Active Sequential Posterior Estimation for Sample-Efficient Simulation-Based Inference

TL;DR

This work tackles the challenge of efficient likelihood-free inference for expensive simulators by introducing ASNPE, an active-learning variant of Sequential Neural Posterior Estimation. ASNPE jointly learns a neural density estimator and an acquisition function that targets epistemic uncertainty to selectively sample informative parameters, enabling substantial sample efficiency gains. The approach is demonstrated on a high-dimensional origin-destination calibration task using the SUMO traffic simulator, where ASNPE outperforms strong baselines and shows favorable performance on standard SBI benchmarks. The study contributes a practical acquisition framework compatible with APT training, a Bayesian OD calibration formulation, and empirical evidence of improved posterior accuracy and sample efficiency with real-world relevance for traffic modeling and SBI problems alike.

Abstract

Computer simulations have long presented the exciting possibility of scientific insight into complex real-world processes. Despite the power of modern computing, however, it remains challenging to systematically perform inference under simulation models. This has led to the rise of simulation-based inference (SBI), a class of machine learning-enabled techniques for approaching inverse problems with stochastic simulators. Many such methods, however, require large numbers of simulation samples and face difficulty scaling to high-dimensional settings, often making inference prohibitive under resource-intensive simulators. To mitigate these drawbacks, we introduce active sequential neural posterior estimation (ASNPE). ASNPE brings an active learning scheme into the inference loop to estimate the utility of simulation parameter candidates to the underlying probabilistic model. The proposed acquisition scheme is easily integrated into existing posterior estimation pipelines, allowing for improved sample efficiency with low computational overhead. We further demonstrate the effectiveness of the proposed method in the travel demand calibration setting, a high-dimensional inverse problem commonly requiring computationally expensive traffic simulators. Our method outperforms well-tuned benchmarks and state-of-the-art posterior estimation methods on a large-scale real-world traffic network, as well as demonstrates a performance advantage over non-active counterparts on a suite of SBI benchmark environments.

Figures (13)

• Figure 1: Depiction of the proposed active learning-integrated method. Demonstrates the high-level ASNPE pipeline. Samples $\theta_i$ are drawn from sequentially updated proposal distributions $\tilde{p}(\theta)$, filtered according to the acquisition function $\alpha(\theta_{1:N}, p(\phi|D))$, and run through the simulator $p(x|\theta)$ to generate $B$ pairs $(\theta_i, x_i)$ for training the approximate posterior $q_\phi$. The learned posterior is then conditioned by the target observation $x_o$, producing the next round's proposal $\tilde{p}(\theta) = q_\phi(\theta|x_o)$.
• Figure 2: Simple depiction of the data acquisition and simulation process for the OD calibration application. The acquisition step selects parameter candidates (OD matrices) to then be simulated (via SUMO) and produce outputs (network flow observations) that are used to update the approximate posterior model.
• Figure 3: Plots of the (averaged) calibration horizons for each of the evaluated methods on the Prior I, Hours 5:00-6:00, Congestion level A scenario. (a) RMSN(E) scores reached throughout the 128 sample simulation horizon for each evaluated method, averaged over five repeated trials (mean line plotted) and with error bars calculated as bootstrapped 95% confidence intervals. (b) The same scores shown in (a), but instead plotted against the wallclock time passed before the score was reached (for each method's single best run). Note that the full 128-sample method trajectories are included, and the variability in line lengths demonstrates both 1) the impact of NPE-based methods' ability to run simulations in parallel, and 2) noisiness in simulation runtimes due to the variable inputs explored by each method. See Appendix \ref{['sec:more-plot']} for all scenario plots.
• Figure 4: Results on various metrics between ASNPE and SNPE-C across four rounds of sequential inference for the Gaussian mixture task.
• Figure 5: Results on various metrics between ASNPE and SNPE-C across four rounds of sequential inference for the Bernoulli GLM task.