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Differentiable Annealed Importance Sampling Minimizes The Jensen-Shannon Divergence Between Initial and Target Distribution
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Shows that the initial distribution of differentiable annealed importance sampling (DAIS) implicitly minimizes the Jensen-Shannon divergence to the target in the many-transition limit, and empirically evaluates this initial distribution (DAIS0) as a compact variational approximation.
Problem
Understanding what the learned initial distribution of differentiable AIS represents, and whether it is a useful compact approximate posterior compared with VI, importance weighted VI, and Markovian score climbing.
Approach
For many transitions K with N=1 and perfect transitions, the gap between log Z and the AIS lower bound is asymptotically proportional to the Jensen-Shannon divergence between the initial distribution q0 and f/Z, so DAIS fits q0 by implicitly minimizing this symmetrized KL; the initial distribution is then used alone (DAIS0) as a variational approximation.
Key results
- Theorem 4.1: for N=1 and large K, the AIS gap equals (1/K) times the Jensen-Shannon divergence between q0 and f/Z up to O(1/K^3) corrections.
- On the bimodal Gaussian experiment, DAIS0 with K=16 covers both modes for larger dimensions across all N, where VI and IWVI collapse to a single mode.
- On Bayesian logistic regression, DAIS0 reaches the best errors on 3 of 5 datasets, with lower std MAE than IWVI, DAIS and MSC8c in several cases.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase DAIS0 transitions K (ablation) | DAIS0 · Bimodal Gaussian target | target-sample log density under q | Helped |
| Increase DAIS0 transitions K (ablation) | DAIS0 · Bimodal Gaussian target, d=3 | mass coverage | Helped |
| Increase the number of particles N (ablation) | DAIS0 · Bimodal Gaussian target | target-sample log density under q | Helped |
| Use DAIS0 (16) instead of IWVI | Gaussian process regression · RBF1, d=10 | standard deviation MAE: 4.34±.0020 · 10 −2 -> 4.54 ±.071 · 10 −3 | Helped |
| Use DAIS0 (16) instead of IWVI | Gaussian process regression · RBF2, d=25 | standard deviation MAE: 4.14±.002 · 10−2 -> 1.31 ±.0030 · 10 −2 | Helped |
| Use DAIS0 (16) instead of IWVI | Bayesian logistic regression · ionosphere | standard deviation MAE: 4.73±.048 · 10−2 -> 3.25 ±.36 · 10 −2 | Helped |
| Use DAIS0 (16) instead of IWVI | Bayesian logistic regression · heart disease | standard deviation MAE: 2.59±.072 · 10−2 -> 1.08 ±.28 · 10 −2 | Helped |
| Use DAIS0 (16) instead of IWVI | Bayesian logistic regression · heart attack | standard deviation MAE: 2.80 ±.15 · 10 −2 -> 3.35±.11 · 10−2 | Hurt |
| Use DAIS0 (16) instead of IWVI | Bayesian logistic regression · sonar | standard deviation MAE: 7.95±.089 · 10−2 -> 4.27 ±.13 · 10 −2 | Helped |
Surprising findings
- MSC with a single chain does not converge for N=1 in the bimodal experiment.
- DAIS0 gives competitive or better standard-deviation estimates than sampling-based DAIS, which is more expensive at inference, even though DAIS is the method being analyzed.
Limitations
- The main theorem holds only for large K, N=1, and perfect transitions, while experiments use moderate K and N>1, so it holds only approximately.
- Mean estimation is sometimes worse for DAIS0 than IWVI, and DAIS0 is more expensive than VI at training time.
- Sampling-based estimates from DAIS can converge poorly in high dimensions.
Experimental setup
Datasets: synthetic bimodal Gaussian target synthetic Gaussian process regression data sonar ionosphere heart disease heart attack loan
Benchmarks: bimodal Gaussian target density GP regression posterior mean and std MAE Bayesian logistic regression MAE vs HMC
Metrics: mean absolute error expected log density under q mode-seeking vs mass-covering classification
Baselines: variational inference importance weighted VI Markovian score climbing DAIS IWVI-SIR
Builds on: differentiable annealed importance sampling importance weighted variational inference Markovian score climbing Monte Carlo diffusion
Closest papers by meaning
- Differentiable Annealed Importance Sampling and the Perils of Gradient Noise (NeurIPS 2021 · similarity 0.92)
- Forward $\chi^2$ Divergence Based Variational Importance Sampling (ICLR 2024 · similarity 0.88)
- Revisiting Unbiased Implicit Variational Inference (ICML 2025 · similarity 0.87)
- Reparameterized Importance Sampling for Robust Variational Bayesian Neural Networks (ICML 2024 · similarity 0.86)
- Stochastic variance-reduced Gaussian variational inference on the Bures-Wasserstein manifold (ICLR 2025 · similarity 0.86)
- Kernel Semi-Implicit Variational Inference (ICML 2024 · similarity 0.86)
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