Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Learning Diffusions under Uncertainty
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Infers a diffusion (influence) network from probabilistic node infection statuses by relaxing a constrained likelihood over edge and propagation-probability variables and solving it with a provably monotone alternating maximization (PIND).
Problem
Diffusion network inference when observations contain only probabilistic (not exact or binary) node infection statuses, rather than exact infection times or eventual binary statuses.
Approach
Formulates network inference under the IC model as a constrained nonlinear regression over relaxed edge-existence probabilities x and propagation probabilities alpha, solved by alternating projected-gradient-style updates with step sizes chosen so the likelihood increases monotonically, plus MI-based pruning of candidate parents and sampling to obtain a binary network.
Key results
- PIND achieves higher F-score than CORMIN, NetRate and TENDS across LFR networks of size 1000-3000 with uncertainty mean 0.3 (reported as outperforming in all compared settings, with TENDS close only at low uncertainty mu<=0.05 on DUNF).
- PIND's accuracy improves with iterations and converges quickly; its propagation-probability MAE is lower than NetRate's (NetRate MAE 0.2822 on DUNF and 0.2791 on DPU).
- Accuracy of PIND, CORMIN and TENDS degrades as uncertainty mean grows, with near-impossible recovery at mu>=0.5.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PIND instead of CORMIN, NetRate, or TENDS | Diffusion network inference · Synthetic networks G1–G5 | F-score | Helped |
| Use PIND instead of the other tested algorithms | Diffusion network inference · Synthetic networks G6–G10 | F-score | Helped |
| Increase network size | CORMIN and NetRate · Synthetic networks G1–G5 | F-score | Hurt |
| Increase network size | PIND and TENDS · Synthetic networks G1–G5 | F-score | No clear effect |
| Increase average degree | PIND · Synthetic networks G6–G10 | F-score | Hurt |
| Increase average degree from 2 to 5, then to 6 | NetRate · Synthetic networks G6–G10 | F-score | Mixed |
| Increase infection-data uncertainty | PIND, CORMIN, and TENDS · DUNF and DPU | F-score | Hurt |
| Increase infection-data uncertainty | NetRate using exact cascades · DUNF and DPU | F-score | No clear effect |
| Use TENDS instead of PIND | Diffusion network inference · DUNF with uncertainty μ ≤ 0.05 | F-score | No clear effect |
| Use TENDS instead of PIND | Diffusion network inference · DPU with uncertainty μ = 0 | F-score | No clear effect |
| Increase the number of diffusion processes | Tested algorithms · DUNF and DPU | F-score | Helped |
| Use PIND instead of other algorithms | Diffusion network inference · DPU with β = 100 or β = 150 | F-score | Mixed |
Surprising findings
- Straightforward sampling of 0/1 statuses from probabilistic data (used for TENDS) performs poorly, indicating sampling is not a suitable way to handle probabilistic observations.
- TENDS matches PIND's accuracy when uncertainty is very low (mu<=0.05 on DUNF, mu=0 on DPU).
Limitations
- Experiments are limited to networks up to 3000 nodes because CORMIN and NetRate become too slow on larger networks.
- Accuracy degrades sharply when uncertainty mean reaches 0.5 or more.
- Assumes the Independent Cascade model; extension to other models such as linear threshold is only claimed, not evaluated.
Experimental setup
Datasets: LFR benchmark graphs (synthetic, G1-G10) DUNF (microblogging network, 750 users) DPU (microblogging network, 1038 users)
Benchmarks: LFR benchmark graphs G1-G10 DUNF DPU
Metrics: F-score of inferred directed edges running time MAE of learned propagation probabilities
Baselines: CORMIN NetRate TENDS
Builds on: Independent Cascade model NetRate TENDS CORMIN
Closest papers by meaning
- Learning Diffusions without Timestamps (AAAI 2019 · similarity 0.93)
- Diffusion Network Inference from Partial Observations (AAAI 2021 · similarity 0.92)
- Network Diffusions via Neural Mean-Field Dynamics (NeurIPS 2020 · similarity 0.88)
- Dynamic Network Model from Partial Observations (NeurIPS 2018 · similarity 0.88)
- Diffusion Source Identification on Networks with Statistical Confidence (ICML 2021 · similarity 0.88)
- The Irrelevance of Influencers: Information Diffusion with Re-Activation and Immunity Lasts Exponentially Long on Social Network Models (AAAI 2024 · similarity 0.85)
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