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Delta-AI: Local objectives for amortized inference in sparse graphical models
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Proposes Δ-AI, a local-constraint objective that trains a Bayesian-network sampler to match conditionals of a sparse Markov network, enabling amortized inference with per-step credit assignment using only a variable and its Markov blanket.
Problem
Amortized sampling from sparse probabilistic graphical models is slow for GFlowNets because the terminal reward requires instantiating all variables, giving linear cost in dimension and poor credit assignment over long trajectories.
Approach
Exploit graph sparsity to derive a local constraint: the ratio of factor energies when one variable is flipped must equal the ratio of its conditional and its children's conditionals in a Bayesian network I-map. Turning this into a squared log-ratio loss yields a local GFlowNet-style objective that only needs one variable and its Markov blanket per update, and can be amortized over multiple DAG or
Key results
- On synthetic Ising and factor graphs, Δ-AI converges significantly faster in wall-clock time than TB, DB, and FL-DB GFlowNet baselines.
- Δ-AI reaches lower MMD than Gibbs and Gibbs-With-Gradients MCMC on peaky energy landscapes after a short training period.
- On MNIST latent-variable modeling with variational EM, Δ-AI gives quicker wall-clock convergence in test NLL than all other posterior inference baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use local Δ-AI objectives instead of TB, DB, or FL-DB | amortized samplers for sparse synthetic PGMs · Synthetic Ising and factor graph models | wall-clock convergence | Helped |
| use Δ-AI instead of MCMC sampling | amortized samplers for peaky synthetic energy models · Synthetic Ising and factor graph models | linear MMD | Helped |
| use Δ-AI instead of the other amortized inference baselines | posterior inference in the MNIST latent-variable model · MNIST | wall-clock convergence | Helped |
| replace the fully-factorized posterior with a structured posterior | mean-field variational EM · MNIST | unconditional sample quality | Helped |
| use importance-weighted wake-sleep instead of sleep-phase wake-sleep | wake-sleep posterior inference · MNIST | wall-clock convergence | Helped |
| use FL-DB instead of other posterior-inference baselines | GFlowNet posterior inference · MNIST | wall-clock convergence | Hurt |
| use Δ-AI instead of TB, DB, or FL-DB | amortized samplers for continuous pose data · AMASS KIT | linear MMD | Helped |
| amortize multiple DAG orders instead of learning conditionals for a single DAG (ablation) | Δ-AI · MNIST | wall-clock convergence | No clear effect |
| use accumulated factors only when all their arguments are instantiated, instead of evaluating factors with masked missing inputs (ablation) | FL-DB partial reward parameterization · Synthetic graphical models | training performance | Hurt |
Surprising findings
- Amortizing over multiple DAG orders barely slows convergence of Δ-AI, suggesting shared conditional structure aids learning.
Limitations
- Scaling is poor for graphs where chordalization yields very large Markov blankets.
- Evaluated only with known PGM structure; structure learning not addressed.
- Only discrete binary variables in main experiments; continuous variant is preliminary.
Experimental setup
Datasets: MNIST AMASS KIT subset of AMASS
Benchmarks: MNIST
Metrics: negative log likelihood linear MMD mean prediction entropy of pretrained MNIST classifier wall-clock convergence
Baselines: trajectory balance detailed balance forward-looking detailed balance subtrajectory balance Gibbs sampling Gibbs-With-Gradients mean-field variational EM wake-sleep importance-weighted wake-sleep
Builds on: generative flow networks trajectory balance detailed balance forward-looking gflownet concrete score matching
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