1/d, and the rankings assumption must hold between source and target.
- Experiments use small sizes (n=200, n_Q=50) for simulations.
Experimental setup
Datasets: BiGG metabolic models iWFL1372 BiGG metabolic models iPC815 BiGG metabolic models iJN1463 Email-EU
Benchmarks: simulated Noisy-MMSB, smooth graphon, latent distance networks BiGG metabolic networks Email-EU temporal networks
Metrics: mean-squared error (scaled by 1e2)
Baselines: Spectral clustering + least-squares projection transfer (Algorithm baseline) Oracle with flipped-edge access to all nodes (USVT)
Builds on: Universal Singular Value Thresholding graph distance from prior inference work (Assumption 3.2 source) Generalized Fano method
Closest papers by meaning
- Transfer Learning on Edge Connecting Probability Estimation Under Graphon Model (NeurIPS 2025 · similarity 0.88)
- Learning General Latent-Variable Graphical Models with Predictive Belief Propagation (AAAI 2020 · similarity 0.87)
- The Limits of Transfer Reinforcement Learning with Latent Low-rank Structure (NeurIPS 2024 · similarity 0.85)
- Learning Latent Graph Structures and their Uncertainty (ICML 2025 · similarity 0.85)
- When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors (NeurIPS 2026 · similarity 0.84)
- On Transferring Transferability: Towards a Theory for Size Generalization (NeurIPS 2025 · similarity 0.84)
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.